graduate university programme in mathematics and computer ...

UNIVERSITY OF ZAGREB

FACULTY OF SCIENCE

DEPARTMENT OF MATHEMATICS

Bijenička cesta 30

10000 Zagreb

GRADUATE UNIVERSITY PROGRAMME IN

MATHEMATICS AND COMPUTER SCIENCE

EDUCATION

Zagreb, January 2015

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CONTENTS

1. INTRODUCTION ................................................................................................................................................. 2

1.1. ARGUMENTS FOR STARTING THE STUDIES ........................................................................................................ 2 1.2. COMPARABILITY WITH INTERNATIONAL PROGRAMMES ................................................................................... 3 1.3. EXPERIENCE SO FAR OF DEPARTMENT OF MATHEMATICS IN CONDUCTING MATHEMATICS STUDIES ................ 3 1.4. STUDIES SUPPORT THE MOBILITY OF STUDENTS ............................................................................................... 4

2. GENERAL INFORMATION ............................................................................................................................... 5

2.1. NAME OF THE PROGRAMME ............................................................................................................................. 5 2.2. PERFORMED BY ................................................................................................................................................ 5 2.3. DURATION ....................................................................................................................................................... 5 2.4. ENTRY REQUIREMENTS .................................................................................................................................... 5 2.5. COMPETENCES ACQUIRED AT THE END OF THE STUDY ..................................................................................... 5 2.6. LEARNING OUTCOMES AT LEVEL OF THE STUDY PROGRAMME ......................................................................... 6 2.7. OCCUPATIONS AND JOB POSTS FOR WHICH STUDENTS ARE QUALIFIED ............................................................. 7 2.8. UNDERGRADUATE PROGRAMMES WHICH ARE (PARTIALLY) ADEQUATE PREREQUISITES .................................. 7 2.9. ACADEMIC TITLE ACQUIRED UPON COMPLETION OF COURSES.......................................................................... 8

3. PROGRAMME DESCRIPTION ......................................................................................................................... 9

3.1. THE LIST OF COURSES INCLUDING THE NUMBER OF CLASSES AND ECTS CREDITS ........................................... 9 3.2. COURSE DESCRIPTION .................................................................................................................................... 13 3.3. COURSE STRUCTURE, RHYTHM OF STUDYING AND STUDENT'S OBLIGATIONS ............................................... 142 3.4. LIST OF ELECTIVE COURSES FROM OTHER STUDIES ...................................................................................... 143 3.5. LIST OF COURSES TO BE TAKEN IN FOREIGN LANGUAGE ............................................................................... 144 3.6. CRITERIA AND CONDITIONS FOR TRANSFER OF ECTS CREDITS FROM OTHER STUDIES ................................. 144 3.7. COMPLETION OF STUDIES ............................................................................................................................. 144 3.8. REQUIREMENTS FOR CONTINUATION OF INTERRUPTED STUDIES .................................................................. 144

4. CONDITIONS FOR REALIZATION OF THE PROGRAMME ................................................................. 145

4.1. PLACE OF REALIZATION OF THE STUDY PROGRAMME .................................................................................. 145 4.2. INFORMATION ON PREMISES AND EQUIPMENT ENVISIONED FOR STUDIES ..................................................... 145 4.3. TEACHERS AND COLLABORATORS TO PARTICIPATE IN EXECUTION OF STUDIES ............................................ 145 4.4. DATA ABOUT EACH OF THE ENGAGED TEACHERS ......................................................................................... 148 4.5. LIST OF TEACHING SITES FOR PRACTICAL TEACHING .................................................................................... 188 4.6. OPTIMUM NUMBER OF STUDENTS CONSIDERING SPACE, EQUIPMENT AND NUMBER OF TEACHERS ............... 188 4.7. ESTIMATED COSTS OF STUDIES PER STUDENT ............................................................................................... 188 4.8. METHODS FOR MONITORING QUALITY AND PERFORMANCE OF STUDY PROGRAMME EXECUTION ................. 188

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1. INTRODUCTION

1.1. Arguments for starting the studies

Today there is no doubt that mathematics is one of the essential sciences for the

development of human civilisation. It has originated from everyday needs of old Egyptian people

in 20th Century B.C. (counting of various object, land measuring, construction of dwellings,

celestial and phenomena at sea, the beginnings of trade and barter), which lead to deliberation on

size relationship and space shapes. Today, mathematics represents “the queen of all sciences”,

developing powerfully and rapidly over an enormously wide and complex field of research and

application with a considerable number of scientist and experts. Its importance in contemporary

society is reflected by the fact that, besides native tongue, mathematics is the most represented

school subject in almost all schools all over the world.

Mathematics is traditionally tied with unbreakable bonds with natural sciences, particularly

with physics, as well as with technical sciences which have served as source for innumerable

examples and inspiration for its own ideas and development. However, recently we have witnessed

the ever increasing breaking of mathematics into economics, medicine, psychology, linguistics and

other scientific fields. It is impossible to even consider performing serious research in all those

fields without various quantitative and analytical, combinatorial, probabilistic, statistical and other

mathematical methods and techniques as well as mathematical models and simulations. It is

sufficient to say that many of Nobel Prize winners for economics have been, by their basic

education, mathematicians and that the biggest scientific achievements in modern medicine have

been achieved through joint work of interdisciplinary research teams with a considerable

contribution of mathematicians. Besides the increasing influence of mathematics, there is rapid

development of information and communication technologies where mathematics has been

participating from the beginning. It is a well-known fact that mathematicians were principal

intellectual initiators for developing the idea of a computer and its construction; therefore, they

were the initiators of an “information revolution” which has changed human society radically.

Finally, modern ways of communication and information search by computer networks (i.e.

Internet) would not be possible without mathematical algorithms developed for that purpose.

Because of the scope and diversity of the research and application, instead of mathematics today

we more often speak of mathematical science.

Modern life all over the world, and in Croatia as well, could not be imagined without

mathematics and mathematicians. Today, mathematicians are to be found in all segments of

Croatian economy and science. They are employed by information and financial sectors (computer

centres, companies dealing with software manufacture for the most diverse purposes, insurance

companies, pension and other funds, etc.) and elsewhere. Many of them work at different higher

education institutions – universities and polytechnics, since almost all study programmes include

mathematics courses. Mathematics is the compulsory subject at all primary and secondary schools;

therefore, many mathematicians work in schools.

The consequence of such wide demand for experts in the field of mathematics and

information and communication technologies is that mathematicians have been successfully

employed in Croatia. We would point out that for years there has been an inexhaustible need for

teachers of mathematics and computer science in the whole Croatia, due to the generation changes

on the educational scene and due to the development of educational standards, particularly in the

field of ICT. This ranks the Faculty of Science, Department of Mathematics among the rare

Croatian higher education institutions which provide its students the possibility of successful

employment after graduation. World experience shows that this trend is not accidental and

fleeting. On the contrary, the demand for mathematicians of various specialisations in labour

market, (both public and private sector), will continue to grow.

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Therefore, it is unnecessary to additionally motivate the need for university studies of

mathematics and computer science education at all levels (undergraduate, graduate and

postgraduate) at the University of Zagreb, and for their constant improvement and updating. In

particular, the Graduate University Programme in Mathematics and Computer Science Education

is the final stage of the compulsory pre-service of the university education of mathematics and

informatics teachers at the lower and higher level of secondary education (higher classes of

elementary schools and secondary schools, i.e. the level ISCED 2 and ISCED 3 according to the

ISCED 19971 classification), i.e. it is the second level, following the Bologna system 3+2, of the

university education of future mathematics and computer science teachers (teachers and

professors, according to the currently valid terminology). The first level of this education is the

three-year Undergraduate University Programme in Mathematics Education (giving the bachelor’s

degree in mathematics education).

Graduate University Programme in Mathematics and Computer Science Education gives

the students university-level education in mathematics and computer science, giving them

professional and didactic competence to teach all programmes in mathematics and ICT at the

elementary and secondary school level, and prepares them for all tasks they are going to have as

teachers in elementary and secondary schools. Upon completing this programme the students

acquire the academic title Master of Mathematics and Computer Science Education.

1.2. Comparability with international programmes

The Graduate University Programme in Mathematics and Computer Science Education has

been brought in line with guidelines given by the international group of experts for harmonization

of university mathematics programmes, the so-called The Mathematics Tuning Group. The

guidelines are published in the following document:

The Mathematics Tuning Group: Towards a common framework for Mathematics degrees in

Europe, E.M.S. Newsletter 45 (2002), pp. 26-28.

This document names the competences to be expected of any university educated mathematician,

in particular teachers of mathematics in secondary schools (levels ISCED 2 and ISCED 3).

Furthermore, the competences in computer science are comparable to the ones given in guidelines

of international association International Society for Technology in Education, presented in the

document:

Educational Computing and Technology Programs: Secondary Computer Science

Education Initial Endorsement, http://cnets.iste.org/ncate/n_cs-stands.html.

The competence in educational science (so-called psychological, pedagogical, and

didactical competence) are tuned up with the educational programmes elsewhere in Europe.

Specifically, we point to the following two programmes:

The Graduate School of Education, University of Bristol, Great Britain,

http://www.bris.ac.uk/education/

Karl – Franzens Universität Graz, Austria,

http://lv-online.uni-graz.at/puba/start/lv-online-en.html.

1.3. Experience so far of Department of Mathematics in conducting mathematics studies

Mathematics has continuously been taught at the University of Zagreb for almost 140

years. Presently, more than 1500 students are studying mathematics at the Department of

Mathematics at two undergraduate studies, seven graduate and one integrated study. The studies

1 ISCED 1997 stands for International Standard Classification of Education which divides education into 7 levels. In

particular, ISCED 2 stand for lower secondary education, and ISCED 3 for higher secondary education.

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have been organised since 2005. Before 2005 there were two study programmes: mathematics

programme and mathematics and physics programme (in cooperation with the Department of

Physics). Mathematics programme is divided into the following study profiles: Mathematics

Graduated Engineer, Professor of Mathematics and Professor of Mathematics and Informatics.

The first year of studies is common to all stated profiles. Later, at the third year of studies,

Mathematics Graduated Engineer profile is divided into the following five directions: Pure

Mathematics, Applied Mathematics, Mathematical Statistics and Computer Science, Computer

Science and Financial and Business Mathematics. The study of mathematics and physics included

only one study profile – professor of mathematics and physics. All our existing programmes are

the successors of the above mentioned studies.

The Graduate University Programme in Mathematics and Computer Science Education

may be viewed as the successor of the last two years (i.e. the third and fourth years of study) of the

programme Professor of Mathematics and Informatics with updated teaching programme and

methods and study regime adapted to European standards and Bologna Declaration.

1.4. Studies support the mobility of students

Graduate University Programme in Mathematics and Computer Science Education

encourages and supports the mobility of students and teachers. The Department of Mathematics

provides the relevant and necessary information such as the teaching plan of the programme and

the study regime including student contact hours in addition to a transcript containing the detailed

achievements and grades of the individual student. These data are an essential prerequisite to

facilitate the transfer of ECTS credits. Details concerning the transfer of ECTS credits between

study programmes are agreed at ECTS coordinator level.

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2. GENERAL INFORMATION

2.1. Name of the programme

Graduate University Programme in Mathematics and Computer Science Education

2.2. Performed by

Faculty of Science, Department of Mathematics, University of Zagreb

2.3. Duration

Two (2) academic years, i.e. four (4) semesters.

2.4. Entry requirements

The basic entry requirement for the the Graduate University Programme in Mathematics and

Computer Science Education is completion of an adequate university undergraduate programme

with at least 180 ECTS credits, which gives necessary competences in mathematics, physics, ICT,

psychology, and pedagogy needed for studying at this graduate programme (see section 2.8. for

details). Moreover, classification procedure requirements for enrolment of new students should be

fulfilled.

Competences of candidates are assessed by examining curricula of their completed

undergraduate studies. Classification procedure involves evaluation of candidate undergraduate

grades, as well as special activities (awards, published scientific or professional papers,

participation in student competitions in mathematics, physics, computer science or economics, the

student assistant status in some undergraduate course, mentoring of high school students taking

part in mathematics, physics or informatics competitions, completion of another undergraduate

study, two written recommendations given by university lecturers, etc). Students are enrolled

according to their total ranking until the quota for that year is fulfilled. Detailed description of

classification process for the enrolment of new students in the first year of graduate programme is

announced for each academic year at the Department of Mathematics web site and in daily press.

Classification procedure does not include any examination.

2.5. Competences acquired at the end of the study


offers university education in mathematics, computer science and information and

communications technologies. Mathematical competence encompasses a fundamental knowledge

and understanding of the results of the main areas of mathematics, such as algebra, analysis,

geometry, differential equations, discrete mathematics, probability theory, and statistics, as well as

numerical mathematics. It also includes the ability to understand and conceive mathematical

proofs, and thus, logical argumentation in general situations, the capacity for mathematical

modelling of situations, and the capacity for creative problem solving by means of mathematical

tools and ICT. Computer science competencies include the knowledge, skills, and ability to design

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and analyse algorithms, structural and object-oriented programming, and databases; familiarity

with the computer architecture, computer networks, operating systems, and some of the advanced

concepts of computer science (computer graphics, multimedia systems, computability theory), as

well as the social socio-ethical and professional implications of ICT.

This programme offers the vocational, didactic, and pedagogical-psychological

competencies necessary for the successful realisation of all educational programmes in the area of

mathematics, computer science and ICT at the primary- and secondary-school level. In addition,

the programme trains students to teach all types of mathematics, computer science and ICT classes

– regular, advanced, elective, and remedial, as well as work with children with special needs –

ranging from work with children who have developmental difficulties to work with those who are

gifted in mathematics and/or computer science. It is important to stress that this programme

specifically educates its students – our future teachers of mathematics and computer science – to

work with groups of pupils with exceptional achievements in mathematics and computer science

in order to prepare them for mathematics and computer science competitions at all levels (from

local to state), and to advise pupils when they are writing term papers and secondary-school

graduation papers and realising interdisciplinary student projects and workshops. The program

didactically educates students in the realisation of various forms of mathematics and computer

science instruction – including traditional frontal instruction, programmed instruction, heuristic

and mentored instruction, and contemporary forms of problem- and project-based mathematics

instruction – as well as in the application of ICT and other media in mathematics instruction.

In addition, students gain competence in working within the educational system and the

school as an organisation, and in all the tasks included among the obligations of teachers (being a

class teacher, keeping pedagogical records, working in cooperation with parents and professional

services, etc.) Finally, the program trains students for further self-education (life-long learning) in

the areas of the mathematical sciences, computer science, ICT, education, and other sciences.

2.6. Learning outcomes at level of the study programme

Upon successful completion of this programme a student is able to:

I-1. demonstrate knowledge and understanding of educational sciences, and basic theories and

methods of teaching mathematics and computer science;

I-2. demonstrate intuitive and formal knowledge and understanding of basic results in analysis,

algebra and geometry, and of selected more advanced results in one of the following: algebra

and foundations of mathematics, analysis, geometry and topology;

I-3. demonstrate formal knowledge of concepts of structural programming, databases, computer

architecture, computer networks, operating systems, and of selected more advanced fields of

computer science (such as computer graphics, multimedia systems, cryptography etc.), and

social and professional implications of information technology;

II-1. argue mathematically, interpret a mathematical proof, and construct a proof of a new

mathematical statement;

II-2. apply the acquired knowledge to solve mathematical problems and to model and solve

problems outside the mathematical context;

II-3. use computational mathematical tools and information and communications technology in

teaching and everyday work, and apply the acquired knowledge to write computer programs

in a contemporary programming language, work with databases, and implement a web-page;

II-4. present mathematical content in written and oral form using mathematical language and

notation;

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II-5. independently plan, organize, realize and analyze teaching of mathematics and computer

science in middle and secondary school by applying contemporary methods and strategies of

teaching, education and evaluation;

II-6. demonstate capability to work in the educational system and in school, and to communicate

with pupils, parents and professional services;

III. independently use mathematical literature in Croatian and English, and deliver a professional

project, both individually and in a team;

IV. take responsibility for their own learning, further professional and scientific education, as

well as ethical and sociological responsibility as a professional teacher.

2.7. Occupations and job posts for which students are qualified

Holders of the degree of Master of Education in Mathematics and Computer Science are

qualified for employment as teachers of mathematics and/or computer science and ICT in primary

school and in all types of secondary school. Besides employment in education, they are also

qualified for various types of intellectual employment in business, state administration, and the

public sector that call for analytical thinking; fundamental and advanced knowledge in

mathematics, computer science and ICT; a capacity for mathematical modelling and solving

different problems; a knowledge of statistics; the ability to organise, analyse, and represent all

types of data (character, numerical, audio, visual, multimedia, etc.); programming; work with

databases; and the broadest application of ICT.

2.8. Undergraduate programmes which are (partially) adequate prerequisites

Prerequisite for quality performance at Graduate University Programme in Mathematics and

Computer Science Education is solid background in mathematics and computer science acquired

in undergraduate studies, i.e. good knowledge and understanding of differential and integral

calculus, function of one and several variables, linear algebra, the basic knowledge of information

and communication technologies, programming skills in any of structured programming languages

(presumably C), and main results of basic (classic and modern) fields of mathematics, such as

differential equations, numerical mathematics, probability and statistics, synthetic and analytic

euclidean geometry, discrete mathematics, data bases and data structures and algorithms.

Important competences for this graduate studies are the ability of proof understanding, the

ability of mathematical modelling of a problem and the ability for problem-solving by using

mathematical tools and computers. Also, the students have to know the basics of psychology of

teaching and education, sociology of education, and pedagogy.

According to our opinion, the following undergraduate programs fulfil the requirements:

a. at the Faculty of Science, Department of Mathematics, University of Zagreb:

- direct entry to the proposed programme (no differential exams and/or study modules):

Undergraduate University Programme in Mathematics Education.,

- with possible substitute elective courses: Undergraduate University Programme in

Mathematics. The explanation: students must take the following courses from

Undergraduate University Programme in Mathematics Education instead of mathematical

elective courses: Personality psychology in education, Developmental psychology,

Educational psychology - theories of learning and teaching, Pedagogy 1 - Theory and

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practice of education, Pedagogy 2 - Educational system. Hence, students will bring their

knowledge to the level of the intended programme of study.

b. at other institutions in the Republic of Croatia:

- direct entry to the proposed programme (no differential exams and/or study modules): any

university undergraduate programme in mathematics education (with or without a second

subject).

- with possible additional study modules and courses: the university undergraduate

programmes in mathematics, the university graduate programmes in technical sciences

(computer science, mechanical engineering, electrical engineering, civil engineering, etc),

the university undergraduate programme in physics.

Undergraduate university programmes proposed by the Department of Mathematics are listed with

their explicit names while for other institutions we have listed only professions from which

bachelors, according to our opinion, could well apply for Graduate University Programme in

Mathematics and Computer Science Education (including the possibility of taking differential

examinations or study modules). The list of professions and undergraduate studies specified here

most certainly is not final.

2.9. Academic title acquired upon completion of courses

Master of Education in Mathematics and Computer Science

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3. PROGRAMME DESCRIPTION

3.1. The list of courses including the number of classes and ECTS credits

The list of courses is presented according to years and semesters of studies. Classes for all

courses are organised as lectures, tutorials and seminars. Letter L indicates the number of lecture

hours per week; letter T indicates the number of tutorial hours per week while the letter S indicates

the number of seminar hours per week. For each elective course, a list of possible selections is

shown in a separate table.

1st YEAR OF STUDIES

COURSE

FALL SEMESTER SPRING SEMESTER

HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

Methods of teaching mathematics 1 2 + 2 + 2 8 0 + 0 + 0 0

Computer architecture 2 + 1 + 0 5 0 + 0 + 0 0

Computer networks 2 + 2 + 0 5 0 + 0 + 0 0

Didactics 1 - Curriculum approach 2 + 0 + 1 4 0 + 0 + 0 0

Elective course in psychology 2 3 0 + 0 + 0 0

Elective module in mathematics 2 + 2 + 0 5 2 + 2 + 0 5


Using technology in mathematics teaching 0 + 0 + 0 0 1 + 2 + 0 5

Operating systems 0 + 0 + 0 0 2 + 1 + 0 5

Didactics 2 - Teaching and educational system 0 + 0 + 0 0 2 + 0 + 1 4

Elective course in pedagogy 1 0 + 0 + 0 0 2 3

TOTAL HOURS PER WEEK AND ECTS CREDITS: 23 30 21 30

Elective course in psychology

COURSE


HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

Educational psychology - theories of learning and

teaching mathematics 2 + 0 + 0 3 0 + 0 + 0 0

Psychopathology in childhood and adolescence 1 + 0 + 1 3 0 + 0 + 0 0

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Elective course in pedagogy 1

COURSE


HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

Teachers education in Europe 0 + 0 + 0 0 1 + 0 + 1 3

Educational communication 0 + 0 + 0 0 2 + 0 + 1 3

Culture of (self)-evaluation 0 + 0 + 0 0 1 + 0 + 1 3

Elective modules in mathematics

COURSE


HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

Algebra and fundamentals of mathematics

Vector spaces 2 + 2 + 0 5 0 + 0 + 0 0

Mathematical logic 2 + 2 + 0 5 0 + 0 + 0 0

Set theory 2 + 2 + 0 5 0 + 0 + 0 0

Algebraic structures 0 + 0 + 0 0 2 + 2 + 0 5

Analysis

Metric spaces 3 + 0 + 0 5 0 + 0 + 0 0

Measure and integration 0 + 0 + 0 0 2 + 2 + 0 5

Fourier series and applications 0 + 0 + 0 0 2 + 2 + 0 5

Methods of mathematical physics 0 + 0 + 0 0 3 + 2 + 0 5

Complex analysis 0 + 0 + 0 0 2 + 2 + 0 5

Geometry and topology

Euclidean spaces 2 + 2 + 0 5 0 + 0 + 0 0

Introduction to differential geometry 0 + 0 + 0 0 2 + 2 + 0 5

General topology 0 + 0 + 0 0 3 + 0 + 0 5

Models of geometry 0 + 0 + 0 0 2 + 2 + 0 5

2nd YEAR OF STUDIES

COURSE


HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS


Methods of teaching computer science 1 2 + 2 + 1 9 0 + 0 + 0 0

Elective course in pedagogy 2 2 3 0 + 0 + 0 0

Elective course in computer science 1 3 5 0 + 0 + 0 0

Mathematics teaching practice in middle school 0 + 2 + 0 2 0 + 0 + 0 0

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Computer science teaching practice in middle school 0 + 2 + 0 2 0 + 0 + 0 0


Methods of teaching computer science 2 0 + 0 + 0 0 2 + 2 + 1 7

Elective course in computer science 2 0 + 0 + 0 0 3 5

Mathematics teaching practice in secondary school 0 + 0 + 0 0 0 + 2 + 0 2

Computer science teaching practice in secondary school 0 + 0 + 0 0 0 + 2 + 0 2

Master's thesis - - - 7

TOTAL HOURS PER WEEK AND ECTS CREDITS: 20 30 18 30

Elective course in pedagogy 2

COURSE


HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

Research methods in education 2 + 0 + 0 3 0 + 0 + 0 0

Antisocial behavior 1 + 0 + 1 3 0 + 0 + 0 0

Abuse and risk behaviour prevention 1 + 0 + 1 3 0 + 0 + 0 0

Intelligent systems in teaching 1 + 0 + 1 3 0 + 0 + 0 0

Assessment in mathematics education 1 + 1 + 0 3 0 + 0 + 0 0

Elective course in computer science 1

COURSE


HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

Design and analysis of algorithms 3 + 0 + 0 5 0 + 0 + 0 0

Computer graphics 3 + 0 + 0 5 0 + 0 + 0 0

Combinatorics 2 + 1 + 0 5 0 + 0 + 0 0

Cryptography and network security 3 + 0 + 0 5 0 + 0 + 0 0

Multimedia systems 2 + 1 + 0 5 0 + 0 + 0 0

Social aspects of information and communication

technologies 1 + 0 + 2 5 0 + 0 + 0 0

Elective course in computer science 2

COURSE


HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

HOURS

PER WEEK

(L + T + S)

ECTS

CREDITS

Object-oriented programming (C++) 0 + 0 + 0 0 2 + 2 + 0 5

Mathematical software 0 + 0 + 0 0 1 + 2 + 0 5

Advanced database systems 0 + 0 + 0 0 2 + 1 + 0 5

Machine learning 0 + 0 + 0 0 2 + 1 + 0 5

Natural language processing 0 + 0 + 0 0 2 + 1 + 0 5

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Facultative courses

COURSE


HRS PER

WEEK

(L + T + S)

ECTS

CREDITS

HRS PER

WEEK

(L + T + S)

ECTS

CREDITS

Students’ competitions in mathematics 0 + 0 + 0 0 2 + 0 + 0 3

Methods of solving Sudoku 0 + 0 + 0 0 2 + 2 + 0 4

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3.2. Course description

COURSE TITLE: Abuse and risk behaviour prevention

PROPOSED BY:

Tajana Ljubin Golub, PhD, associate professor, Faculty of Teacher Education, University of

Zagreb

PROGRAMME:

MSc in Mathematics Education

MSc in Mathematics and Computer Science Education

MSc in Mathematics and Physics Education

YEAR OF STUDY: second (elective course)

SEMESTER: third (fall)

TYPES OF

INSTRUCTION

CONTACT HRS

PER WEEK DELIVERED BY

Lectures 1 lecturer

Tutorials 0 -

Seminars 1 assistant

ECTS CREDITS: 3

COURSE AIMS AND OBJECTIVES:

Student will be able to recognize abuse, bullying, as well as risk behaviors, emotional crises and

posttraumatic reactions in students; and will know basics of working students exibiting such

symptoms and behaviors in classroom. They will understand the role and possibilities of the

teacher- and school-based prevention of abuse and risk behaviors of students.

LEARNING OUTCOMES: Upon successful completion of the course, the student is able to:

to understand the symptoms and consequences of physical, sexual and emotional abuse of

children;

to give basic legal regulation in the field of child protection;

to understand the obligation of teacher to act in accordance with the legal norms of child

protection;

to recognize bullying;

to understand the role of stress and trauma in the development of risky behaviors;

to explain the role of teachers in the prevention of child abuse and the development of risky

behaviors.

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By its content, teaching and evaluation methods, the course contributes to the following learning

outcomes at the level of the study programme: I-1, II-5, II-6, IV.

COURSE DESCRIPTION AND SYLLABUS:

1. Introduction to course: the role of prevention in development of normal personality

2. The role of stressors and trauma, types of traumas and consequences

3. Legal aspects of child and juvenile protection

4. Neglect and emotional abuse

5. Physical abuse

6. Sexual abuse

7. Maltreatment between teachers and students

8. Bullying

9. Conflicts and their resolution by peer mediation

10. Juvenile delinquency

11. Depression, suicidal tendencies and other psychological disturbances

12. Addictions

13. The role of school and teachers in prevention of risk behaviors

14. Cooperation between teachers and parents, police and community in risk behavior prevention

TEACHING AND ASSESSMENT METHODS:

Teaching will be performed in a series of lectures and exercise classes. Students will be graded

through take-home assignments, written exams during the semester and the final (written or oral)

examination.

PREREQUISITES: none

READING LIST:

1. Buljan-Flander, G., Kocijan-Hercigonja, D. (2003). Zlostavljanje i zanemarivanje djece.

Zagreb: Marko M.

2. Ajduković, M. (2001). Prevencija zlostavljanja i zanemarivanja djece. Dijete i društvo, 1-2, 161-

172.

3. Ajduković, M. (2001). Utjecaj zlostavljanja i zanemarivanja u obitelji na psihosocijalni razvoj

djece. Dijete i društvo, 1-2, 59-75.

ADDITIONAL READING:

1. Killen, K. (2001). Izdani: Zlostavljana djeca su odgovornost svih nas. Zagreb: DPP.

2. Bilić, V., Zloković, J. (2004). Fenomen maltretiranja djece: Prepoznavanje i oblici pomoći

obitelji školi. Zagreb: Naklada Ljevak.

3. Maleš, D., Stričević, I. (2005). Zlostavljanje među učenicima može se spriječiti. Zagreb:

Udruženje Djeca prva.

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4. Essau, C., Conradt, J. (2006). Agresivnost u djece i mladeži. Jastrebarsko: Naklada Slap.

5. Vulić-Prtorić, A. (2003). Depresivnost u djece i adolescenata. Jastrebarsko: Naklada Slap.

6. Bujišić, G. (2005). Dijete i kriza. Priručnik za odgajatelje, učitelje i roditelje. Zagreb:

Goldenmarketing-Tehnička knjiga.

7. Vrselja, I. (2011). Etiologija delinkventnog ponašanja: Prikaz Pattersonove i Moffittine teorije

razvojne psihopatologije. Psihologijske teme 19, 1, 145-168.

16

COURSE TITLE: Advanced database systems

PROPOSED BY:

Robert Manger, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:

MSc in Computer Science and Mathematics



SEMESTER: fourth (spring)

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer

Tutorials 1 assistant

Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Getting familiar with some advanced topics in the area of

database systems. Extending knowledge about database systems beyond the framework given by a

typical introductory course on relational databases and SQL.


demonstrate knowledge of basic concepts and technologies of distributed databases;

demonstrate knowledge of concepts and basics of practical work with databases that

expand the classical relational model (object-oriented databases, nested relational

databases, deductive databases);

demonstrate knowledge of basic functioning of data warehouses and techniques of data

mining;

use selected software tools for advanced databases.




1. Distributed database systems. Aims, objectives, advantages, and drawbacks of distributing

data. Structure of a distributed database: replication, fragmentation. Distributed transaction

protocols. Integrity, recovery, concurrent access, and security in distributed databases.

Software support for distributing data.

2. Extensions of the relational database model. Object-oriented databases. Nested-relational

databases. Deductive databases. Hybrid models. Non-relational database languages. Non-

17

relational database management systems.

3. Data warehouses. Aims and objectives of data warehousing. Logical structure of a data

warehouse. Representation of a warehouse by a relational scheme. Data mining. Software tools

for warehousing and data mining.


Students’ obligations during classes: Lecture and tutorial attendance, participation in structuring a

study project.

Signature requirements: Attendance at 70% of lectures and tutorials, undertaking a study project.

Taking of exams: Exam consists of solving the study project and of a final examination, which is

taken either in written or in oral form. Successful solution of the project is a necessary condition

for admittance to the final examination. Final grade is based on grade for the study project solution

(or grade for the seminar presentation) and final examination grade.

PREREQUISITES: None.

READING LIST:

1. R. Ramakrishnan et al, Database Management Systems, 3rd Edition, McGraw - Hill, 2002.

ADDITIONAL READING:

1. C. J. Date, An Introduction to Database Systems, 8th edition, Addison-Wesley, 2003.

2. A. Silberschatz, H. F. Korth, S. Sudarshan, Database System Concepts, 4th edition. McGraw-

Hill, 2001.

3. C. Dye, Oracle Distributed Systems, O'Reilly and Associates, 1999.

4. J. L. Harrington, Object-Oriented Database Design Clearly Explained, Morgan Kaufmann,

1999.

5. R. M. Colomb, Deductive Databases and their Applications, CRC Press, 1998.

6. R. Kimball, M. Ross, The Data Warehouse Toolkit – The Complete Guide to Dimensional

Modeling, 2nd edition. John Wiley & Sons, 2002.

18

COURSE TITLE: Algebraic structures

PROPOSED BY:

Marcela Hanzer, PhD, associate professor, Faculty of Science, Department of Mathematics,

University of Zagreb

Tomislav Šikić, PhD, assistant professor, Faculty of Electrical Engineering and Computer Science,


Boris Širola, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:

BSc in Mathematics

BSc in Mathematics Education


YEAR OF STUDY: first (elective course)

SEMESTER: second (spring)

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: The purpose of the course is to present at an introductory

level some basic algebraic structures: groups, rings, algebras and modules. The roles that these

structures play in some other important branches of mathematics will be explained; e.g., in number

theory and representation theory.

The lecturing style is ``from general toward more special’’. Besides we point at the parallelism

among the theories for various structures. The presentation will be accompanied by a number of

examples of algebraic structures which will give the foundation and motivation for further

learning.

LEARNING OUTCOMES: Upon successful completion of the course the student is able to:

recognize the role of groups, rings and fields in various mathematical disciplines and/or

considerations;

apply the acquired knowledge into solving certain problems of linear algebra and

elementary/algebraic number theory, and more advanced algebra as well;

classify the observed algebraic objects and understand their basic structures;

construct and/or recognize new algebraic structures, from the given ones, via standard

constructions and methods;

19

analyze morphisms between algebraic objects, and in particular, recognize isomorphic

structures;

think abstractly and make conclusions while solving some simpler algebraic problems and

analyzing models set in an algebraic context.


outcomes at the level of the study programme: I-2, II-1, II-4, III, IV.


1. Groups. We introduce some basic structural notions (group, subgroup, cosets of a subgroup

in a group, normal subgroup, quotient group, direct and semidirect product of groups…)

We also present some first results abouzt group homomorphisms. This part of the course

concludes with some interesting examples of groups; with a special emphasis on the group

GL_n and some of its subgroups. (6 weeks).

2. Rings, fields and algebras. First we introduce rings, and then ideals as their basic

accompanying objects. Next we treat ring homomorphisms. As very important examples

we study the polynomial rings. Then we give some basics about principal ideal domains

and factorial rings. We proceed with elementary field theory. This part of the course

concludes with definitions and some examples of algebras. First we treat the associative

algebras (matrix algebras, group algebras, quaternion algebras, Weyl algebras), and then

Lie algebras as representatives of the non-associative ones. (7 weeks)

3. Modules. We introduce the following notions: module, submodule, quotient module,

simple and semisimple module etc. We present some basic results of the structure theory,

and some examples of modules as well. (2 weeks)


Students’ obligations during classes: Lecture attendance and active participation in tutorials,

solving homework problems, passing 2 mid-term exams.

Signature requirements: Recorded activity at 70% of lectures and tutorials, submission of 70% of

written homework problems, passing grade at all mid-term exams.

Taking of exams: The final examination is in a written or oral form. The final grade is based on

solving homework problems results, the grades for mid-term exams and the grade for the final

examination.

PREREQUISITES: None

READING LIST:

1. B. Širola; Algebraic structures (in Croatian), http//web.math.hr/nastava/alg/predavanja.php

ADDITIONAL READING:

1. T. W. Hungerford; Algebra (2nd ed.), Springer-Verlag, New York, 1980.

2. S Lang; ; Algebra (3rd ed.), Addison-Wesley, Reading, 1993.

3. M. F. Atiyah, I. G. Macdonald; Introduction to commutative algebra, Addison-Wesley,

Reading, 1969.

20

COURSE TITLE: Antisocial behavior

PROPOSED BY:

Renata Marinković, PhD, assistant professor, Teacher Education Academy, University of Zagreb

Tajana Ljubin Golub, PhD,associate professor, Teacher Education Academy, University of Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 1 Lecturer

Tutorials 0 -

Seminars 1 Lecturer

ECTS CREDITS: 3


Through insight into a programme such as this one, which has a theoretical and practical tone,

young people gain insight into range of life situations and problems that loom at them. Students

get answers to questions – what to do if they recognise such a situation or is something similar

happens to them. They learn which experts to consult and how to help themselves and others. The

course treats life from the other side.


describe and differentiate various types of antisocial behaviors;

describe and explain the key concepts and theories in studying antisocial behavior;

explain the influence of the biological and environmental factors and their interaction on

the antisocial behavior;

understand the role of a teacher in the prevention of antisocial behavior and resilience

development;

understand the need for implementation the prevention activities for antisocial behavior in

curriculum.


outcomes at the level of the study programme: I-2, IV.


1. What is socially unacceptable behaviour. Conduct disorders (causes and consequences).

21

Oppositional and spiteful disorders (causes and consequences). The relationship between

cause and consequences – psychological, emotional, physical. Analysis of cause and

consequences from the scientific/medical point of view. From the point of view of

educational neglect, and the point of view of the inability to adjust socially and therefore be

unaccepted. Visible and hidden effects: rejection, humiliation, intimidation isolation,

inappropriate socialising, denying emotions and protection, abuse (physical and

psychical).

2. Circumstances and environments within which socially unacceptable behaviour takes

place. Family, school (teachers, students), media, work place, the street... Types of socially

unacceptable behaviour: Violence or aggression (over children, women and all segments of

society), intolerance and lack of understanding, verbal offences and conflicts, addictions

(drugs, alcohol...), delinquency (juvenile), crime (sanctioning), incestuous relationships,

paedophilia, rape (physical and psychological), separation from family due to bad or

harmful relationships.

3. Reactions to socially unacceptable behaviour. Fear, stress, lack of self-confidence,

depression. How to recognize, discover and physically approach such a person. Knowing

how to reach those people on an emotional level and how to help them.

4. Knowledge and disciplines which may help. Psychological knowledge. Knowledge from

the field of education (pre-school and family upbringing). Knowledge from the field of

special education. Medical knowledge (gynaecology, paediatrics, psychiatry). Specific

information in the area of social work. Legal knowledge (family law, parental rights and

duties).

5. Securing a human development for the educational population. The preventive-curative

relationship analysis (professional and social). The analysis of the altruistic and egoistic

relationship. Encouraging emotional, moral, intellectual values. Encouraging criticism,

analytical thought and responsibility (what is missing). Development of a civil and

civilisational society, migrations and demographic. Changes that result in a multiple

approaches to life and therefore have consequences.


Lessons will be carried out in two parts – theoretical and practical, that is, lectures and fieldwork,

which implies visits to institutions mentioned in article 6 of the programme, and which

professionally tackle the issues of socially unacceptable behaviour – or educate how to prevent

that from happening. Reports, analyses and discussions, elaborated on after those visits, will take

on the assessment role in a comparative analysis with the theoretical presentations of the teacher.

This course does not imply subject matter that could be tested in a traditional way. In that respect,

we believe that it is more useful to link theoretical knowledge gained from lectures and students’

practical knowledge, and newly gained experience through visits to institutions that are concerned

with this issue.

PREREQUISITES: None

READING LIST:

1. J. Bašić, J. Janković (eds.), Rizični i zaštitni čimbenici u razvoju i poremećaja u ponašanju

djece i mladeži, Kratis, Zagreb, 2000.

2. G. Buljan - Flander, D. Kocijan - Hercigonja, Zlostavljanje i zanemarivanje djece, Marko

Marulić, Zagreb, 2003.

22

3. D. Olweus, Nasilje među djecom u školi, Školska knjiga, Zagreb, 1998.

4. F. Page - Glascoe, Suradnja s roditeljima, Naklada Slap, Jastrebarsko, 2001.

ADDITIONAL READING:

1. P. Dixon, The Truth about Drugs (Facing the big issue of the new millenium), Hooder and

Stroughton, London, 1998.

2. L. Field, Kako razviti samopouzdanje, Mozaik knjiga, Zagreb, 1993.

3. K. A. Hansen, R. K. Kaufman, S. Saifer, Odgoj za demokratsko društvo, Mali profesor,

Zagreb, 1999.

4. J. Kovačević - Čavlović, Protiv zloupotrebe droga, Narodne novine, Zagreb, 1996.

5. K. Lacković - Grgin, Stres u djece i adolescenata – izvori, posrednici i učinci, Naklada Slap,

Jastrebarsko, 2001.

6. P. Lauster, Postanite samopouzdani, Naklada Slap, Jastrebarsko, 2001.

7. G. Lindenfield, Samopouzdanje tinejđera, Veble, Zagreb, 2002.

23

COURSE TITLE: Assessment in mathematics education

PROPOSED BY:

Aleksandra Čižmešija, PhD, associate professor, Faculty of Science, Department of

Mathematics, University of Zagreb

Željka Milin Šipuš, PhD, associate professor, Faculty of Science, Department of Mathematics,


PROGRAMME:



YEAR OF STUDY: second (required course) /second (elective course)


TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 1 lecturer

Tutorials 1 lecturer

Seminars 0 -

ECTS CREDITS: 3

COURSE AIMS AND OBJECTIVES: To train students for appropriate and efficient

monitoring, assessment and grading of students in mathematics education, for self-

assessment, and for critical assessment and interpretation of various assessments results of

students' achievements.


set up clear goals in mathematics teaching and learning in accordance with standard

taxonomies and official curriculum;

distinguish between types of assessment in education;

use efficient and appropriate methods of monitoring and assessment of work, effort

and progress, and self-assessment of students in mathematics;

use monitoring and assessment results for mathematics teaching planning, for

implemented and school mathematics curriculum development, and for improvement

of school quality;

critically assess and interpret various assessments results of students' achievements;

give correct and efficient feedback to students and their parents on their work,

progress and achievements in mathematics;

recognize non-ethical and non-appropriate assessments methods and grading in

mathematics education.

By its content, teaching and evaluation methods, the course contributes to the following

learning outcomes at the level of the study programme: I-1, II-5, III, IV.

24


1. Goals of mathematics education and learning outcomes in mathematics. Mathematical

concepts and processes. Taxonomies of cognitive processes. Taxonomies appropriate to

mathematics education. Construction of clear (measurable and observable) learning

outcomes in mathematics.

2. Role and types of assessment in (mathematics) education. Internal and external,

formative and summative, criterion-referenced, norm-referenced, and ipsative

assessment of students' achievements in mathematics; assessment and self-assessment

of teachers' work; assessment of school quality.

3. Assessment and grading as a part of the process of learning and teaching mathematics.

Assessment as a mechanism to enhance the learning quality (assessment for learning);

assessment as a mechanism to enhance the teaching quality (assessment as learning);

assessment and grading of achievements (assessment of learning). Current trends in

assessment in mathematics education.

4. Measurement and observation of achieving goals and learning outcomes. Methods for

monitoring and assessment of students’ progress in mathematics.

5. Criterion-referenced assessment. Rubrics and achievements indicators. The construction

of sample simple and complex (multidimensional) rubrics in specific mathematical

contents.

6. Methods of monitoring students’ work and progress in mathematics. Monitoring and

observation of the development of students’ mathematical processes. Record keeping.

Observation rubrics. Checklists for whole class and for individual students. Assessing

the productive disposition towards mathematics. Students' self-assessment. Portfolio.

Methods of diagnostic assessment.

7. The construction of a mathematical task in the context of measurements of achievement

against set goals, learning outcomes and taxonomy of cognitive processes. Types of

mathematical tasks.

8. The construction of a written test of students' mathematics achievement in the context

of measurement of achievement against set goals, learning outcomes and taxonomy of

cognitive processes. Reliability, validity, objectivity, fairness. Standardized tests.

9. Formative and summative assessment. Grading and reporting. Feedback to students and

their parents.

10. Standardized tests. External assessment. National exams and state matura in

mathematics. Comparison with other educational systems.


Students are expected to read and reflect on assigned literature, to work individually and

collaboratively, to contribute to group discussions, and to use ICT to analyze test results and

write reports. Students will be graded through take-home assignments and the final (oral)

examination.

PREREQUISITES: Methods of teaching mathematics 2

25

READING LIST:

1. C. R. Tobey, P. D. Keeley, Mathematics Formative Assessment: 75 Practical Strategies

for Linking Assessment, Instruction, and Learning, Corwin Pr Inc, 2011.

2. E. Depka, Designing Assessment for Mathematics, 2nd edition Corwin Pr Inc, 2007.

3. N. E. Gronlund, Assessment of student achievement, Allyn and Bacon, Boston, 2002.

4. J. H. McMillan, Classroom Assessment: Principles and Practice for Effective

Instruction,3rd edition, Allyn & Bacon, Boston, 2004.

5. W. J. Popham, Classroom assessment: What teachers need to know, 3rd edition, Allyn

and Bacon, Boston, 2001.

ADDITIONAL READING:

1. M. Niss (Ed.), Investigations into Assessment in Mathematics Education: An ICMI Study

(New ICMI Study Series), 2nd reprint, Springer, 2010.

2. A. Nitko, Educational Assessment of Students, 3rd edition, Merrill Prentice Hall, 2001.

26

COURSE TITLE: Combinatorics

PROPOSED BY:

Dragutin Svrtan, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

Darko Veljan, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:

MSc in Theoretical Mathematics

MSc in Mathematical Statistics





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Introducing students to combinatorial and discrete

structures and objects. This course is important for theoretical mathematics and computer science

and especially in analysis of algorithms, because it deals with fundamental mathematical

techniques with many concrete examples (I.M. Gelfand: The older I get, the more I believe that at

the bottom of most deep mathematical problems there is a combinatorial problem.)


define various conventions on sums and basic rules for manipulation of sums;

use method of repertoaire, perturbation method and the method of summation factors;

define indefinite and definite sums, to prove discrete Newton-Leibnitz formula and partial

summation formula, discrete analogs of exponential and logarithmic functions;

use techniques of enumerative combinatorics (words, permutations, multisets,

compositions, partitions, rearrangements);

use elements of bijective combinatorics (combinatorial identities and recursions-

(non)commutative multinomial formula, recursions for multisets, compositions, partitions,

rearrangements, lattice paths, Catalan recursions, Stirling numbers);

explain enumeration of walks in directed graphs by linear algebra methods;

state and prove the Moebius inversion formula on partially ordered sets;

define ordinary and exponential generating functions and prove exponential formula;

27

define formal Laurent series and prove Lagrange inversion formula with applications to

Cayley formula for the number of rooted trees and generating function for Bell numbers;

prove Polya’s theorem on enumerating orbits under actions of finite groups on finite sets.


outcomes at the level of the study programme: I-2, II-1, II-2, II-4.

COURSE DESCRIPTION AND SYLLABUS (by weeks):

1. Combinatorial enumeration (by many examples);

2. Recursive problems;

3. Computing sums – discrete calculus;

4. Binomial and q-binomial coefficients;

5. Partial ordered sets and Moebius inversion;

6. Ordinary and exponential generating functions;

7. Recursions and generating functions;

8. Formal languages and symbolic methods;

9. Lagrange's inversion formula;

10. Hypergeometric series. Gosper's algorithm;

11. Asymptotics of some important combinatorial sequences;

12. Some theorems in extremal combinatorics (Sperner's, Turan's theorem etc.);

13. Elements of algebraic graph theory;

14. Elements of geometric combinatorics;

15. Probabilistic methods.


Students’ obligations during classes: Lecture and tutorials attendance, elaboration of homework,

passing 2 mid-term exams.

Signature requirements: Attendance at 70% of lectures and tutorials, submission of results for 70%

of homework, passing grade at all mid-term exams.

Taking of exams: Final examination is taken either in written or oral form. Final grade is based on

successful elaboration of homework, grades for mid-term exams and final examination grade.


READING LIST:

1. D. Veljan, Kombinatorna i diskretna matematika, Algoritam, Zagreb, 2001.

2. R. Graham, D. Knuth, O. Patashnik, Concrete Mathematics. A Foundation for Computer

Science, Addison-Wesley, 1994.

ADDITIONAL READING:

1. D. Knuth, Selected Papers on Discrete Mathematics, CSLI Lecture Notes No. 106, Stanford,

CA, 2003.

2. J. van Lint, R. Wilson, A Course in Combinatorics, Cambridge University Press, Cambridge,

28

1992.

3. K. Rosen (Ed.), Handbook of Discrete and Combinatorial Mathematics, CRC Press, Boca

Raton, FI, 2000.

4. S. K. Lando, Lectures on Generating Functions, American Mathematical Society, 2003.

5. R. P. Stanley, Enumerative Combinatorics, Vol. I & II, Cambridge University Press,

Cambridge, 1999.

29

COURSE TITLE: Complex analysis

PROPOSED BY:

Ljiljana Arambašić, PhD, associate professor, Faculty of Science, Department of Mathematics,


Dražen Adamović, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

Goran Muić, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

Hrvoje Šikić, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

Šime Ungar, PhD, professor, Department of Mathematics, University of Osijek

PROGRAMME:

BSc in Mathematics





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer

Examples Classes 2 assistant

Seminars 0 -

ECTS CREDITS: 5


The students are introduced to the basic notions and techniques of the theory of functions of a

complex variable


define elementary complex functions (polynomial, rational, exponential, trigonometric and

logarythmic functions), and check their basic properties;

analyze differentiability of a complex function using the definition or Cauchy-Riemann

equations, and determine the complex derivative of the function;

calculate the integral of a complex function along a path, state and apply Cauchy's integral

theorem and Cauchy's integral formula;

determine the radius of convergence of a power series, compute Taylor series and Laurent

series of a complex function;

30

determine the singularities of a function and their character, compute residues, state and

apply the residue theorem to computing integrals along a simple closed curve.


outcomes at the level of the study programme: I-2, II-1, II-2, II-4, IV.


Subjects by weeks:

1. Complex numbers and functions. Graphical presentation of complex functions. Continuity and

limits of complex function.

2. Holomorphic functions. Exponential and logarithmic function.

3. Integral of a complex function. Indedx of a closed curve.

4. Square root. Cauchy’s theorem.

5. Cauchy’s integral formula. Morera’s theorem.

6. Sequences and series of functions. Power series.

7. Taylor series. Uniqueness of holomorpic function. Liouville’s theorem. First fundamental

theorem of algebra.

8. Laurent series. Isolated singularities.

9. Residue theorem and applications to evaluating integrals.

10. Aplications of residue theorem to series, partial fractions and infinite products. Gamma

function.

11. Zeros and poles of meromorphic functions. Argument principle.

12. Rouché’s theorem. Second fundamental theorem of algebra. Weierstrass’ preparatory theorem.

13. Open mapping theorem. Holomorphic isomorphism theorem. Maximal module principal.

Schwarz lemma.


Students’ obligations during classes: Lecture and exercise attendance, elaboration of homework,

passing 2 (or 3) preliminary exams.

Signature requirements: Attendance at 70% of lectures and exercises, submission of results for

70% of homework, passing grade at all preliminary exams.


successful elaboration of homework, grades for preliminary exams and final examination grade.

PREREQUISITES: None

READING LIST:

1. M. Rao, H. Stetkoer, Complex Analysis: An Invitation, World Scientific, 1991.

2. Š. Ungar, Matematička analiza 4, http://www.math.hr/~ungar/Analiza4.pdf

ADDITIONAL READING:

1. L. V. Ahlfors, Complex Analysis, McGraw - Hill, 1979.

2. H. Kraljević, S. Kurepa, Matematička analiza 4/I: Funkcije kompleksne varijable, Tehnička

31

knjiga, Zagreb, 1986.

3. W. Rudin, Real and Complex Analysis, McGraw-Hill , 1966.

32

COURSE TITLE: Computer architecture

PROPOSED BY:

Slobodan Ribarić, PhD, professor, Faculty of EE and Computing, University of Zagreb

PROGRAMME:



YEAR OF STUDY: first (required course)

SEMESTER: first (fall)

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Getting introduced to computer architecture and

organization. Getting introduced to assembly programming.


understand and distinguish the functions of major components of a computer including

processor (control unit and ALU), memory, I/O units and buses;

predict activity on the bus of a simple processor, as a consequence of execution of short

machine code sequences (snippets);

understand the design principles of RISC and CISC architectures;

understand and distinguish the measures for evaluation of performance processors /

computers;

understand memory hierarchy and illustrate stages of physical address generation in

presence of cache and virtual memory;

cope in details different U/I techniques (programmed I/O, interrupt I/O and DMA).


outcomes at the level of the study programme: I-3, II-3, III, IV.


Definition of the Computer Architecture. Computer Architecture Classification. Turing Machine.

Von Neumann Computer Model. Simplified Models of CISC and RISC Processors. ISA

Architecture. Control Unit: Hardware and Microprogramming Implementation. Arithmetic-Logic

Unit. Data Path. Memory Unit. Hierarchical Organization of Memory System. Cache Memory.

Virtual memory. Input/Output Subsystem. Programmed I/O. Interrupt. DMA. Exceptions. Speed-

33

up techniques. Pipelining. Fine- and Coarse-Parallelism. Features of CISC and RISC. Examples

of Advanced RISC and CISC Processors.

Exercises are organized as oral lectures as well as laboratory training. The students have to

become familiar with assembly programming techniques by using simulators for 16- and 32-bit

processors/computers.


Students’ obligations during classes: Lecture and tutorial attendance, elaboration of homework,






PREREQUISITES: None

READING LIST:

1. S. Ribarić, Naprednije arhitekture mikroprocesora, Element, Zagreb 2002.

2. S. Ribarić, Arhitektura računala RISC i CISC, Školska knjiga, Zagreb 1996.

3. S. Ribarić, Arhitektura mikroprocesora, Tehnička knjiga, Zagreb 1990.

ADDITIONAL READING:

1. A.S. Tannenbaum, Structured Computer Organization, Prentice-Hall Int, 1990.

2. J.L.Hennessy, D.Patterson, Computer Architecture, A Quantitative Approach, Morgan

Kaufmann Pub., 1996.

34

COURSE TITLE: Computer Graphics

PROPOSED BY:

Željka Mihajlović, PhD, assistant professor, Faculty of Electronic Engineering and Computing,


Mladen Rogina, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0

ECTS CREDITS: 5


Introducing the basics and foundations of Computer Graphics.


differentiate the rendering pipeline stages;

handle the basics of OpenGL;

use the mathematical background of the geometric transformations and projections;

apply the basic properties and constructive algorithms of the conics, Bézier and B-spline

curves (polynomial and rational) and surfaces;

combine the acquired knowledge in programming a simple program for visualization of a

given problem.


outcomes at the level of the study programme: I-3, II-1, III, IV.


1. Introduction. Computer graphics pipeline: geometry, raster, display subsystem.

2. Hardware support for implementation of graphics functions. Fundamentals of graphics

unit, input and display devices.

3. Software support for implementation of graphics functions.

35

4. The mathematical tools needed for the geometrical aspects of computer graphics:

homogeneous coordinates, straight line, plane.

5. Two- and three-dimensional transformations, viewing and perspective.

6. Theory of parametric curve: Bezier curve, de Casteljau subdivision.

7. Continuity constraints, segmentation and B-splines.

8. Interpolation curves. Rational curves. Surface models.

9. Algorithms for visible surface determination.

10. Illumination, local and global shading models: empirical model, ray tracing, and radiosity.

11. Theories of color vision, color models.

12. Visualization. Volume rendering.


Students’ obligations during classes: Lecture attendance, active participation in tutorials,

elaboration of homework, passing 2 mid-term exams, participation in structuring a study project.

Signature requirements: Recorded activity at 70% of tutorials, submission of results for 70% of

homework, passing grade at all mid-term exams, undertaking a study project.

Taking of exams: Final examination consists of solving the study project and presenting the

solution to the teacher. Final grade is based on activity at tutorials, successful elaboration of

homework, grades for mid-term exams and grade for the study project solution.

PREREQUISITES: none

READING LIST:

[1] J.D.Foley, A.Van-Dam, S.K.Feiner and J.F.Hughes: Computer Graphics - Principles and

Practice (2nd Edition in C). Addison-Wesley, Reading, Mass., 1996. ISBN 0 201 84840 6.

ADDITIONAL READING:

[1] Allan Watt, Alan Watt: 3D Computer Graphics (3d Computer Graphics, Ed 3)

Addison-Wesley, 2000. ISBN: 0201398559.

[2] Donald Hearn and M. Pauline Baker: Computer Graphics with OpenGL, third edition.

Prentice Hall, 2003. ISBN: 0130153907.

http://www.amazon.com/exec/obidos/ISBN=0201398559/ultimate3dlinksA/

36

COURSE TITLE: Computer networks

PROPOSED BY:

Luka Grubišić, PhD, Assistant Professor, Faculty of Science, Department of Mathematics,


Robert Manger, PhD, Professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:

BSc in Mathematics




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Introducing computer networks based on the Internet

protocol. Getting familiar with up-to-date networking technologies and applications, especially

world-wide-web. Acquiring skills in writing simple web pages and documents in HTML and

XML.


demonstrate knowledge of basic concepts, technologies and protocols upon which local

(LAN) and wide area (WAN) computer networks, as well as Internet, are based;

describe the layered hierarchy of network protocols, and the role that network devices

(such as network interface cards, routers, switches, modems) and the associated network

protocols (Ethernet, IP, UDP/TCP, etc.) have in that hierarchy;

use the basic networking software (such as ssh, ftp, ping, traceroute, nslookup);

design a simple application protocol for client-server communication;

implement a simple client and server (e.g. by using the SocketAPI library and the C

programming language);

implement a simple web-page by using HTML and CSS.



37


1. Communications and networking. Network standards and standardization bodies. The

ISO/OSI 7-layer reference model and its instantiation in TCP/IP. Circuit switching and

packet switching. Physical layer networking concepts. Data link layer concepts.

Internetworking and routing. Transport layer services. Local-area networks, global-area

networks, Internet.

2. The web as an example of client-server computing. Web technologies. Characteristics of

web servers. Role of client computers. Nature of the client-server relationship. Web

protocols, particularly HTML and XML. Support tools for web-site creation and

management. Publishing on web. Developing web applications.

3. Network management. Basics of network management. Issues for Internet service

providers. Security issues and firewalls. Quality of service issues.

4. Multimedia. Review of multimedia technologies. Multimedia standards. Input and output

devices for multimedia. Multimedia servers. Tools to support multimedia development.

Basics of data compression and decompression.

5. Wireless and mobile technologies. History, evolution and compatibility of wireless

standards. The special problems of wireless and mobile computing. Wireless local area

networks. Satellite-based networks. Wireless local loops. Mobile Internet protocols.

Emerging technologies.


Students’ obligations during classes: Lecture attendance, active participation in exercises,

elaboration of homework, passing 2 (or 3) preliminary exams, participation in structuring study

project.

Signature requirements: Recorded activity at 70% of exercises, submission of results for 70% of

homework, passing grade at all preliminary exams, undertaking a study project.

Taking of exams: Final examination consists of elaboration of study project solution and its

presentation to the teacher. Final grade is based on activity at exercises, successful elaboration of

homework, grades for preliminary exams and grade for study project solution.

PREREQUISITES: None

READING LIST:

1. D. E. Comer, R. E. Droms, Computer Networks and Internets, 4th edition, Prentice Hall,

2003.

ADDITIONAL READING:

1. B. C. Cole, The Emergence of Net-Centric Computing: Network Computers, Internet

Appliances, and Connected PCs, Prentice Hall PTR, 1999.

2. S. Tanenbaum, Computer Networks, 4th edition, Prentice Hall PTR, 2002.

3. M. Morrison, HTML & XML for Beginners, Microsoft Press, 2001.

38

COURSE TITLE: Computer science teaching practice in middle school

PROPOSED BY:

Aleksandra Čižmešija, PhD, professor, Faculty of Science, Department of Mathematics, University

of Zagreb

Goranka Nogo, PhD, assistant professor, Faculty of Science, Department of Mathematics,


PROGRAMME:


YEAR OF STUDY: second (required course)


TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 0 -

Tutorials 2 lecturer and middle school teacher

Seminars 0 -

ECTS CREDITS: 2

COURSE AIMS AND OBJECTIVES: The computer science teaching practice aims to provide

students – informatics/computer science teachers with necessary knowledge and skills for effective

planning, management, delivering and reflecting lessons at middle school level, as well as prepare

them for lifelong learning in the field of information-communication technologies (ICTs). Also,

the course aims to provide opportunities for students to integrate theory and practice and work

collaboratively with and learn from the school teachers.


independently plan, prepare, and deliver a lesson in the middle school;

analyze with a mentor his own lesson;

create learning activities;

select appropriate information and communication technologies and knowledge resources;

supervise and evaluate student achievements.




Computer science teaching practice takes place in selected schools, under supervision of a school

teacher. At practice, students will

1. gain knowledge about the school organization and administration

2. gain knowledge legislation regarding to elementary education in the Republic of Croatia (the

39

related laws and bylaws - regulations, the Statute of the school, etc.)

3. get an insight into pedagogical documentation

4. get an insight implemented curriculum of informatics/computer science for middle school

5. learn about the organization of teaching computer science at the school

6. become familiar with computer classroom where the teaching takes place

7. attend the lessons of a supervising teacher and other school activities regarding computer

science and school life

8. plan, prepare, and deliver several lessons with an assistance of the teacher and independently

9. deliver demonstration teaching hour in front of a lecturer

10. keep a written log of practice

11. write a detailed lesson plan for each teaching hour delivered.

Students will attend computer science teaching practice divided into groups with a maximum of 5

members.


Students are required to

attend computer science teaching practice regularly, with an active participation

keep a written log of practice

plan, prepare, and deliver several lessons in presence other group members and a

supervising school teacher

independently plan, prepare, and deliver a demonstration lecture/lesson in presence of

lecturer.

To achieve a pass students should be positively evaluated in each of the mentioned elements. Final

grade is based on activity at teaching practice, successfully delivered lessons, and grade for the log

of practice.


READING LIST:

1. The curriculum of informatics/computer science for elementary and secondary school,

Ministry of Science, Education and Sport of the Republic of Croatia

2. Computer science textbooks for middle school

ADDITIONAL READING:

1. Manuals for various software packages

2. Kniewald, Logo 4.0, programski jezik, Alfej, Zagreb, 1999.

3. Kniewald, Terrapin Logo, SysPrint, Zagreb, 2005.

4. Journal Enter, all issues, www.enter.bug.hr

http://www.enter.bug.hr/

40

COURSE TITLE: Computer science teaching practice in secondary school

PROPOSED BY:

Aleksandra Čižmešija, PhD, professor, Faculty of Science, Department of Mathematics, University

of Zagreb



PROGRAMME:




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 0 -

Tutorials 2 lecturer and secondary school teacher

Seminars 0 -

ECTS CREDITS: 2

COURSE AIMS AND OBJECTIVES: The computer science teaching practice aims to provide

students – informatics/computer science teachers with necessary knowledge and skills for effective

planning, management, delivering and reflecting lessons at secondary school level, as well as

prepare them for lifelong learning in the field of information-communication technologies (ICTs).

Also, the course aims to provide opportunities for student to integrate theory and practice and work

collaboratively with and learn from the school teachers.


independently plan, prepare, and deliver a lesson in the secondary school;


41







Computer science teaching practice takes place in selected schools, under supervision of a school

teacher. At practice, students will

1. gain knowledge about the school organization and administration

2. gain knowledge legislation related to secondary education in the Republic of Croatia (the

related laws and bylaws - regulations, the Statute of the school, etc.)

3. get an insight into pedagogical documentation

4. get an insight implemented curriculum of informatics/computer science for secondary school

5. learn about the organization of teaching computer science at the school

6. become familiar with computer classroom where the teaching takes place

7. attend the lessons of supervising a teacher and other school activities regarding computer

science and school life

8. plan, prepare, and deliver several lessons with an assistance of the teacher and independently

9. deliver demonstration teaching hour in presence of a lecturer

10. keep a written log of practice

11. write a detailed lesson plan for each teaching hour delivered.

Students will attend computer science teaching practice divided into groups with a maximum of 5

members.


Students are required to

attend computer science teaching practice regularly, with an active participation

keep a written log of practice

plan, prepare, and deliver several lessons in front of other group members and a

supervising school teacher

independently plan, prepare, and deliver a demonstration lecture/lesson in presence of

lecturer.

To achieve a pass students should be positively evaluated in each of the mentioned elements. Final

grade is based on activity at teaching practice, successfully delivered lessons, and grade for the log

of practice.

PREREQUISITES: Methods of Teaching Computer Science 1, Computer Science Teaching

Practice in Middle School

READING LIST:

1. The curriculum of informatics/computer science for elementary and secondary school,

42

Ministry of Science, Education and Sport of the Republic of Croatia

2. Computer science textbooks for secondary school

ADDITIONAL READING:




43

COURSE TITLE: Cryptography and Network Security

PROPOSED BY:

Andrej Dujella, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME: MSc in Computer Science and Mathematics




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: The course aim is to make student familiar with basic

methods used in cryptography and with mathematical background of these methods.


decrypt messages encrypted using the substitution cipher, Vigenère cipher and columnar

transposition;

apply chosen-plaintext attack for breaking Hill's cipher;

describe basic steps in modern block cryptosystems DES and AES;

describe ideas of public key and digital signature, define RSA cryptosystem and its

connection with factorization of large integers;

encrypt messages using public key cryptosystems (RSA, Rabin, ElGamal, Merkle-

Hellman);

cryptanalyze RSA cryptosystem with small public or secret exponent;

define notions of (Euler, strong) pseudoprime numbers and determine whether an integer is

pseudoprime;

apply Fermat's factorization method.




1. Classical cryptography. Basic notions. Substitution ciphers. Vigenère, Playfair and Hill

chiphers. Transposition ciphers. Rotor machines (Enigma). (4 weeks)

2. Modern block ciphers. Data Encryption Standard (DES). Cryptoanalysis of DES. Advanced

44

Encryption Standard (AES). (2 - 3 weeks)

3. Public key cryptography. Idea of public key cryptography. RSA cryptosystem. Cryptanalysis of

RSA. Other public-key cryptosystems. (3 weeks)

4. Primality tests and factoring. Pseudoprimes. Soloway-Strassen and Miller-Rabin primality tests.

Factor bases. Quadratic sieve method. (2 weeks)

5. Network security. Hash functions. Digital signature. Electronic mail security. IP security. (2 - 3

weeks)


Students’ obligations during classes: Lecture and tutorial attendance, elaboration of homework,







READING LIST:

1. D. R. Stinson, Cryptography. Theory and Practice, CRC Press, 2002.

2. W. Stallings, Cryptography and Network Security. Principles and Practice, Prentice Hall, 1999.

ADDITIONAL READING:

1. N. Koblitz, A Course in Number Theory and Cryptography, Springer Verlag, 1994.

2. J. Daemen, V. Rijmen, The Design of Rijndael. AES - The Advanced Encryption Standard,

Springer Verlag, 2002.

3. D. Kahn, The Codebreakers. The Story of Secret Writing, Scribner, 1996.

4. J. Menezes, P. C. Oorschot, S. A. Vanstone, Handbook of Apllied Cryptography, CRC Press,

1996.

5. A. Salomaa, Public-Key Cryptography, Springer Verlag, 1996.

6. B. Schneier, Applied Cryptography, John Wiley & Sons, 1995.

7. J. Simmons (ed.), Contemporary Cryptology, The Science of Information Integrity, IEEE

Press, 1992.

8. S. Singh, The Code Book, Fourth Estate, London, 1999.

9. N. Smart, Cryptography. An Introduction, McGraw-Hill, 2002.

10. M. Welschenbach, Cryptography in C and C++, Apress, 2001.

45

COURSE TITLE: Culture of (self)-evaluation

PROPOSED BY:

Daria Tot, PhD, assistant professor, Faculty of Teacher Education, University of Zagreb

PROGRAMME:





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 1 Lecturer

Tutorials 0 Assistant

Seminars 1 lecturer

ECTS CREDITS: 3

COURSE AIMS AND OBJECTIVES: To enable students for self-evaluation, organization,

implementation and evaluation of educational (teaching) process and students’ achievements. To

acquire competences for independent and effective professional work.


handle real school and teaching situations of evaluation and self-evaluation more easily;

understand evaluation and self-evaluation as components of the curriculum and their

development in the context of school and national curriculum;

self-evaluate the teaching process of the subject they are being educated for;

choose and apply effective strategies, methods and procedures of evaluation and self-

evaluation;

use the results of evaluation and self-evaluation to develop curriculum and improve the

quality of teaching and school as a whole.


outcomes at the level of the study programme: II-5, II-6, IV.


Introduction: the concept and importance of evaluation and self-evaluation in education; the

concept and meaning of the teacher's self-evaluation; beginnings and development of (self-)

evaluation; self-evaluation of teachers in the world and in Croatia (2)

Motivation of teachers and other participants for the evaluation and self-evaluation; key

prerequisites for quality self-evaluation: participant’s competence, school environment,

compliance with the development plan in schools, monitoring and self-evaluation and professional

46

development of teachers, information and communication support; planning the evaluation

process, teacher self-evaluation goals (2)

The content of self-evaluation of teachers; teacher self-evaluation methodology: methods,

techniques, procedures and instruments, self-observation, data collection from participant

evaluations, the results of action research and other research in the function of self-evaluation of

teachers, teacher's portfolio in the function of self-evaluation (2)

Participants in the evaluation of teachers and their roles; criteria and indicators of teacher self-

assessment: determining the quality indicators of self-evaluation, indicators of teachers'

professional competence (2)

Processing and analysis of the collected data; Evaluation of the quality of self-evaluation of

teachers – meta-evaluation; Reporting on and interpreting results of evaluation and self-evaluation

(2)

Self-evaluation of teachers within different concepts of the school self-evaluation; Principles of

self-evaluation of teachers (1)

Projection of professional development of teachers and their work as a result of teacher self-

evaluation; Possibilities of using the results of teacher self-evaluation; Teacher self-evaluation

results and operational planning of professional performance of teachers (2)

Contribution to the planning and implementation of the school development plan and action plan

for professional development and work of teachers; Criteria and indicators of teacher competence

and quality of teaching (2)

TEACHING AND ASSESSMENT METHODS: Teaching will be performed in a series of

lectures and exercise classes. Students will be graded through take-home assignments, written

exams during the semester and the final (written or oral) examination.

PREREQUISITES: none

READING LIST:

1. Meyer, H. (2005). Što je dobra nastava? Zagreb: Erudita.

2. Glasser, W. (2006). Objašnjavanje samoevaluacije u kvalitetnoj školi.

3. Pasaric, B. (2003). Vrednovanje obrazovne djelatnosti. Knjiga 1. Konceptualna studija. Rijeka:

vlastita naklada.

ADDITIONAL READING:

1. Bašic, S. (2007). Nacionalni obrazovni standard – instrument kontroliranja ucinkovitosti

obrazovnog sustava, unapredivanja kvalitete nastave ili standardiziranja razvoja osobnosti?

Pedagogijska istraživanja, 1, 25-41.

2. Bezinovic, P. (2004). Vrednovanje u obrazovanju. Zagreb: Institut za društvena istraživanja u

Zagrebu: Centar za istraživanje i razvoj obrazovanja. Dostupno na

http://www.idi.hr/vrednovanje/razno/mapa.htm

3. Bruner, J. (2000). Kultura obrazovanja. Zagreb: Educa.

4. Cindric, M. (1995). Profesija ucitelj u svijetu i u Hrvatskoj: obrazovanje, zapošljavanje, radne

norme, place, napredovanje u zvanju, odlazak u mirovinu. Zagreb: Persona.

47

5. Gronlund, N. E. (2002). Assessment of student achievement. Boston: Allyn and Bacon.

6. Maleš, D. i Mužic, V. (1990). Mogucnost vrednovanja nastavnika od strane ucenika, Život i

škola, 39 (1), 1-22.

7. Medveš, Z. (2000). Kakovost v šoli. Sodobna pedagogika, 51, 4, 8-28.

8. Prange, K. (2005). Kompetencije izmedu profesionalizacije i evaluacije. Pedagogijska

istraživanja, 1, Zagreb, 49-57.

9. Schon, D. (1987). Educating the Reflective Practitioner: Toward a new design for Teaching

and Learning in the Professions. San Francisco: Jossey Bass.

10. Sentocnik, S. (1999). Pomen refleksije za kakovostno edukacijo: Uciteljev portfolio:

instrument za procesno spremljanje in vrednotenje uciteljevega strokovnega in osebnostnega

razvoja. Ljubljana: Vzgoja in izobraževanje, 30/5, 40-43.

11. Strugar, V. (2004). Vanjsko vrjednovanje i kvaliteta odgojno-obrazovnih postignuca. U:

Unaprjedujemo kvalitetu odgoja i obrazovanja. Zagreb: Hrvatski pedagoško-književni zbor,

169-178.

12. Terhart, E. (2005). Standardi za obrazovanje nastavnika. Pedagogijska istraživanja, br. 1,

Zagreb, str. 69-83.

14. Tot, D., Cindric, M. i Šimovic, V. (2008). Bitna pretpostavka (samo)vrednovanja ucitelja:

spremnost sudionika. U: Pedagogija i društvo znanja. Zagreb: Uciteljski fakultet u Zagrebu,

385-398.

15. Tot, D. i Jurcec, L. (2009). Procjene sudionika samovrjednovanja ucitelja o indikatorima

kvalitete nastave i ucenja. Napredak, 1, 21-38.

48

COURSE TITLE: Design and analysis of algorithms

PROPOSED BY:

Saša Singer, PhD, associate professor, Faculty of Science, Department of Mathematics, University

of Zagreb

PROGRAMME:





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Design of efficient algorithms and precise analysis of

their theoretical and practical complexity. Intractable problems and efficient approximate

algorithms.


explain types and measures of algorithms complexity;

analyze the complexity of iterative and recursive algorithms;

design efficient algorithms for various problems and analyze their complexity;

describe efficient arithmetical algorithms for numbers, polynomials and matrices;

argument the average complexity of the quicksort algorithm;

describe the Fast Fourier Transform and some of its applications.




1. Introduction. Notion of complexity. Asymptotic behavior of functions. Order of growth.

Notation of complexity.

2. Recursive algorithms. Recurrence relations. Examples of recursive algorithms and their

complexity.

3. Sorting. Simple sorting by comparison. More complex algorithms: Quicksort, Heapsort,

Mergesort. Practical complexity analysis of these algorithms. Lower bound for complexity of

sorting by comparisons. Average complexity of Quicksort.

49

4. Design of efficient algorithms. Shortest path, spanning trees and connected components

problems. Efficient realization by disjoint set structure. Fast Fourier transform and applications.

5. Intractable problems. Intuitive notion of classes P and NP. Some NP–complete i NP–hard

problems. Integer knapsack and traveling salesperson problems. Design of exact and

approximate algorithms for solution of these problems.



READING LIST:

1. Saša Singer, Oblikovanje i analiza algoritama, lecture notes in preparation, Department of

Mathematics, University of Zagreb, 2005.

ADDITIONAL READING:

1. G. Brassard, P. Bratley, Algorithmics, Prentice–Hall, 1988.

2. T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein, Introduction to Algorithms, 2nd edition,

MIT Press, 2001.

3. M. H. Alsuwaiyel, Algorithms – Design Techniques and Analysis, World Scientific, 1999.

4. D. E. Knuth, The Art of Computer Programming, Vols. 1, 2, 3, Addison–Wesley, 1997/98.

5. H. S. Wilf, Algorithms and Complexity, Prentice–Hall, 1986.

50

COURSE TITLE: Didactics 1 - Curriculum approach

PROPOSED BY:

Vlatka Domović, PhD, Assistant Professor, Teacher Education Academy, University of Zagreb

Mijo Cindrić, PhD, Assistant Professor, Teacher Education Academy, University of Zagreb

Daria Tot, PhD, Assistant Professor, Teacher Education Academy, University of Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer

Tutorials 0 -

Seminars 1 Lecturer

ECTS CREDITS: 4


The course should qualify students for orientating themselves in the school/educational context,

understanding the goals and tasks of modern education and making it possible to understand the

theoretical/scientific notions in the area of the curriculum theory. During their work students will

gain practical skills necessary for participating in the development, creation, implementation and

evaluation of the curriculum.


independently perceive educational needs of students and „translate“ them into learning

objectives and tasks;

independently choose and implement effective teaching strategies, methods and procedures

while taking account of requirements of modern didactic principles;

plan, organize, implement and evaluate teaching and learning process and its outcomes;

develop teaching (subject) curriculum and participate in development of school curriculum;

know how to make optimal didactic decisions during the preparation of the teaching

process, during the teaching process itself and after analyzing the process;

know how to independently prepare for organizing and implementing the teaching process

with an emphasis on taking account of psychological, material- technical, methodical and

cognitive aspects of teaching;

at the micro level, single out and analyze factors which affect (positively or negatively)

51

teaching environment and school culture;

spot the modalities and essence of the hidden curriculum, as well as its educational

implications.




1. The historical development of school and the didactic idea. The historical review of the

development of organized education and the theory of education. Modern didactic theories.

2. The subject-matter and tasks of didactics and the relation between didactics and other

educational sciences. The definition of the subjet didactics - changes in the definitions

throughout history. The relation between didactics and pedagogy, didactics and the

anthropology of education, didactics and educational sociology, didactics and the

philosophy of education.

3. Fundamental didactic concepts. The definition of notions and concepts: teaching,

education, schooling, training, upbringing the educational process, socialization, informal

education, self-education, learning by doing(experiential learning).

4. The organization and goals of « the traditional school» and the modern concept of the

development of schools. The scientific and political-social conditional quality of defining/

redefining the goals of education/schooling. Modern tendencies and perspectives of the

development of schools in the world, in Europe ( the analysis of the documents of the

European Union) and in Croatia.

5. The concept of life-long education/learning. The beinning , development and definition of

the concept o life-long education/learning. The crisis of traditional schools and its causes.

The reconceptualization of schooling. Changes in the educational environment- (economic,

social-political, cultural changes) and their educational implications. The European trends

and problems in the realization of the concept of life-long learning. The system of the life-

long education of teachers. The key competences of the teacher in a «society of

knowledge».

6. The curriculum theory. The concept and definition of the curriculum and the curriculum

theories. Changes in modern societies and the development and changes of the curriculum.

The core curriculum, the development of the school based curriculum. The implementation

of the curriculum. The curriculum and the role of the teacher.

7. The establishment of educaional needs and defining the educational goals. Inner and outer

educational goals. The stages of the research of educational needs. Educational needs and

goals of learning.The taxonomy of goals.

8. The content of learning and educational system. The educational programme –the criteria

of choice, organization, scope, depth, order.

9. Learning conditions. The inner and outer learning conditions. Teaching, organizational

processes, school and class environment, classroom management.

10. Evaluation of the curriculum. The meaning of evaluation in education. Internal and

52

external evaluation. The state secondary graduation exam as external evaluation-avantages

and disadvantages. The international research of student achievements (e.g. Programme for

International Student Assessment – PISA 2000. i 2003.).

11. The evaluation of teacher's work. The evaluation and improvement of one's own work.Self-

evaluation techniques.


The course realization through 45 hours of lectures. Students need to prepare for seminars, write a

term paper and prepare for the exam. The course realization is conducted through lectures and

seminars. Students must attend lectures, prepare for each topic by reading the proposed literature.

At the end of the Didactics 1 course each student has write a term paper as a prerequisite to attend

the Didactics 2 course. The exam is in written form. The final grade depends on students'

attendance record, active participation during lectures and the quality of the tasks they have

created.

PREREQUISITES: None

READING LIST: Chapters choosen from:

1. H. L. Erickson, Concept – Based Curriculum and Instruction, Corwin Press, 2002.

2. A. C. Ornstein, F. P. Hunkins, Curriculum – Foundations, Principles, and Issues, Allyn

and Bacon, 2004.

3. N. Pastuović, Edukologija, Znamen, Zagreb, 1999.

4. E. Terhart, Metode poučavanja i učenja, Educa, Zagreb, 2001.

ADDITIONAL READING: Chapters choosen from:

1. A. Bežen (ur.), Temeljne edukacijske znanosti i metodike nastave, AOZH i Profil, Zagreb,

2004.

2. L. Bognar, M. Matijević, Didaktika, Školska knjiga, Zagreb, 2002.

3. V. Domović, Školsko ozračje i učinkovitost škole, Naklada Slap, Jastrebarsko, 2004.

4. F. Jelavić, Didaktika, Naklada Slap, Jastrebarsko, 1998.

5. C. Kyriacou, Temeljna nastavna umijeća, Educa, Zagreb, 2001.

6. H. Gudjons, R. Teske, R. Winkel, Didaktičke teorije, Educa, Zagreb, 1994.

7. E. Jensen, Super nastava, Educa, Zagreb, 2003.

8. V. Poljak, Didaktika, Školska knjiga, Zagreb, 1990.

9. www.oecd.org

10. www.eurydice.org

11. http://europa.eu.int/comm/education

53

COURSE TITLE: Didactics 2 – Teaching and educational system

PROPOSED BY:

Mijo Cindrić, PhD, Assistant Professor, Teacher Education Academy, University of Zagreb

Vlatka Domović, PhD, Assistant Professor, Teacher Education Academy, University of Zagreb

Dubravka Miljković, PhD, associate professor, Teacher Education Academy, University of Zagreb

Daria Tot, PhD, Assistant Professor, Teacher Education Academy, University of Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer

Tutorials 0 -

Seminars 1 Lecturer

ECTS CREDITS: 4


The goal of the course is to introduce students with modern didactic theories, strategies and

methods of teaching and to enable (qualify) them for using all this for practical purposes in

primary and secondary schools. The course should make it easier for the students to cope with

concrete school situations which , on one hand, reffer to the realization of the subject teaching plan

which they are educating themselves for. It also reffers to the competences in communicating and

co-operating with parents, local community, development of schools, creating the programme,etc.


independently perceive educational needs of students and „translate“ them into learning

objectives and tasks;

independently choose and implement effective teaching strategies, methods and procedures

while taking account of requirements of modern didactic principles;

plan, organize, implement and evaluate teaching and learning process and its outcomes;

develop teaching (subject) curriculum and participate in development of school curriculum;

know how to make optimal didactic decisions during the preparation of the teaching

process, during the teaching process itself and after analyzing the process;

know how to independently prepare for organizing and implementing the teaching process

54

with an emphasis on taking account of psychological, material- technical, methodical and

cognitive aspects of teaching;

at the micro level, single out and analyze factors which affect (positively or negatively)

teaching environment and school culture;

spot the modalities and essence of the hidden curriculum, as well as its educational

implications.




1. Teaching. The definition and the historical development. The macro and micro structure of

the teaching process. Aspects of situations in teaching and learning: teleological,

axiological, progamme-organizational, methodics, integrational. Classes-learning and

teaching. Teaching factors-teacher, student, content, teaching technology, communication.

Types of teaching. Teaching dramaturgy.

2. Teaching tasks. Substantial task (knowledge and coordinaton skills). Functional task (the

development of skills). Educational task (values, attitudes, habits). The concretezation of

teaching tasks. Analyzing the influence of inner and outer factors on the task definig. The

ability of measuring and the clarity of tasks (levels of knowledge, skills,etc.).

3. Communication in teaching and learning. The importance of communicating. The structure

of the communication cycle and the flowing of information. Prejudice regarding

communication. Dialogue as a process of exchanging information, remodelling of

information and the final processing of information. Communication cycle. Murmurs in

communication. Types of communication. Communication at a distance.

Metacommunication. Listening as communication (active listening).

4. The material-technical and psychological aspects of teaching and learning. Place for class

realization. Equipment:original situation, teaching devices, technical aids, instruments and

equipment,. Original situation. Teaching aids/devices. The information value of teaching

devices and other sources of information. Technical devices. The psychological and

emotional experience of learning and teaching. The theory of expectation and motivation.

5. The cognitive aspect of teaching and learning. Gnoseological learning (sensualism,

rationalism,pragmatism). The gnoseological triangle ( observing-thinking-practice) and

how it is applied in teaching and learning situations. Sources of information in view of

how concrete the level is. Assumptions and conditions of high quality cognition.

6. The methodics aspect of teaching and learning. The dimensions of methodics problems.

The orientation towards the learning goals and the student goals.Method in relation to the

subject (mutual dependence between content and methods).Research methods. Researching

the efficiency of teaching methods. Using methods in teaching. Types of methods.

7. Macrocomponents (situations) of teaching and learning: introducing; reception and

processing teaching contents- the use of notion of the cognitive model of processing

information. Teaching as the process of learning and discovering and researching. The

unity of concrete and abstract, senses and logical-rational. The intensity and extensity of

the microstructual components of teaching. Didactics. Possible mistakes in the cognitive

process. The choice and dimensionalization of teaching contents.

8. Macrocomponents of teaching and learning: repetition and practice. The reproductive and

55

productive repetition and their transfer value. Active thinking operating. Types, freuency

and organization of repetition. The proces of practicing. The contents of practicing.

Corrective practicing.

9. Macrocomponents of teaching and learning: evaluation, testing, grading. What is

evaluated? The procedures of measuring and estimating. Possible mistakes. What is the

technique of testing (oral and written). Demands for observing, testing and evaluating the

student' s development and progress.

10. Organizational (sociological) teaching and learning forms. The frontal form. The individual

form. Pair work. Group work.The structure of organizational forms, ways of choosing the

members, ways of givng tasks, the presentation of tasks, dicussion,synthetizing and

conlusion.

11. Team Teaching (learning). The concept of teams and team learning. The purpose and goals

of team teaching (learning). The necessary conditions for the realization of team learning.

The organization and forms of team learning. The leaders of team learning.

Communication during team learning Team work as a teaching strategy. Advantages of

team teaching.

12. Planning and preparing students and teachers for teaching (classes). The planning of

learning. The preparation for introducing and analyzing he goals. Preparing the content of

teaching (choice, structure, correlations, previou student's knowledge, the level and quality

of of expected knowledge, the choice of contents for individual work, differentiation).

Didactic-methodics decison making (the working out of fundamental teaching and learning

situations (events), choice of methods, procedures, work forms, technique, time dynamics).

13. Teaching and learning systems. The relationship among modern teaching factors. Systems:

Lectures. Teaching in connection with the methods of researching new notions.

Programmed teaching. Exemplary teaching. Problem-research teaching. Mentorship and

autodidactic work.

14. Teaching principles. The principle of: equal opportunities, social integration, the effect

(success), the scientific aspects of teaching and learning, individualization, differentiation,

activities, understanding.


The realization of each course is conducted through 45 hours of classes. Students need to prepare

for the seminars, write a term paper and prepare for the exam. The course realization will be

conducted through lectures and seminars. Students must attend classes, prepare for each topic by

completing their independent reading. During the course realization students must also attend

seminars and prepare for these seminars according to the course leader's instructions. The

prerequisite for taking the exam are successfully completed tasks.

PREREQUISITES: Didactics 1 – Curriculum approach

READING LIST:

Chapters chosen from:

1. L. Bognar, M. Matijević, Didaktika,Školska knjiga, Zagreb, 2002.

2. C. Desforges, Uspješno učenje i poučavanje, Educa, Zagreb, 2001.

3. H. Giesecke, Uvod u pedagogiju, Educa, Zagreb, 1993.

4. B. Greene, Nove paradigme za stvaranje kvalitetnih škola, Alinea, Zagreb, 1996.

56

5. F. Jelavić, Didaktika, Naklada Slap, Jastrebarsko, 1998.

6. C. Kyriacou, Temeljna nastavna umijeća, Educa, Zagreb, 2001.

7. I. Lavrnja, Poglavlja iz didaktike, Pedagoški fakultet, Rijeka, 1996.

8. H. Meyer, Didaktika razredne kvake, Educa, Zagreb, 2002.

9. V. Poljak, Didaktika, Školska knjga, Zagreb, 1990.

ADDITIONAL READING:

Chapters chosen from:

1. M. Cindrić, Profesija učitelj u svijetu i u Hrvatskoj, Persona, Zagreb – Velika Gorica, 1995.

2. P. Jarvis, Poučavanje – teorija i praksa, Andragoški centar, Zagreb, 2003.

3. E. Jensen, Super nastava, Educa, Zagreb, 2003.

4. H. Klippert, Kako uspješno učiti u timu, Educa, Zagreb, 2001.

5. P. Thompson, Tajna komunikacije, Barka, Zagreb, 1998.

57

COURSE TITLE: Educational communication

PROPOSED BY:

Dubravka Miljković, PhD, associate professor, Faculty of Teacher Education, University of

Zagreb

PROGRAMME:





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer

Tutorials 0

Seminars 1 lecturer

ECTS CREDITS: 3

COURSE AIMS AND OBJECTIVES: The program enables students to develop knowledge and

skills needed to communicate effectively in school environment, to understand the principles of

effective communication and the ways to apply them, and to constructively resolve communication

conflicts.


apply the principles of effective communication;

apply the skills of conversation, active listening, presenting educational content,

constructive discussion in communication with students, their parents and peers;

resolve communication conflicts constructively;

apply these skills in personal development.




1. Types and Forms of Communication; (what is communication, communication motives,

verbal

2. and non-verbal communication, interpersonal and intrapersonal communication, small-

group, median-group and large-group communication) (2+2)

3. Communication in Organizations; (communication schemes, organizational climate, formal

and informal/non-formal communication, horizontal and vertical communication, rumours

as means of communication) (1+1)

58

4. Communication in the Classroom (students, first impressions, message congruity, attention

distracters, non-verbal communication (2+2)

5. Speed reading – basic principals (1+1)

6. Listening skills in teaching profession (1+1)

7. Assertiveness; (definition, specific techniques for assertive behaviour, the causes of (non)-

assertiveness, assertive vs. aggressive behaviour, I and You Messages) (2+2)

8. Praise and Criticism in education (1+1)

9. Conflict Communications; (the causes of conflict, overcoming conflicts) (2+2)

10. How to cope with difficult students / parents (1+1)

11. Stress and communication - Communication Fears (overcoming communication fears)

(2+2)


lectures and exercise classes. Students will be graded through take-home assignments, written

exams during the semester and the final (written or oral) examination.

PREREQUISITES: none

READING LIST:

1. Miljković, D., Rijavec, M. (2002.) Kako rješavati konflikte?, IEP-D2 & Vern', Zagreb.

2. Miljković, D., Rijavec, M. (2002.) Kako se zauzeti za sebe?, IEP-D2 & Vern', Zagreb.

3. Miljković, D., Rijavec, M. (2002.) Komuniciranje u organizaciji, IEP-D2 & Vern', Zagreb.

4. Miljković, D., Rijavec, M. (2012.) Razgovori sa zrcalom - sedmo izdanje, IEP-D2, Zagreb

(poglavlja, 6-10)

5. Rijavec, M., Miljković, D. (2002.) Neverbalna komunikacija, IEP-D2 & Vern', Zagreb.

ADDITIONAL READING:

1. Rosenberg, M. (2003.) Nonviolent Communication – A Language of Life, A PuddleDancer

Press Book, Encinitas California.

59

COURSE TITLE: Educational psychology - theories of learning and teaching mathematics

PROPOSED BY:

Vesna Vlahović Štetić, PhD, professor, Faculty of Philosophy, University of Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer

Tutorials 0 -

Seminars 0 -

ECTS CREDITS: 3

COURSE AIMS AND OBJECTIVES: The students will get to know cognitive and socio-

emotional characteristics of children of different ages and the way they influence math learning.

They will learn educational psychology approaches to math learning.


describe cognitive and socio-emotional characteristics of children of different ages and

their impact on math learning;

explain children's development of mathematical concepts and the acquisition of declarative

and procedural knowledge;

evaluate different approaches to teaching mathematics and explain the influence of

personal and social factors on math teaching;

critically analyze studies in the field of mathematical behavior (effects of teaching, gender

differences).


outcomes at the level of the study programme: I-1, II-6, IV.


1. Educational psychology and math learning and teaching (why and in what way is educational

psychology interested in math learning and teaching).

2. Results of comparative studies of mathematical behavior (researches of animal mathematical

behavior)

60

3. Cross-cultural differences in math behavior and attitudes.

4. Sex differences in attitudes towards mathematics and math achievement.

5. Development of mathematical knowledge and skills (from toddlers to preschool and school

children).

6. Declarative and procedural knowledge in mathematics.

7. Learning and teaching mathematical concepts.

8. Learning and teaching mathematical operations.

9. Learning and teaching word-problems.

10. Different approaches to learning and teaching mathematics (sociological and anthropological

perspective, cognitive approach, constructivism).

11. Socio-emotional factors of math learning and teaching (attitudes of teachers and parents,

mathematics anxiety).


Written exam. The grade depends on course attendance and student activity.

PREREQUISITES: None

READING LIST:

1. V. Vlahović - Štetić, V. Vizek Vidović, Kladim se da možeš – psihološki aspekti početnog

učenja matematike, Udruga roditelja Korak po korak, Zagreb, 2003.

2. P. Liebeck, Kako djeca uče matematiku, Educa, Zagreb, 1995.

ADDITIONAL READING:

1. V. Vizek Vidović, M. Rijavec, V. Vlahović - Štetić, D. Miljković, Psihologija obrazovanja,

IEP, Zagreb, 2003.

61

COURSE TITLE: Euclidean spaces

PROPOSED BY:

Mirko Polonijo, PhD, Professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:

BSc in Mathematics





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Give an axiomatic approach to the notions of affine and

euclidean spaces as generalizations of standard three-dimensional space. Introduce all fundamental

notions and prove corresponding theorems.


define affine space and Euclidean space and provide examples;

study planes in affine space and relation of parallelism;

identify the group and subgroup structure of Euclidean plane isometries;

define and apply the intersection and summ of planes;

define and apply simplexes and parallelotopes;

identify the structure of the affine group of an affine space;

find the distance between two points, the angle between two lines, the volume of the

parallelotope and simplex in Euclidean space;

define isometries in general and investigate their special classes.


outcomes at the level of the study programme: I-2, II-1, II-2, II-4, III, IV.


1. Definitions of affine and euclidean spaces. Examples. Elementary properties.

2. Planes in affine space (affine subspaces). Parallelism of the planes.

62

3. Intersection of the planes. Sum of the planes.

4. Coordinate system in an affine space.

5. Equations of a plane, hyperplane and straight line.

6. Convex sets. Halfspaces.

7. Parallelotope. Simplex.

8. Affine transformations. Affine group of an affine space.

9. Analytic representation of an affine transformation.

10. Euclidean space. Cartesian (rectangular) coordinates.

11. Distance. Angle.

12. Volume.

13. Analytic geometry of an euclidean space.

14. Isometry. Isometric operators.

15. Subgroups of the group of isometries.








PREREQUISITES: None

READING LIST:

1. D. M. Bloom, Linear Algebra and Geometry, Cambridge Univ. Press, Cambridge, 1988.

2. S. Kurepa, Konačno dimenzionalni vektorski prostori i primjene, Liber, Zagreb, 1992.

ADDITIONAL READING:

1. K. W. Gruenberg, A. J. Weir, Linear Geometry, Springer, New York, 1977

2. J. R. Silvester, Geometry: ancient and modern, Oxford Univ. Press, 2001.

3. Roger Fenn, Geometry, Springer, New York, 2001.

63

COURSE TITLE: Fourier series and applications

PROPOSED BY: Hrvoje Šikić, PhD, professor, Faculty of Science, Department of Mathematics,


PROGRAMME:

BSc in Mathematics




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: To introduce students to the basis of Fourier analysis

and to provide a strong motivation for continuation of their study in this direction.


associate to a given function its Fourier series, both in the trigonometric and the

exponential form;

formulate and compare basic and advanced results on the convergence of the Fourier

series;

apply the results on the convergence of the Fourier series to the Weierstrass approximation,

the isoperimetric problem, and the heat equation;

name another three classical problems from different branches of mathematics to which the

techniques of Fourier analysis can be applied.




1. Introduction. Normed spaces L1 and L2. Bases in L2.

2. Fourier coefficients. Fourier series. Complex form. Examples. L2 - convergence. Plancherel

identity.

3. The question of pointwise convergence. Riemann - Lebesgue lemma.

4. Dirichlet kernel. Dirichlet integral. Riemann localization principle. Dini test. Lipschitz test.

64

5. Dirichlet theorem. Uniform convergence.

6. Gibbs phenomenon. Convergence discussion: Kolmogorov example, Carleson theorem.

7. Cesaro summability. Fejer theorem.

8. Various applications: Weierstrass aproximation, isoperimetric problem, heat equation.

9. Motivational lecture 1: Group structure and generalizations.

10. Motivational lecture 2: Fourier integral, applications to differential equations, applications to

central limit theorem.

11. Motivational lecture 3: Heisenberg inequality, applications to information theory, Gabor

systems.

12. Motivational lecture 4: Signal analysis and synthesis, wavelets.

13. Motivational lecture 5: Prime number theorem.

TEACHING AND ASSESSMENT METHODS: Regular attendance, homeworks, tests and

exams.

PREREQUISITES: None

READING LIST: H. Dym, H. P. McKean, Fourier Series and Integrals, Academic Press, 1972.

ADDITIONAL READING: J. Duoandikoetxea, Fourier Analysis, GSM Vol. 29, American

Mathematical Society, 2001.

65

COURSE TITLE: General Topology

PROPOSED BY:

Šime Ungar, PhD, Professor, Department of Mathematics, University of Osijek

PROGRAMME:





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer


Seminars 0 -

ECTS CREDITS: 5


Introduce the students to some basic topological facts and methods as a followup of ideas they

encounterd earlier in analysis, geometry and elewhere.


demonstrate intuitive and formal knowledge and understanding of basic concepts and

results of general topology;

mathematically argue and interpret proofs of some results;

apply the acquired knowledge to solve a mathematical problem;

present the content of the course in written and oral form using mathematical language and

notation.

By its content, teaching and evaluation methods, the course significantly contributes to the

following learning outcomes at the level of the study programme: I-2, II-1, II-2, II-4.


Subjects by weeks:

1. From metric to topological spaces. Separation axioms.

2. Normal spaces. Urysohn’s lemma. Tietze’s extension theorem.

3. Connectedness. Path connectedness. Local (path) connectedness.

4. Compactness. σ-compactness. Local compacness.

5. Baire spaces. Compactification.

66

6. Product of topological spaces. Tyhonov’s theorem.

7. Inverse systems and inverse limits. Dyadic solenoid.

8. Function spaces. Topology of pointwise convergence, topology of uniform convergence

and comptact-open topology.

9. Quotient and adjunction spaces. Orbit spaces.

10. Weak and strong topology. CW complexes.

11. Paracompactness. Partition of unity.

12. Metrizability of topological spaces.

13. Extending continuous maps. Homotopy.








PREREQUISITES: Metric Spaces

READING LIST:

1. C. O. Christenson, W. L. Voxman, Aspects of Topology, Marcel Dekker, 1977.

2. J. R. Munkres, Topology, 2nd edition, Prentice-Hall, 2000.

ADDITIONAL READING:

1. R. Engelking, General Topology, 2nd edition, Heldermann Verlag, 1989.

2. J. Dugundiji, Topology, Allyn and Bacon, 1966.

3. J. G. Hocking, G. S. Young, Topology, Addison-Wesley, 1961.

4. J. L. Kelly, General Topology, D. Van Nostrand Company, 1995.

67

COURSE TITLE: Intelligent Systems in Teaching

PROPOSED BY:

Renata Marinković, PhD, Assistant Professor, Department of The Pedagogical, Psychological and

Didactic Education of Subject Area Teachers Teacher Education Academy, University of Zagreb

Ivana Batarelo, PhD, Senior Assistant, Centre for Educational Research and Development,

Institute for Social Research, Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 1 Lecturer

Tutorials 0 -

Seminars 1 Lecturer

ECTS CREDITS: 3


The primary goal is to popularise the issues, and then to professionally and scientifically introduce

it to the milieu of pedagogical experts and to students of pedagogy and other teacher education

programmes of study. In that way, the teaching process would be accepted from a different point

of view.



1. Development of computer application in education, with emphasis on the development of

artificial intelligence. Application of artificial intelligence: training, general problem

solving, expert systems, introducing or using natural language, artificial vision, languages

of artificial intelligence.

2. Educational system – technology, theories, models. Educational systems and their

frameworks. Educational technology as a product and process. Systematic approach to

educational processes. A systematic approach to pedagogical formation.

3. Possibilities for programming intelligent learning. Courseware – instructional computer

programme. Research in artificial intelligence: application of artificial intelligence in

68

education, intelligent computer assisted teaching, macro level and micro level in

determining teaching conditions, expert systems in the function of education.

4. Intelligent system components for teaching. Expert module. Subject modelling. Teaching

module. Environment module IST. Man-computer interaction in IST. Pragmatics IST.

Evaluation IST: evaluating results of domestic research, the role of evaluation in the

creation, of teaching, evaluation of the teaching system.

5. Communicability of knowledge and IST systems. Knowledge – goal of the information-

communicative processes. Skill development in the role of knowledge acquisition.

Knowledge and skill in the role of successful teaching. Communicability of knowledge

model: communicative and diagnostic components of knowledge dynamics, diagnostics

systems and IST systems.

6. Developmental trends in education and IST.


This elective course covers theoretical considerations as well as the application in practice. In

addition to lectures, practical work will consist of practical exercises and a few seminars so that

students could become involved with the issue and in order to fully understand the essence of IST.

We believe that this course does not require an exam at the end of the semester because the

practical part of the course is set up in such a way that students must participate actively in class,

and through practical work must support their engagement and knowledge.


READING LIST:

1. P. Goodyear, Teaching Knowledge and Intelligent Tutoring, Ablex Publ, Corporation

Norwood, New Jersey, 1991.

2. G. P. Kearsley (ed.), Artificial Intelligence and Instruction – Application and Methods,

Addison-Wesley, 1987.

3. E. Wenger, Artificial Intelligence and Tutoring Systems (Computational and Cognitive

Approaches to the Communication of Knowledge), Morgan Kaufman, Los Altos, 1987.

4. H. Mandl, A. Lesgold (eds.), Learning Issues for Intelligent Tutoring Systems, Springer-

Verlag, New York, 1988.

5. R. Marinković, Inteligentni sustavi za poučavanje, HZTK, Zagreb, 2004.

ADDITIONAL READING:

1. A. A. Di Sessa, K. Koedinger, M. Sharples (eds.), Advanced Models of Learning for the Wired

and Wireless Future, Proceedings of the 10th International Conference on Artificial Intelligence

in Education (AIED, 2001), San Antonio, Texas, 2001.

2. B. Du Boulay, R. Luckin, Modelling Human Teaching Tactics and Strategies for Tutoring

Systems, International Journal of Artificial Intelligence in Education, 2001. Vol. 12.

3. C. Frasson, G. Gauthier, G. I. Mc Calla (eds.), Intelligent Tutoring Systems, Proceedings of

the Second International Conference, ITS – 92, Springer- Verlag, Montreal, 1992.

69

COURSE TITLE: Introduction to Differential Geometry

PROPOSED BY:

Željka Milin Šipuš, PhD, Associate professor, Faculty of Science, Department of Mathematics,


PROGRAMME:

BSc in Mathematics




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Students will be introduced to the basic concepts of

differential geometry of curves and surfaces in space in the local aspect. The geometric point of

view will be emphasized. Mathematica/Maple software will be used to visualize introduced

concepts.


determine weather a given set in the three-dimensional Euclidean space forms a smooth

regular curve/surface, and locally parametrize curves and surfaces with given properties;

determine a tangent plane, first and second fundamnetal form of a surface, and calculate

the arc-length of a curve and area of a surface patch;

prove properties and determine the shape operator of a given surface;

calculate curvatures of a curve and a surface and recognize classes of curves and surfaces

with given curvatures;

determine special curves on a surface (principal and asymptotic curves, geodesics);

use Gauss' Theorema Egregium and basic theorems of global theory of curves and

surfaces (Rotation Index Theorem, Four Vertices Theorem, Gauss-Bonnet Theorem).


outcomes at the level of the study programme: I-2, II-1, II-2, II-3, II-4, IV.


1. Curves in space. Regular curves. Arc length. Parametrization by the arc length. Frenet’s

moving frame. Frenet’s formulas. Flexion and torsion. Fundamental theorem for space

70

curves.

2. Surfaces in space. Regular surfaces. Tangent plane. Differential of a mapping. First

fundamental form. Orientation of a surface. Shape operator (Weingarten map). Second

fundamental form. Normal curvature. Principal curvatures and vectors. Gaussian and

mean curvature.

3. Special curves on a surface: lines of curvatures, asymptotic lines, geodesics. Parallel

transport. Local isometry of surfaces. Christoffel symbols. Gauss's Theorema Egregium.

Fundamental theorem for surfaces in space.

TEACHING AND ASSESSMENT METHODS: Teaching will be carried out through lectures

and tutorials.

Students’ obligations during classes: Lecture and tutorials attendance, active participation in

tutorial classes, elaboration of homework, passing 2 mid-term exams.

Signature requirements: Recorded activity at 70% of lecture and tutorials, submission of results

for 100% of homework, passing grade at all mid-term exams.

Taking of exams: Final grade is based on activity at tutorial classes, successful elaboration of

homework, grades for mid-term exams and final examination grade.


READING LIST:

1. A. Pressley, Elementary Differential Geometry, Springer, 2005.

2. W. Kühnel, Differential geometry- Curves- Surfaces- Manifolds, AMS, 2002.

3. A. Grey, Modern differential geometry of curves and surfaces with Mathematica", CRC

Press, 2006.

ADDITIONAL READING:

1. M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976.

2. R. S. Millman, G. D. Parker, Elements of Differential Geometry, Prentice-Hall, 1977.

3. B. O’Neill, Elementary Differential Geometry, Academic Press, New York, 1966.

71

COURSE TITLE: Machine learning

PROPOSED BY:

Bojana Dalbelo Bašić, PhD, professor, Faculty of Electrical Engineering and Computing,


Tomislav Šmuc, PhD, Ruđer Bošković Institute

PROGRAMME:





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Course aim is to present the key algorithms and theory

from the core of machine learning and to learn how to construct the computer programs that

automatically improve with experience (data).


analyze any suitable practical learning problem and formulate solution using the

methodology of machine learning;

use basic unsupervised learning techniques to cluster data and/or find statistically

significant patterns in data;

use techniques for selection and transformation of variables for dimensionality reduction:

k-means, hierarchical clustering methods, principal component analysis;

use supervised learning techniques and build predictive, classification or regression

models using basic algorithms like: decision trees, Naive Bayes, k-nearest neighbors,

neural networks, SVM, ensemble techniques;

compare performances of algorithms or models using different performance measures.




Introduction to machine learning. Solving classification, clustering and regression problem based

on machine learning methods. Concept learning. Generalization. Supervised unsupervised and

72

reinforcement learning.

Percepron. Perceptron learning. Linear regression and least squares methods. Gradient descent and

Delta rule. Kernel perceptron.

Neural networks. Neural network learning. Multilayer networks and backpropagation algorithm.

Neural networks for regression and clussification problems.

Classification. Fisher's linear discriminat analysis. Logistic regression. Support vector machines.

Examples of use in bioinformatics and automatic document classification.

Non-parametric learning techniques. k-nearest neighbor algorithm. Decision tree learning.

Bayesian learning. MAP i ML hypotheses. MDL principle. Bayes optimal classifier and Bayes

naive classifier. EM-algorithm.

Unsupervised learning and data mining. Hierarchical Clustering. k-means clustering.

Dimensionality reduction and principal component analysis. Applications and examples.

Statistical learning theory. PAC learnability. Vapnik - Chervonenkis dimension.










READING LIST:

1. T. Hastie, R. Tibshirani, J. H. Friedman, The Elements of Statistical learning, Springer Verlag,

2001.

2. T. M. Mitchell, Machine Learning, McGraw-Hill, 1997.

ADDITIONAL READING:

1. V. Vapnik, The Nature of Statistical Learning Theory, Springer Verlag, 1995.

2. N. Cristianini, J. Shawe - Taylor, An Introduction to Support Vector Machines, Cambridge

University Press, 2000.

73

COURSE TITLE: Mathematical logic

PROPOSED BY:

Dean Rosenzweig, PhD, Associate Professor, Faculty of Mechanical Engineering and Naval

Architecture, University of Zagreb

Mladen Vuković, PhD, Associate Professor, Faculty of Science, Department of Mathematics,


PROGRAMME:

BSc in Mathematics





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: The course begins with study of syntax and semantics of

propositional logic. The basic aim is to define the notions of formula, interpretation, truth and

validity, proof, theorem and consistency, for the very simple theory. Hilbert-style system and

natural deduction for propositional logic are defined, and the Soundness and Completeness

theorems are proved.

The first order theories are considered in the second part. The syntax and semantics are defined.

Sketch of Henkin's proof of the completeness theorem and its consequences are given.


convert a formula of propositional logic to normal form;

define notions of proof and theorem;

apply compactness theorem;

formulate the kinds of derivation rules of natural deduction;

define the notion of model for a first-order theory;

convert a first-order formula to prenex normal form;

apply semantic tableux for first-order logic.


outcomes at the level of the study programme: II-1, II-2, II-4, IV.

74


I. Propositional logic

1. Introduction. Syntax, formulas, interpretations and truth. Validity and satisfiability.

2. Normal forms. Craig interpolation lemma.

3. Compactness theorem. Applications (ordering of abelian groups and graph coloring)

4. Frege - Łukasievicz system, proof, theorem, deduction. Soundness theorem. Deduction

5. theorem.

6. Completeness theorem for Frege-Łukasievicz system.

7. Consistency. Generalized completeness theorem.

8. Natural deduction. Soundness theorem.

9. Completeness theorem for natural deduction.

10. Some non-classical propositional logic: modal and intuitionistic logic

II. First order logic.

1. Signature of first order theories. First order logic. Structures and interpretations. The truth

of formulas. Validity and satisfiability.

2. Prenex normal forms. Semantic trees.

3. Hilbert system. Deduction theorem.

4. Generalized completeness theorem (sketch of Henkin's proof). Consequences: Gödel

completeness theorem, compactness theorem, Löwenheim-Skolem theorem.

5. Some examples of first order theories: theories with equality, Peano arithmetic and

Zermelo-Fraenkel set theory.








PREREQUISITES: None

READING LIST:

1. M. Vuković, Matematička logika 1, PMF-Matematički odjel, 2004.

ADDITIONAL READING:

1. D.van Dalen, Logic and structures, Springer-Verlag, 1997.

2. E.Mendelson, Introduction to Math. Logic, D. van Nostrand Company, Inc. Princeton,

75

1997.

3. 3. J.R.Shoenfield, Mathematical Logic, Addison-Wesley Publishing Company,

Massachusetts, 1973.

76

COURSE TITLE: Mathematics teaching practice in middle school

PROPOSED BY:

Aleksandra Čižmešija, PhD, professor, Faculty of Science, Department of Mathematics,


Sanja Varošanec, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 0


Seminars 0

ECTS CREDITS: 2

COURSE AIMS AND OBJECTIVES: The course aims are to train students – prospective

mathematics teachers for successful preparation, performing and analysis of mathematical lessons

at primary school level.


independently plan, prepare, and deliver a lesson in the middle school;







COURSE DESCRIPTION AND SYLLABUS: Mathematical teaching practice takes place in

primary schools. Groups of students (max 5) will attend lessons of mathematics taken by chosen

teachers from elementary schools. They will be acquainted with law regulations and school

organization. They will be introduced with pedagogical documentation, mathematical syllabus at

primary school level. They will plan, prepare for teaching and teach several lessons in class.

77

During the practice, student will write a log-book. For each lesson they will write a detailed

didactical preparation. Afterward, they will prepare and perform a public lesson.


Students are expected to attend practice lessons in primary school with an active participation.

Each student has to prepare and perform several lessons and one public lesson in class. Also,

student will write a log-book and preparations for each lesson which he/she holds. Final grade is

based on grade given by mathematical teacher in school, successful preparing and performing a

public lesson, grades for written preparations and the log-book of practice.


READING LIST:

1. Mathematics curricula and syllabuses in the primary school level

2. Textbooks for mathematics in primary schools

ADDITIONAL READING:

Journals, textbooks, pedagogical documentation and other materials suitable for

mathematics instructions

78

COURSE TITLE: Mathematics teaching practice in secondary school

PROPOSED BY:




Zagreb

PROGRAMME:





SEMESTER: forth (spring)

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 0


Seminars 0

ECTS CREDITS: 2

COURSE AIMS AND OBJECTIVES: The course aims are to train students – prospective

mathematics teachers for successful preparation, performing and analysis of mathematical lessons

at secondary school level.


independently plan, prepare, and deliver a lesson in the secondary school;







COURSE DESCRIPTION AND SYLLABUS: Mathematical teaching practice takes place in

secondary schools. Groups of students (max 5) will attend lessons of mathematics taken by chosen

teachers from secondary schools. They will be acquainted with law regulations and school

organization. They will be introduced with pedagogical documentation, mathematical syllabus at

primary school level. They will plan, prepare for teaching and teach several lessons in class.

During the practice, student will write a log-book. For each lesson they will write a detailed

79

didactical preparation. Afterward, they will prepare and perform a public lesson.


Students are expected to attend practice lessons in secondary school with an active participation.

Each student has to prepare and perform several lessons and one public lesson in class. Also,

student will write a log-book and preparations for each lesson which he/she holds. Final grade is

based on grade given by mathematical teacher in school, successful preparing and performing a

public lesson, grades for written preparations and the log-book of practice.

PREREQUISITES: Methods of teaching mathematics 3, Mathematics Teaching Practice in

Middle School

READING LIST:

1. Mathematics curricula and syllabuses in the secondary school level

2. Textbooks for mathematics in secondary schools

ADDITIONAL READING:

Journals, textbooks, pedagogical documentation and other materials suitable for

mathematics instructions

80

COURSE TITLE: Mathematical software

PROPOSED BY:



Ivica Nakić, PhD, assistant professor, Faculty of Science, Department of Mathematics, University

of Zagreb

PROGRAMME:




SEMESTER: sfourth (spring)

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 1 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Insight into current matematical software and its

capabilities.


use the Python programming language to solve simple problems in the field of

mathematics, statistics, scientific computing and informatics;

use Python packages Numpy, Scipy, Matplotlib, Pandas and Sympy;

use the Sage application to solve the symbolic problems;

write complex mathematical formulas within the HTML and PDF documents using LaTeX

notation;

write HTML and similar documents using Markdown language;

write PDF documents using LaTeX.




1. WRI Mathematica. Running Mathematica. Numerical Calculations. Symbolic Computation.

Lists. Graphics and sound. Functions. Packages. Mathematica as programming language.

Mathematica as tool in mathematical analysis and linear algebra.

2. MATLAB. Syntax. Matrices and vectors. Variables and operators. Functions. Programming in

81

MATLAB. Graphical features. Built-in functions. Applications: numerical methods with

MATLAB.

3. LaTeX. Basic concepts. Matters of style. Environments. Typesetting mathematics. Preparing

large documents. Defininig your own commands. The picture environment. Errors.










READING LIST:

1. Original manuals.

ADDITIONAL READING:

1. Web resources available at www.wolfram.com, www.mathworks.com and www.latex-

project.org

http://www.wolfram.com/

http://www.mathworks.com/

http://www.latex-project.org/

http://www.latex-project.org/

82

COURSE TITLE: Measure and integration

PROPOSED BY:

Hrvoje Šikić, PhD, Professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:

BSc in Mathematics




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: To introduce notions of measure, measurable functions

and abstract integration, as well as main theorems of measure and integral.


enumerate and define the basic collections of subsets and recognize them in concrete

examples;

define the notions of a measure and an outer measure and verify their defining axioms on a

given example;

demonstrate the construction of the Lebesgue measure and the general procedure for

extending set functions;

describe Lebesgue's construction of the integral;

formulate the monotone and the dominated convergence theorems and apply them correctly

in a given problem.




1. Introduction. Semirings and rings of sets. Sigma - ring of sets.

2. Finitely and countably additive functions. Measures on rings.

3. Caratheodory construction.

4. Lebesgue measure. Regularity. Measures on reals.

83

5. Measurable functions. Integral of a simple function.

6. Integral of a nonnegative function. Monotone convergence theorem.

7. Integrable functions. Dominated convergence theorem.

8. Lebesgue Lp - spaces.

9. Hahn and Jordan decomposition of a measure. Absolute continuity. Singularity.

10. Radon - Nikodym theorem. Lebesgue decomposition.

11. Convergence types. Egorov theorem.

12. Product measures. Fubini - Tonelli theorem.

13. Riesz representation theorem of positive linear functionals.








PREREQUISITES: None

READING LIST:

D. L. Cohn, Measure Theory, Birkhauser, 1980.

ADDITIONAL READING:

S. Mardešić, Matematička analiza 2. Integral i mjera, Školska knjiga, Zagreb, 1977.

84

COURSE TITLE: Methods of mathematical physics

PROPOSED BY:

Eduard Marušić Paloka, PhD, Professor, Faculty of Science, Department of Mathematics,


Arko Vrdoljak, PhD, Assistant Professor, Faculty of Science, Department of Mathematics,


PROGRAMME:

BSc in Mathematics




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 3 Lecturer


Seminars 0 Lecturer

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Introduction to mathematical modeling through

analytical mechanics. Introduction to Partial Differential Equations.


formulate the equations of motion in Lagrangian and Newtonian mechanics,

derive Euler-Lagrange equations in the calculus of variations (the scalar case),

classify a linear second order partial differential equation and transform it to its canonical

form,

derive the solution of initial value problem for the wave equation,

associate trigonometric Fourier series to a given function and use basic results on its

convergence,

apply the method of separation to the boundary or initial-boundary value problems for

linear second order partial differential equations.




1. Newtons Mechanics. Newton axioms. Moments. Energy. Relative sistems of reference

85

2. Lagrange mechanics. Variational calculus. Lagrange equations. Hamilton equations.

Smooth manifolds.

3. Solid body. Tensor of inertia. Eulers equations.

4. Partial differential equations. Sistems of equations of the first order. Dalambert formula for

wave equation in one dimension. Poisson formula for the diffusion equation in one

dimension. Classification of the second order equations. Separation of variables: wave

equation. Fourier sequences. Sturm – Liouville problem. Laplace equation.


READING LIST:

1. I. Aganović, K. Veselić, Uvod u analitičku mehaniku, skripta PMF - Matematičkog odjela,

Zagreb, 1990.

2. I. Aganović, K. Veselić, Linearne diferencijalne jednadžbe. Uvod u rubne probleme, skripta

PMF - Matematičkog odjela, Zagreb, 1992.

ADDITIONAL READING:

1. V. I. Arnold, Mathematical methods of classical mechanics, Springer Verlag, 1978.

2. A. P. Arya, Classical mechanics, 2nd edition, Prentice Hall, 1998.

3. Z. Janković, Teorijska mehanika, 3. izdanje, skripta, PMF, Zagreb, 1982.

4. C. Lanczos, The variational principles of mechanics, 4th edition, Dover, 1986.

5. M. R. Spiegel, Fourier analysis with applications to boundary value problems, Schaum'e,

McGraw - Hill, 1974.

86

COURSE TITLE: Methods of solving Sudoku

PROPOSED BY:

Nikola Sarapa, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

Žarko Čulić, MSc, lecturer, Faculty of Science, Department of Mathematics, University of Zagreb

PROGRAMME: All undergraduate and graduate programs at Department of Mathematics

YEAR OF STUDY: All (facultative course)

SEMESTER: Spring

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0

ECTS CREDITS: 4

COURSE AIMS AND OBJECTIVES: Teach students to solve Sudoku, from easy to difficult

tasks by applying mathematical logic.


define the basic concepts and rules of the game sudoku;

distinguish more than 50 methods for solving sudoku game;

apply basic methods such as cross hatching, scanning and determing naked (locked)/hidden

single or full house(last digit);

apply standard methods of elimination of candidates based on one-choice, subsets and

pointing/claming locked candidates;

explain the concept of uniqueness in sudoku and apply appropriate methods;

apply advanced methods such as wings, fishes and chains;

use advanced concepts such as weak and strong links, conjugated pairs and almost locked

sets;

solve sudoku selecting and applying the most effective methods;

apply advanced methods to solve sudoku, such as nice loops, forcing chains and Nishio

methods.


outcomes at the level of the study programme: II-2, III.

87


1. Brief history and rules of the game; types of sudoku games

2. Concepts and terminology

3. Solving of easy sudoku (very easy, easy), medium heavy sudoku (moderate, advanced) to

heavy sudoku (hard, very hard)

4. Short presentation / instructions for solving extreme heavy sudoku (fiendish, nightmare)

and the most difficult (beyond nightmare)

5. Solving methods:

a) Basic methods (easy sudoku): cross hatching (hidden single, naked single, full

house)

b) Standard methods (medium sudoku): enter candidates, eliminations of candidates:

one-choice (determining the exact number in the blank fields before proceeding to

eliminate candidates); subsets: pairs, triplets, quadruplets, quintuplets; intersections:

locked candidates type 1 (pointing), locked candidates type 2 (claiming), almost

locked candidates (ALC)

c) Advanced methods (hard sudoku): remote pairs, XY-wing, XYZ-wing, W-wing,

fishes: X-Wing, swordfish, jellyfish, finned fishes and sashimi fishes

d) Highly advanced methods: X-chain (skyscraper, two-strike kite, empty rectangles),

XY-chain, simple colors, unique rectangles type 1 to type 6, hidden rectangles,

deadly paterns, BUG

e) Other highly advanced methods: APE (aligned pair exclusion), ALS-XZ (Almost

locked set – XZ), ALS XY-wing, Sue de Coq, nice loops, forcing chains, Nishio


Students’ obligations during classes: active participation in tutorials, elaboration of homework,


Signature requirements: attendance at all mid-term exam.

Taking of exams: solving a minimum of 70% of mid-term exams and final written exam.

PREREQUISITES: none

READING LIST:

1. Nikola Sarapa, Dušan Sarapa: "SUDOKU IZAZOV - Od početnika do majstora", Školska

knjiga, Zagreb, 2011.

ADDITIONAL READING:

1. Peter Gordon: "Mensa Guide to Solving Sudoku: Hundreds of Puzzles Plus Techniques to

Help You Crack Them All", Sterling Publishing, N.Y., 2006.

89

COURSE TITLE: Methods of teaching computer science 1

PROPOSED BY:





PROGRAMME:




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 1 lecturer

ECTS CREDITS: 9

COURSE AIMS AND OBJECTIVES: The course aims to provide students –

informatics/computer science teachers with necessary knowledge and skills for effective planning,

management, delivering, and reflecting computer science lessons at middle and secondary school

level, as well as prepare them for lifelong learning in the field of information-communication

technologies (ICTs).


implement the national curricula at a school level;

explain the fundamental concepts relating to computer science at the middle school level;

identify typical pupils misconceptions;

formulate problems in a way that enables us to use a computer;

create appropriate learning activities.




The course contains lectures, tutorials, and seminars. Theoretical part (lectures) focuses on the

basics of computer science teaching and learning. Students - prospective teachers will become

familiar with the ICT curriculum for middle and secondary schools (all levels of planning and

programming). In tutorials, acquired theoretical knowledge will be applied to selected examples -

topics from school curriculum, through various forms of instruction and working methods

(individual study, hands - on activities, pair work, group work, team - collaborative work, project

90

work). Practical work takes place in computer classroom connected to Internet and equipped with

multimedia and presentation equipment. Seminars consist of students' group or individual oral

presentations of assigned topics, followed up by group discussions.

The headlines of the course are:

1. Information-Communication Technology (ICT). Concept, characteristics and development

of ICT. Scientific aspects of ICT: theoretical computer science as a fundamental

mathematical discipline as well as technical computing science, information science as

social science, ICT as an important tool of all scientific fields. ICT as an activity: ICT as a

profession, the use of ICT in all spheres of human activity. ICT terminology: the problem

of standardizing ICT terminology in Croatia. ICT in education: education in the field of

ICT, the use of ICT in education from other fields, the need for lifelong learning in the

field of ICT.

2. Education in the field of ICT. Concepts of computer, digital and information literacy.

Educational standards in the field of ICT. International standards for information literacy:

European Computer Driving License (ECDL) and International Computer Driving License

(ICDL). ICT in the education system in Croatia.

3. Didactics of education in the field of ICT. Methods of teaching computer science and its

role in the education of future teachers. Methodology of teaching skills as well as a

multidisciplinary scientific field. Specificity of methods of teaching computer science in

relation to the methodology of other fields of education.

4. Informatics/computer science in middle and secondary education in Croatia. The history of

introducing information technology into the curriculum of Croatian middle and secondary

education. The current status of informatics/computer science as a required subject and

elective activity in middle and secondary school. Equipping computer classroom.

Educational software.

5. Aim and tasks. The goal of teaching computer science: general purpose and special

objectives for each stage of education. The three basic components of computer science

education: knowledge of basic ICT concepts (time invariant - a prerequisite for lifelong

learning), development of ICT skills using the available hardware and software,

development of problem solving skills using ICT. The tasks of teaching computer science:

material, functional and educational.

6. Reasoning methods in computer science teaching. Method of analysis and synthesis

(especially in programming). Method of analogy (especially during practical work in

computer classroom). Method of generalization and specialization. Method of abstraction

and concretization.

7. Selected topics. Presentation of various didactical approaches to selected topics, followed

up by group discussions.

8. Drawing using computer. Software tools for drawing. Software tools for drawing designed

for children. Resolution.

9. Logo programming language. Turtle basics. Procedures. Loops. Variables. Composition of

functions - complex procedures. Decisions. Recursion. Lists. Coordinate graphics.

Sequences. Working with multiple turtles.


Student's achievements will be measured through continuous assessment during semester. Students

are expected to follow lectures, tutorials, and seminars regularly, with an active participation, and

to write assigned homeworks. There will be two in-class examinations during the semester (one of

91

them mid-term and the other at the end of the semester – both of them containing theoretical

questions and problem solving), and a final oral exam. Each student will be assigned to write an

essay focused on a selected topic related to the course syllabus and to prepare an oral presentation

of the main findings of this independent research.

A student's grade will be determined according to the following elements: recorded activity in

classes, homeworks, two in-class examinations, written essay and its oral presentation, and final

oral exam. To achieve a pass students should gain a minimum of 50% in each of the mentioned

elements.

PREREQUISITES None.

READING LIST:

1. The curricula of informatics/computer science for middle and secondary school, Ministry of

Science, Education and Sport of the Republic of Croatia

2. Textbooks for elementary and secondary schools

3. I. Kniewald, Logo 4.0, programski jezik, Alfej, Zagreb, 1999.

4. I. Kniewald, Terrapin Logo, SysPrint, Zagreb, 2005.


6. Computer science textbooks, problems books and other didactical resources for middle and

secondary school

ADDITIONAL READING:


2. F. Glavan, MSWLogo, Početnica naprednog programiranja, Alfej, Zagreb, 2000

3. Journals BUG, VIDI, PCChip, various issues

4. Before It's Too Late, A Report to the Nation from the National Commission on Mathematics

and Science Teaching for the 21st Century, www.ed.gov./americacounts/glenn

5. Standards for Technological Literacy: Content for the Study of Technology, Executive

Summary, International Technology Education Association (ITEA), Reston, Virginia, USA,

2000 (www.iteawww.org)

6. A Guide to Develop Standard-Based Curriculum for K-12 Technology Education, International

Technology Education Association (ITEA), Reston, Virginia, USA, 2000 (www.iteawww.org)

7. A. Tucker, F. Deck, J. Jones, D. McCowan, C. Stephenson, A.Verno, A Model Curriculum for

K – 12 Computer Science: Final Report of the ACM K – 12 Education Task Force Curriculum

Committee, www.acm.org/education/k12, 2003.

8. Being Fluent with Information Technology, Committee on Information Technology Literacy,

National Academy Press, Washington, D.C, USA, 1999.

9. European Computer Driving Licence Syllabus Version 4.0, www.ecdl.com

10. www.hsin.hr (Hrvatski savez informatičara)

11. www.hdpio.hr (Hrvatsko društvo za promicanje informatičkog obrazovanja)



http://www.hsin.hr/

http://www.hdpio.hr/

92

COURSE TITLE: Methods of teaching computer science 2

PROPOSED BY:





PROGRAMME:




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 1 lecturer

ECTS CREDITS: 7

COURSE AIMS AND OBJECTIVES: The course aims to provide students –

informatics/computer science teachers with necessary knowledge and skills for effective planning,

management, delivering, and reflecting computer science lessons at middle and secondary school

level, as well as prepare them for lifelong learning in the field of information-communication

technologies (ICTs).


implement the national curricula at a school level;

explain the fundamental concepts relating to computer science at the secondary school

level;

identify typical pupils misconceptions;

formulate problems in a way that enables us to use a computer;

create appropriate learning activities.




The course contains lectures, tutorials, and seminars. Theoretical part (lectures) focuses on the

basics of computer science teaching and learning. Students - prospective teachers will become

familiar with the ICT curriculum for middle and secondary schools (all levels of planning and

programming). In tutorials, acquired theoretical knowledge will be applied to selected examples -

topics from school curriculum, through various forms of instruction and working methods

93


work). Practical work takes place in computer classroom connected to Internet and equipped with

multimedia and presentation equipment. Seminars consist of students group or individual oral

presentations of assigned topics, followed up by group discussions.


1. Computer science curriculum in middle and secondary school. Specific tasks for each stage of

education (middle and secondary education). The curriculum of informatics / computer science

in middle and secondary school - a framework curriculum (Ministry of Science, Education and

Sports), detailed plans and programs. Textbooks - required and additional.

2. Pedagogical and didactic methods in computer science teaching. Verbal methods (method of

lecture, method of dialogue) and visual methods (documentation methods – method of working

on text, methods of working with other didactic materials); methods of demonstration,

observation, and experimentation.

3. Different types of computer science teaching. Individual study, hands - on activities, pair work,

group work, team - collaborative work, project work, problem-based learning, e-learning.

4. Preparation of teacher for computer science lesson. Learning resources. Written preparation for

lesson. Planning board. Proper use of educational tools and resources. Preparing of

presentation.

5. Monitoring and evaluation of student achievements. Continuous monitoring of students

achievements. Methods of knowledge checking. Computer-based tests. Methods of evaluation.

Elements of the assessment.

6. Selected topics in computer science education - didactic approach. Spreadsheet calculations.

Presentation of data using computers. Computer networks and services. Communication using

computers. Publishing content on the Internet. Algorithms and programming. Databases and

information systems.

7. Computer networks and services. Publishing content on the Internet. Concept and types of

computer networks. Internet and its organization. Internet services. Communication using

computers. Web design. Publishing content on Internet.

8. IT competitions in Croatia and abroad. Croatian informatics competitions and international IT

competitions for school students and students. School students prepare for the competitions.

Topics for competitions in middle and secondary school. Selected problems from the

competitions.



are expected to follow lectures, tutorials, and seminars regularly, with an active participation, and









elements.

PREREQUISITES: Methods of Teaching Computer Science 1, Computer Science Teaching

94

Practice in Middle School

READING LIST:

1. The curricula of informatics/computer science for middle and secondary school, Ministry of

Science, Education and Sport of the Republic of Croatia

2. Textbooks for elementary and secondary schools

3. I. Kniewald, Logo 4.0, programski jezik, Alfej, Zagreb, 1999.

4. I. Kniewald, Terrapin Logo, SysPrint, Zagreb, 2005.


6. Computer science textbooks, problems books and other didactical resources for middle and

secondary school

ADDITIONAL READING:


2. F. Glavan, MSWLogo, Početnica naprednog programiranja, Alfej, Zagreb, 2000

3. Journals BUG, VIDI, PCChip, various issues

4. Before It's Too Late, A Report to the Nation from the National Commission on Mathematics

and Science Teaching for the 21st Century, www.ed.gov./americacounts/glenn

5. Standards for Technological Literacy: Content for the Study of Technology, Executive

Summary, International Technology Education Association (ITEA), Reston, Virginia, USA,

2000 (www.iteawww.org)

6. A Guide to Develop Standard-Based Curriculum for K-12 Technology Education, International

Technology Education Association (ITEA), Reston, Virginia, USA, 2000 (www.iteawww.org)

7. A. Tucker, F. Deck, J. Jones, D. McCowan, C. Stephenson, A.Verno, A Model Curriculum for

K – 12 Computer Science: Final Report of the ACM K – 12 Education Task Force Curriculum

Committee, www.acm.org/education/k12, 2003.

8. Being Fluent with Information Technology, Committee on Information Technology Literacy,

National Academy Press, Washington, D.C, USA, 1999.

9. European Computer Driving Licence Syllabus Version 4.0, www.ecdl.com

10. www.hsin.hr (Hrvatski savez informatičara)

11. www.hdpio.hr (Hrvatsko društvo za promicanje informatičkog obrazovanja)



http://www.hsin.hr/

http://www.hdpio.hr/

95

COURSE TITLE: Methods of teaching mathematics 1

PROPOSED BY:




Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 2 lecturer

ECTS CREDITS: 8

COURSE AIMS AND OBJECTIVES: The course aims to introduce students - prospective

mathematics teachers to the basic concepts of mathematics teaching and learning (that is, to the

mathematical didactics) at primary and secondary school level. Particular attention will be paid to

various forms and methods of mathematical thinking and reasoning and to formulation, proving

and implementation theorems, as prerequisites for understanding processes of teaching and

learning mathematics.


understand and can explain the contemporary concept of school mathematics;

has a detailed insight into the general and specific objectives of school mathematics, the

basic components of mathematics education and the goals of didactics of mathematics;

has insight into the various forms of mathematical thinking and methods of reasoning in

mathematics;

apply adequate forms and methods of mathematical thinking and reasoning in mathematics

teaching;

prepare and present a topic related to the objectives of mathematics teaching, learning

outcomes and methods and forms of reasoning in mathematics.



96

COURSE DESCRIPTION AND SYLLABUS: The course contains lectures, tutorials and

seminars. Lectures provide theoretical foundation of teaching and learning mathematics. In

tutorials, acquired theoretical knowledge will be applied to selected examples - concrete topics

from the school mathematics, through various forms of instruction and working methods


work). Seminars consist of students' group or individual oral presentations of assigned topics from

school mathematics, followed up by group discussions.


1. Introduction. Mathematics as a science and a subject taught in primary and secondary education

- their definitions and relations. Position of mathematics in the Croatian national curriculum and a

comparison to selected European countries.

2. Aims and learning objectives of mathematics education. General and specific aims. Three

crucial components of mathematics education: mathematical concepts, strategies (problem solving,

theorem proving, model building etc.) and algorithms. Learning objectives snd strands (contents)

for each education level (according to ISCED 1997). Educational standards (in Croatia and

elsewhere).

3. Didactics of mathematics. The notion of the field (mathematical) didactics - interdisciplinary

scientific discipline and a theoretical and practical guidance (the know-how) for successfull

mathematics teaching and learning.

4. Forms of mathematical thinking and reasoning. The language of mathematics (development,

use, symbols). Basics of logic (mathematical ideas, assumptions and concept development).

Mathematical notions. Example and counterexample construction. Interpretation and

implementation of the definitions of mathematical concepts. Formulation, proving and

implementation of theorems in mathematics education. Inductive reasoning - complete and

incomplete induction. Deductive reasoning.

5. Methods of mathematical reasoning. Analysis and synthesis. Variation. Analogy. Generalization

and specialization. Abstraction and concretization. Distinguishing cases. Superposition of

particular cases. Descartes' method. Experiment. The method of undetermined coefficients.

Substitution. The method of recurrence relations.



are expected to follow lectures, tutorials and seminars regularly, with an active participation, and









elements.

PREREQUISITES: none

READING LIST:

1. M. Pavleković, Metodika nastave matematike s informatikom 1, Element, Zagreb, 1996.

97


ADDITIONAL READING:

1. B. Pavković, D. Veljan, Elementarna matematika 1, Tehnička knjiga, Zagreb, 1991.

2. B. Pavković, D. Veljan, Elementarna matematika 2, Školska knjiga, Zagreb, 1995.

3. D. Palman, Planimetrija, Element, Zagreb, 1998.

4. D. Palman, Stereometrija, Element, Zagreb, 2005.

5. journals Matematika i škola, Poučak, Matka, Matematičko-fizički list, Math-e, Mathematics

Teacher, Quantum, Mathematics and Informatics Quarterly etc

6. textbooks and other didactical materials for primary and secondary schools

7. A. S. Posamentier, J. Stepelman, Teaching Secondary School Mathematics: Techniques and

Enrichment Units, Prentice Hall, 1998.

8. B. Dougherty (Ed.), Research in Mathematics Education, Information Age Publ, 2002.

9. M. A. Sobel, E. M. Maletsky, Teaching Mathematics: A Sourcebook of Aids, Activities, and

Strategies, Allyn & Bacon, 1998.

10. J. A. Van De Walle, Elementary and Middle School Mathematics: Teaching

Developmentally,5th edition, Addison-Wesley, 2003.

11. C. J. Brahier, Teaching Secondary and Middle School Mathematics, Allyn & Bacon, 1999.

12. M. Serra, Discovering Geometry: An Inductive Approach, Key Curriculum Press, 2001.

13. J. Murdock, Ellen Kamischke, Eric Kamischke, Discovering Advanced Algebra: An

Investigative Approach, Key Curriculum Press, 2002.

14. K. Johnson, T. Herr, Problem Solving Strategies – Crossing the River with Dogs and Other

Mathematical Adventures, Key Curriculum Press, 2002.

15. R. L. Scheaffer, M. Gnanadesikan, A. Watkins, J. A. Witmer, Activity – Based Statistics, Key

Curriculum Press, 2004.

16. A. Watkins, R. L. Scheaffer, G. W. Cobb, Statistics in Action: Understanding the World of

Data, Key Curriculum Press, 2004.

98


PROPOSED BY:




Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 2 lecturer

ECTS CREDITS: 8

COURSE AIMS AND OBJECTIVES: The course aims to introduce students - prospective

mathematics teachers to the basic concepts of mathematics teaching and learning (that is, to the

mathematical didactics) at primary and secondary school level. It provides insight into various

forms, methods and strategies of mathematics teaching (instruction) and learning and provides

students with necessary skills to develop proper didactical approaches in their own mathematics

classroom. Particular attention will be paid to the didactics of arithmetics and algebra.


apply various methods of introducing mathematical concepts, of discovering and proving

mathematical theorems in classroom.

identify adequate teaching/learning strategies and to develop appropriate activities in fields

of arithmetic and algebra

demonstrate a firm content knowledge in school mathematics in fields of arithmetic and

algebra

prepare and present the topic from school mathematics related to arithmetic and algebra.




99

The course contains lectures, tutorials and seminars. Theoretical part (lectures) focuses on the

basics of mathematics teaching and learning. Students - prospective teachers will be introduced to

the didactics of arithmetics and algebra in primary and secondary school curricula. In tutorials,

acquired theoretical knowledge will be applied to selected examples - topics from school

mathematics, through various forms of instruction and working methods (individual study, hands -

on activities, pair work, group work, team - collaborative work, project work). Seminars consist of

students' group or individual oral presentations of assigned topics from school mathematics,

followed up by group discussions.


1. Didactical principles of mathematics teaching. Principle of adequacy (suitability for child's

age). Principle of a systematic and gradual approach (from the whole to the detail, from the

known to the unknown, from the simple to the complicated). Teaching based on scientific

foundations. Principle of students' motivation, interest, consciousness and activity (linking

mathematics teaching to the reality, action learning). Principle of clearness (visuality) and

abstraction (from the concrete to the abstract, inquiery of exemplary problems). Principle of

problem posing and solving (the so-called problem approach). Principle of creativity. Principle

of knowledge, skills, and habits permanency (repeating and reviewing through applications).

Principle of effective teaching. Principle of individual pedagogical approach to each student

considering personal features and cognitive abilities of the students (learning through

individual learning paths). Principle of contemporaneity and historycism. Principle of

integration of different knowledge and skills. Principle of holism (interdisciplinary approach).

2. Teaching forms and methods. Social forms of mathematics teaching and learning: frontal and

individual work forms. Methods and instructional models for teaching mathematics: project

work, problem solving, heuristics, experiments, demonstration, discovery learning,

programmed learning, working with written materials (reading techniques), working with

other media etc.

3. Teaching mathematical concepts, theorems and proofs. Various methods of introducing proofs

and proving in a mathematical classroom. Motivation. Establishing balance between

heuristical approach and formal proving in mathematics teaching and learning.

4. Didactics of arithmetics and algebra. Construction of the real and complex numbers -

introducing N, Z, Q, R and C. Related didactic approaches. Selected topics from K-12

mathematics curriculum and basic algebra. Various teaching methods, curriculum materials

and psychological factors for developing natural, integer, rational, and real number structures,

as well as other algebraic concepts.












elements.

100


READING LIST:



ADDITIONAL READING:

























101


PROPOSED BY:




Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 2 lecturer

ECTS CREDITS: 9

COURSE AIMS AND OBJECTIVES: The course aims to provide student - mathematics

teachers with necessary knowledge and skills for effective planning, management, implementing

and reflecting mathematical lessons at primary and secondary school level. Particular attention will

be paid to the didactics of combinatorics, statistics, probability and mathematical analysis.


has reflective insights into a curricula of mathematics at national level;

implement the curriculum in the school curriculum of the middle schools and secondary

schools;

construct mathematical problems of different types on a given topic from school

mathematics;


of combinatorics, probability, statistics and mathematical analysis;

demonstrate a firm content knowledge in school mathematics in fields of combinatorics,

probability, statistics and mathematical analysis;

prepare and present the topic from school mathematics related to combinatorics,

probability, statistics or mathematical analysis.


outcomes at the level of the study programme: I-1, I-2, II-3, II-5, II-6, IV.

102

COURSE DESCRIPTION AND SYLLABUS: The course contains lectures, tutorials and

seminars. Theoretical part (lectures) focuses on the basics of mathematics teaching and learning.

Students - prospective teachers will be introduced to the didactics of combinatorics, stochastics

and mathematical analysis in primary and secondary school curricula. In tutorials, acquired

theoretical knowledge will be applied to selected examples - topics from school mathematics,

through various forms of instruction and working methods (individual study, hands - on activities,

pair work, group work, team - collaborative work, project work). Seminars consist of students'

group or individual oral presentations of assigned topics from school mathematics, followed up by

group discussions.


1. Types of mathematical subjects (courses) approaches to children with special needs.

Compulsory, elective, optional, additional and remedial courses. Modified curriculum for

students with special needs (with mild mental retardation or fine motor problems).

Mathematically gifted children. Mathematical competitions in Croatia and abroad.

2. Lesson planning and classroom management. Insight into mathematics curricula and

syllabuses in the primary and secondary education. Pedagogical documentation. Lesson

planning and preparing. Lesson structure. Development of materials for mathematics

instruction. Didactical means.

3. Mathematical problems. Theories and methods of mathematical problem solving. Open -

ended and close - ended problems. Posing, solving and extending mathematical problems.

Problem solving strategies. Communicating mathematical problems and solutions.

4. Didactics of combinatorics, probability and statistics. Basics combinatorial concepts. Dirichlet

(pigeonhole) principle. Basic principles of counting. Inclusion - exclusion principle and its

connection to the operations with sets. Data handling and statistics. Different conceptions of

randomness and probability. Fundamental stochastic ideas. Exploratory data analysis.

Association and causality. Inference and induction. Various teaching methods, curriculum

materials and psychological factors for developing combinatorial and stochastical concepts.

Errors, difficulties and misconceptions in probability, graphing, averages, association,

distributions and inference.

5. Didactics of mathematical analysis. Developing the fundamental concepts of real analysis at

different educational stages: functions, limits, differential and integral calculus. Presentation of

various didactical approaches to selected topics, followed up by group disscusions.












elements.


103

READING LIST:



ADDITIONAL READING:

























104


PROPOSED BY:




Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 2 lecturer

ECTS CREDITS: 7

COURSE AIMS AND OBJECTIVES: This course provides student - mathematics teachers with

necessary knowledge and skills for effective planning, management, implementing and reflecting

mathematical lessons at primary and secondary school level and with various assessment

techniques. Particular attention will be paid to the didactics of geometry, trigonometry and

mathematical modelling, and to mathematical applications in other fields.


has insight into the techniques of evaluation and assessment of student achievement and is

able to demonstrate knowledge about factors which impact to evaluation;

create own test materials for topics from school mathematics;


of geometry and mathematical modelling;

demonstrate a firm content knowledge in school mathematics in fields of geometry and

mathematical modelling;

prepare and present the topic from school mathematics related to geometry and

mathematical modelling.


outcomes at the level of the study programme: I-1, I-2, II-3, II-5, II-6, IV.

105


The course contains lectures, tutorials and seminars. Theoretical part (lectures) focuses on the

basics of mathematics teaching and learning. Students - prospective teachers will be introduced to

the didactics of geometry, trigonometry and mathematical modelling, as well as to some frequent

mathematical applications from primary and secondary school curricula. In tutorials, acquired

theoretical knowledge will be applied to selected examples - topics from school mathematics,

through various forms of instruction and working methods (individual study, hands - on activities,

pair work, group work, team - collaborative work, project work). Seminars consist of students'

group or individual oral presentations of assigned topics from school mathematics, followed up by

group discussions.


1. Assessment of students' achievments. Continuous (classroom) assessment and grading

methods. Self-assessment. Assessment of group work. Development of written proofs and

tests.

2. Didactics of geometry and trigonometry. Goals of teaching and learning geometry and

trigonometry. Axiomatic approach to the plane and space geometry in the primary and

secondary mathematics education. Development of the spacial orientation and reasoning.

Syntetic and analytic (coordinate) geometry. Gender differences in the spacial reasoning.

Teaching methods, curriculum materials, psychological factors for developing geometric and

measurement concepts.

3. Didactics of mathematical modelling. Mathematics of finance and business. Role of

applications in mathematics curriculum. Applications in the natural and social sciences

(especially in business and finances). Notion of mathematical model - relation between "real

world" and mathematical problems. The process of mathematical modelling. Design and

development of mathematical models. Teaching methods and curriculum materials.












elements.

PREREQUISITES: Methods of teaching mathematics 3, Mathematical Teaching Practice in

Primary School

READING LIST:



ADDITIONAL READING:

106

























107

COURSE TITLE: Metric spaces

PROPOSED BY:

Zvonko Čerin, PhD, Professor, Faculty of Science, Department of Mathematics, University of

Zagreb

Darko Veljan, PhD, Professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:


MSc in Mathematical Statistics

MSc in Financial and Business Mathematics





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Introduce students to the structures of metric and

topological spaces.


demonstrate intuitive and formal knowledge and understanding of basic concepts and

results of theory of metric and topological spaces;

mathematically argue and interpret proofs of some results;

apply the acquired knowledge to solve a mathematical problem;

present the content of the course in written and oral form using mathematical language and

notation.

By its content, teaching and evaluation methods, the course significantly contributes to the

following learning outcomes at the level of the study programme: I-2, II-1, II-2, II-4.

COURSE DESCRIPTION AND SYLLABUS (by weeks):

1. Basic and more complex examples from mathematical analysis and motivation for the

concept of metric space;

108

2. Metric spaces. Examples, open and closed sets, equivalent metrics, continuous mappings;

3. Topological spaces. Topological structures, basis, subbasis, subspaces, product of spaces,

quotion space, homeomorphism;

4. Hausdorff's spaces. Examples, properties, continuous mapping on compact space,

compactness in Rn , uniform continuous mappings and compactness;

5. Connected spaces.

6. Complete metric spaces. Banach's theorem, Cantor's theorem, Baire's theorem,

completeness of metric space;

7. Arzela-Ascolli's theorem.








PREREQUISITES: None

READING LIST:

1. S. Mardešić, Matematička analiza u n-dimenzionalnom realnom prostoru I, Školska knjiga,

Zagreb, 1974.

ADDITIONAL READING:

1. W. Sutherland, Introduction to Metric and Topological Spaces, Oxford University Press,

1975.

2. J. Dugundji, Topology, Allyn & Bacon, 1966.

3. Z. Čerin, Metrički prostori, internal script (web-available)

4. K. Jänich, Topology, Springer Verlag, 1995.

109

COURSE TITLE: Models of Geometry

PROPOSED BY:

Vladimir Volenec, PhD, Professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:

BSc in Mathematics





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer


Seminars 0 -

ECTS CREDITS: 5


To introduce the basic concepts of Euclidian and non-Euclidian geometries.


define points and lines in Euclidean plane (R^2), describe incidence relation.

study and apply the position of two lines, the distance between two points, pencils in

Euclidean plane.

identify the group and subgroup structure of Euclidean plane isometries.

define points and lines in Spherical plane (R^3), describe incidence relation.


Spherical plane.

identify the group and subgroup structure of Spherical plane isometries.

define points and lines in Projective plane (R^3), describe incidence relation.

formulate and prove Pappus' theorem and Desargues' theorem.

identify the structure of the group of collineations and the group of isometries in Projective

(Eliptic) plane.

define points and lines in Hyperbolic plane (in R^3), describe incidence relation.


Hyperbolic plane.

describe and apply Klein (projective) model of Hyperbolic plane.


110




1. Euclidian plane (analytical approach)

2. Equimorfic group. Affine group

3. The group of isometries

4. Geometry on a sphere

5. Distances. Isometries.

6. Sphere trigonometry.

7. Projective plane. Homogeneous coordinates.

8. Desargue and Pappus theorem.

9. Projective group. Polarity.

10. Eliptic plane.

11. Hiperbolic plane.

12. Distances. Isometries.

13. Hiperbolic geometry. Circles.







successful elaboration of homework, grades for mid-term exams and final examination grade


READING LIST:

P. J. Ryan, Euclidean and non-Euclidean Geometry – an Analytic Approach, Cambridge

University Press, 1991.

ADDITIONAL READING:

A. I. Fetisov, O euklidskoj i neeuklidskim geometrijama, Školska knjiga, Zagreb, 1981.

111

COURSE TITLE: Multimedia systems

PROPOSED BY:



Goran Igaly, PhD, Faculty of Science, Department of Mathematics, University of Zagreb

PROGRAMME:



YEAR OF STUDY: second (elective)


TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: This course aims to introduce students to theoretical

concepts, principles and standards related to digital media and multimedia elements and systems,

and to introduce them to current multimedia technologies and their capabilities. Students will gain

hands-on experience in this area, acquire skills to create various multimedia elements using the

available hardware and software, and learn how to develop own multimedia products and systems.


define the term multimedia system;

make simple content by using modern tools;

compare multimedia applications depending upon the time and available technology;

make a simple application that includes various media types;

distinguish various ways for delivery of media content.


outcomes at the level of the study programme: I-3, II-3, II-4 i III.


Theoretical topics (lectures):

1. Introduction to multimedia. History of multimedia systems. Hypertext, hypermedia and

multimedia. Examples of multimedia applications. Hardware and devices for multimedia

applications. Overview of multimedia software tools.

2. Issues in multimedia authoring. Multimedia authoring metaphors. Content design (choice of

112

multimedia elements: text, image, graphics, animation, video, audio, interactivity). Visual

design. Technical design.

3. Multimedia data representations. Basics of digital audio (digitalization of sound, introduction to

MIDI). Graphic/Image file formats (graphic/image data structures, standard system independent

formats, system dependant formats). Color in image and video (basics of color, color models in

images, color models in video). Basics of video (types of color video signals, analog and digital

video).

4. Multimedia data compression. Lossless compression algorithms (basics of information theory,

Huffman coding, adaptive Huffman coding, LZW algorithm), image compression – JPEG

(algorithm, structure of JPEG format, 4 JPEG modes, JPEG 2000), video compression (H.261,

H.263, MPEG, newer MPEG standards), audio compression (simple audio compression

methods, psychoacoustics, MPEG audio compression – mp3).

5. Multimedia databases. Text indexing. Multimedia data indexing. Metadata, Dublin Core,

MPEG-7. Storage and delivery (re-coding on demand).

6. Multimedia and internet. Limitations of Internet as media. Specific forms of multimedia data –

audio and video streaming (video conferencing, Voice-Over-IP...)

7. Advanced multimedia. Multimedia communications. Wireless technologies. Video-on-Demand.

Current state-of-the-art of multimedia systems.

Tutorials in multimedia laboratory:

This course will use a multimedia laboratory equipped with multimedia computers (that is, with

hardware that supports multimedia), software for designing multimedia elements and applications

(for image, sound, video and animation generating and processing and for development of

multimedia applications). Classroom should also be equipped with additional equipment necessary

for multimedia, like digital photo camera, digital video camera, scanner... Through tutorials

students will get introduced to available hardware and software tools needed for production of

multimedia elements and applications.


Students are expected to follow lectures and tutorials regularly, with an active participation in the

labs. There will be two in-class examinations during the semester (one of them mid-term and the

other at the end of the semester – both of them labs assignments in a multimedia laboratory), and a

final oral exam. Additionaly, students are expected to carry out a semester-long project.

A student's grade will be determined by a weighted average of the project (30%), the first in-class

examination (20%), the second in-class examination (20%), and the final oral exam (30%).

PREREQUISITES: Computer Graphics

READING LIST:

1. R. Steinmetz, K. Nahrstedt, Multimedia: Computing, Communications and Applications,

Prentice Hall Series in Innovative Technology, Prentice Hall, 1995.

ADDITIONAL READING:

1. R. S. Tannenbaum, Theoretical Foundations of Multimedia, W. H. Freeman & Co. Computer

Science Press, New York, 2000.

2. N. Chapman, J. Chapman, Digital Multimedia, 2nd edition, John Wiley & Sons, 2004.

3. N. Chapman, J. Chapman, Digital Media Tools, 2nd edition, John Wiley & Sons, 2003.

113

4. V. Bhaskaran, K. Konstantinides, Image and Video Compression Standards: Algorithms and

Architectures, 2nd edition, Kluwer Academic Publishers, 1997.

5. J. D. Gibson et al, Digital Compression for Multimedia: Principles and Standards, Morgan

Kaufmann, 1998.

6. T. Vaughan, Multimedia: Making It Work, 2nd edition, Osborne/McGraw-Hill, 1994.

7. User's guides for different software tools for multimedia elements and systems development

(eg. Adobe Photoshop®, CakeWalk Home Studio®, Adobe Premiere®, Macromedia Flash®,

Macromedia Dreamweaver®, Macromedia Director®, Macromedia Authorware® etc.)

114

COURSE TITLE: Natural language processing

PROPOSED BY:

Bojana Dalbelo Bašić, PhD, professor, Faculty of Electrical Engineering and Computing,


PROGRAMME:





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Acquiring basic knowledge and skills related to natural

language processing.


demonstrate knowledge of basic challenges in natural language processing, and limitations

of current approaches;

demonstrate knowledge of concepts of processing morphology and syntax, as well as the

main approaches to development of parsers;

demonstrate knowledge of basic challenges in semantic interpretation and the common

schemes of knowledge representation;

demonstrate knowledge of main techniques of statistical natural language processing, for

purposes such as automatic indexing and text categorization;

implement select methods and techniques of natural language processing in a modern

programming language.




1. Introduction. Computer science and linguistics; computational linguistics and natural language

understanding. Artificial intelligence and natural language, Turing test, shallow AI and the

ELIZE system, knowledge-based systems. Levels of natural language processing; the role of

statistics in NLP. Overview of research in the field of NLP; available tools; typical applications.

115

2. Morphological processing. Language morphology, overview of English and Croatian

morphology. Morphological processing; morphological processing and lexical ambiguity.

3. Syntactic processing. Elements of syntax, overview of English and Croatian syntax. Formal

grammars and associated computational models, Chomsky hierarchy, rewrite rules, finite state

automata, transition networks, augmented and recursive networks, syntactic patterns. Formal

grammars vs. natural language grammars; the problem of ambiguity. Typical parsers:

interpreted, procedural, top-down, bottom-up parsers; complexity comparison, efficiency and

expressiveness of underlying grammars. Statistically guided parsing.

4. Semantic interpretation. The role of semantic interpretation. Semantic interpretation during

parsing. Ambiguity problem; statistics and restriction based disambiguation. Other methods of

semantic interpretation: pattern matching, dependency grammars. Scope and interpretation of

pronoun phrases; anaphora.

5. Knowledge representation and reasoning. Common knowledge representation schemes: first

order predicate logic, semantic net, frames; methods of automated reasoning. Statistical

methods for disambiguation. Logic and natural language: referential transparency, modal logic

and corresponding semantic models; fuzziness of natural language, linguistic variable and fuzzy

logic; common-sense knowledge; verb tense and temporal logic.

6. Statistical processing of natural language. Text mining and information retrieval: text

preprocessing, automated indexing, text categorization and clustering. Probabilistic language

models, hidden Markov models, POS tagging. Probabilistic context-free grammars; training

algorithm.

7. Intelligent agents and communication.. Agent; multi-agent system; speech-act theory and

intentional systems. Conversation modeling; examples of Petri Nets models. Languages FIPA

ACL and content language SL.










READING LIST:

1. J. Allen, Natural Language Understanding, 2nd edition, Benjamin/Cummings, 1995.

2. C. Manning, H. Schütze, Foundations of Statistical Natural Language Processing, MIT Press,

1999.

ADDITIONAL READING:

1. E. Charniak, Statistical Language Learning, MIT Press, 1996.

2. M. D. Harris, Introduction to Natural Language Processing, Reston Pub. & Co, 1985.

3. D. Jurafsky, J. Martin, Speech and Language Processing, Prentice-Hall, 2000.

116

COURSE TITLE: Object-oriented programming (C++)

PROPOSED BY:

Robert Manger, PhD, professor, Faculty of Science, Department of Mathematics, University of

Zagreb

Dean Rosenzweig, PhD, professor, Faculty of Mechanical Engineering and Naval Architecture,


Maja Starčević, PhD, assistant professor, Faculty of Science, Department of Mathematics,


PROGRAMME:

BSc in Mathematics





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Mastering an object-oriented programming language, for

instance C++. Introducing methods and tools of object-oriented software engineering. Putting

emphasis on up-to-date mainstream technologies and on individual work of students.


use object oriented programming techniques in programming language C++;

use generic programming techniques in programming language C++;

apply basic software design patterns in code construction;

use one of integrated development enviroment in code developement.


outcomes at the level of the study programme: I-3, II-2, II-3.


1. Details of the object-oriented paradigm and C++: objects, classes, inheritance, aggregation,

polymorphism, overloading, encapsulation, interfaces, templates.

2. Basics of object-oriented software engineering: Unified Modeling Language – UML, Rational

117

Unified Process – RUP.

3. Object-oriented programming in C++ by using a programmer's workbench such as MS Visual

Studio .NET










READING LIST:

1. B. Stroustrup, The C++ Programming Language, 3rd edition. Addison - Wesley, 1998.

2. G. Booch, J. Rumbaugh, I. Jacobson, The Unified Modeling Language User Guide, Addison -

Wesley, 1998.

ADDITIONAL READING:

1. P. Kroll, P. Kruchten, The Rational Unified Process Made Easy: A Practitioner's Guide to

Rational Unified Process, Addison - Wesley, 2003.

2. A. Alexandrescu, Modern C++ Design – Generic Programming and Design Patterns Applied,

Addison - Wesley, 2001.

3. J. Arlow, I. Neustadt, UML and the Unified Process - Practical OO Analysis and Design,

Addison - Wesley, 2001.

4. J. Prosise, Programming Microsoft .NET, Microsoft Press, 2002.

5. J. Richter, Applied Microsoft .NET Framework Programming, Microsoft Press, 2002.

6. D. Box, Essential .NET, Addison - Wesley, 2002.

7. Original programming manuals and network resources.

118

COURSE TITLE: Operating systems

PROPOSED BY:

Leo Budin, PhD, professor, Faculty of EE and Computing, University of Zagreb

Leonardo Jelenković, PhD, assistant professor, Faculty of EE and Computing, University of

Zagreb

PROGRAMME:





TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: Introducing the concepts of modern operating systems .


write an multithreaded program and program which creates multiple processes;

demonstrate how interrupt service routine works;

apply synchronization mechanisms;

list components of operating system kernel;

analyze deterministic and non-deterministic task system behavior;

list and explain CPU scheduling algorithms;

employ memory allocation mechanisms;

develop file-system functions.




Hierarchically layered structure of the operating systems. Operating system as the interface

between users and computing devices. Model of thread (instruction stream) in rudimentary

computer. Multithreading based on context switching. Broadening of rudimentary computer with

input-output devices. Single character transfer. Interrupt synchronization of input-output.

Hardware and software interrupts. Transferring blocks of characters by direct memory access.

Execution of threads in multiprocessor systems. Programs, processes, threads. Threads address

119

spaces as process subspaces. Multithreaded realization of systems of tasks. Independent and

dependent threads. Determinate systems of threads. Mutual exclusion of threads. Hardware

support for mutual exclusion. Model of simple kernel as an environment for thread execution.

Kernel functions for binary and general semaphores, for input-output and for time delay. Producer-

consumer problem. Thread synchronization. Deadlocks. Concept of monitor. Additional kernel

functions for monitor realization. Thread coordination and synchronization by monitors. Timing

analysis in computer systems. Deterministic thread scheduling. Basic scheduling models in non-

deterministic systems. First-come-first-served and round robin scheduling. Storage management.

Properties of backing-store devices. Static and dynamic memory allocation. Problem of

fragmentation. Overlaid allocation. Memory allocation by paging. Demand paging. Hardware

support for paging: translations look-aside buffer (TLB). Slowdown of process execution caused

by page faults. Page replacement strategies. Working set of pages. The role of files in computer

systems. File structures. File allocation on disks. File descriptors and file directories. Basic

properties of functions for creation and deletion, opening and closing, reading and writing of files.

Inter-process communication inside single computer system: shared memory, message passing

(between threads in different processes). Basics of networking. Communication in distributed

systems: message passing, remote procedure call, distributed shared memory. Mutual exclusion in

distributed systems: time ordering of events, local and global clocks. Mutual exclusion protocols:

centralized protocol, moving token protocol, distributed Lamport’s protocol.








PREREQUISITES: Computer Architecture

READING LIST:

1. L. Budin, Operacijski sustavi, Element, Zagreb, 2005. (in Croatian)

ADDITIONAL READING:

1. A. Silbershatz, P. Galvin, G. Gagne, Applied Operating Systems Concepts, John Wiley &

Sons, 2002.

120

COURSE TITLE: Psychopatology in childhood and adolescence

PROPOSED BY:

Krunoslav Matešić, PhD, Assistant Professor, Department of The Pedagogical, Psychological and

Didactic Education of Subject Area Teachers, Teacher Education Academy, University of Zagreb

PROGRAMME:





SEMESTER: first (spring)

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 1 Lecturer

Tutorials 0 -

Seminars 1 Lecturer

ECTS CREDITS: 3

COURSE AIMS AND OBJECTIVES: Acquisition of general knowledge in the area of

psychopathological behaviour. The above-mentioned forms of deviation from what is considered

to be normal behaviour and are observed in educational practice. An important element of this

course is the synchronization of topics and content with the official classification of the

psychopathology of behaviour that is valid in the Republic of Croatia.


understand criteria for determining atypical psychological and behavioral functioning and

recognize deviations from normal psychological development in childhood and

adolescence;

differentiate and describe the main characteristic of the most common psychological and

developmental disorders in childhood and adolescence;

explain the role of different factors contributing to onset of psychological and

developmental disorders;

understand and apply the main principles of interventions for adapting instruction to meet

the needs of students with disabilities;

identify the adjustment problems of students with disabilities in real-life situations;

understand the need for providing support for to the students with psychological and

developmental disorders in collaboration with the school expert team.

By its content, teching and evaluation methods, the course contributes to the following learning


121


1. Course introduction: Determining psychopathology in childhood and adolescence

according to the MKB-10 and DSM-IV systems of classification; historical approaches to

the problem; current theories and discussions on the roles of hereditary and environmental

factors in the onset of the disorder.

2. Mental retardation: Classification of mental retardation, genetic and environmental causes

of developing mental deficiency, achievements in learning and possible training for living

independently, that is, welfare and care for intellectually deficient persons, taking into

consideration the categories of mental insufficiency.

3. Learning disorders: General prerequisites for diagnosing disorders, reading disorder,

disorders in mathematical abilities disorder, writing disorder. Symptomatology,

identification/diagnosis, prevalence, line of development, help and therapeutic

interventions.

4. Communication disorders: Speech disorder, phonological disorder, stuttering. Criteria for

identifying/diagnosing, prevalence, line of development, help and therapeutic

interventions.

5. Attention Deficit Hyperactivity Disorder - AD/HD: Symptoms, identification/diagnosis,

theoretical discussions on the causes of disorders, general prevalence and differences with

respect to gender, concentration exercises, psychotherapeutic and medical treatment, that

is, Ritalin treatment, general learning difficulties.

6. Behaviour disorder - defiance and opposition: Symptoms, identification/diagnosis, theories

on the onset of a disorder, prevalence and differences with respect to gender,

psychotherapeutic contributions and help, possible line of development and developmental

outcomes. Behaviour disorders as a prerequisite for diagnosing antisocial personality

disorder.

7. Developmental risks in adolescence: Eating disorders, bulimia, anorexia, substance abuse

and development of addiction/smoking, alcohol, drugs/. Risks from homosexual identity.

8. Anxiety in children and youth: Anxiety as a state and a personality characteristic, fears and

phobias, school phobia, the separation syndrome, excessive self-control and obsessive-

compulsive behaviour, anxiety in the structure of later personality disorders.

9. Depression and depressive states in children and youth: Depression and tendency for

depressive reactions, causality, prevalence and differences with respect to gender,

childhood and adolescent suicide.

10. Schizophrenia in school aged children and adolescence: Illness structure, appearance and

diagnosis, the role of hereditary factors, prevalence and differences with respect to gender,

treatment and prognosis for successful treatment, recommendations for the selecting a

profession, that is, limitations in the area of employment.

11. Physical illness and brain damage: All types of physical handicap, their statistical look

minimal cerebral dysfunction; preserving the intellect of handicapped, counselling in

selecting a profession and area of employment.

12. Stress in children and youth: Psychological theory of stress, comparison with the

physiological approach to stress, stressors, outcomes of stressful situations. Important

stressors in children and youth, divorce of parents, illness and death of family members,

failure in school, changes in puberty, separation, social isolation, etc. The concept of post-

traumatic stress disorder.

13. Problems of violence towards children and youth: Physical and psychological violence,

122

alcoholism and criminal behaviour of parents, socially high-risk families, generational

transfer/pattern of abuse, sexual abuse on children and youth, identification, help and

recommendations for preventing sexual abuse.

14. Psychotherapeutic methods and techniques and medical treatment: An overview of

psychotherapeutic methods, differentiating socially verified from alternative approaches,

risk of quacks esotericism and „new age“, explanations on the application of medication

when necessary.

15. Personality disorders: A concise overview of the 10 personality disorders that occur at the

onset of the adult life. General prerequisites for diagnosing personality disorders, criteria

for certain disorders, prevalence and differences with respect to gender, the hereditary

factor and the environment, notes on psychotherapeutic procedures.


The teaching will be carried out in form of lectures and seminars. Students are required to attend

classes, prepare for each seminar topic by reading the required headings and to prepare one term

paper. The examination is oral.

PREREQUISITES: None

READING LIST:

1. Američka psihijatrijska udruga, Dijagnostički i statistički priručnik za duševne poremećaje, 4.

izdanje - međunarodna verzija, Naklada Slap, Jastrebarsko, 1996.

2. Višeosna klasifikacija psihijatrijskih poremećaja u djece i adolescenata, MKB-10, Naklada

Slap, Jastrebarsko, 2003.

4. Ch. Wenar, Razvojna psihopatologija i psihijatrija, Naklada Slap, Jastrebarsko, 2003.

ADDITIONAL READING:

1. N. Ambrosi - Randić, Razvoj poremećaja hranjenja, Naklada Slap, Jastrebarsko, 2004.

2. A. Brajša, Dijete i obitelj, Emocionalni i socijalni razvoj, Naklada Slap, Jastrebarsko, 2003.

3. M. Duran, Dijete i igra, 3. izdanje, Naklada Slap, Jastrebarsko, 2003.

4. J. E. Edgerton, R. J. Campbell (eds.), Psihijatrijski rječnik, 2. hrvatsko izdanje, Naklada Slap,

Jastrebarsko, 2002.

5. F. P. Glascoe, Suradnja s roditeljima. Upotreba roditeljske procjene dječjeg razvojnog

statusa u otkrivanju razvojnih problema i problema ponašanja te bavljenja tim problemima,

Naklada Slap, Jastrebarsko, 2002.

6. G. Keresteš, Dječje agresivno i prosocijalno ponašanje u kontekstu rata, Naklada Slap,

Jastrebarsko, 2002.

7. D. Kocijan - Hercigonja, G. Buljan - Flander, D. Vučković, Hiperaktivno dijete. Uznemireni

roditelji i odgajatelji, 4. izdanje, Naklada Slap, Jastrebarsko, 2004.

8. K. Lacković - Grgin, Stres u djece i adolescenata, Naklada Slap, Jastrebarsko, 2000.

9. R. S. Lazarus, S. Folkman, Stres, procjena i suočavanje, Naklada Slap, Jastrebarsko, 2004.

10. N. Pećnik, Međugeneracijski prijenos zlostavljanja djece, Naklada Slap, Jastrebarsko, 2003.

11. P. Zarevski, M. Mamula, Pobijedite sramežljivost, a djecu cijepite protiv nje, 2. izdanje,

123

Naklada Slap, Jastrebarsko, 1998.

124

COURSE TITLE: Research methods in education

PROPOSED BY:

Nikola Pastuović, PhD, Professor, Department of The Pedagogical, Psychological and Didactic

Education of Subject Area Teachers, Teacher Education Academy, University of Zagreb

Siniša Opić, PhD, Assistant professor, Faculty of Teacher Education, University of Zagreb

PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer

Tutorials 0 -

Seminars 0 -

ECTS CREDITS: 3


The aim of the course is to develope the following competences: understanding the principles of a

scientific approach to educational research, knowledge of the phases of scientific research,

differentiating and knowledge of advantages and disadvantages of qualitative and quantitative

research, ability to participate in conducting scientific educational research and the ability for

applying research results for the purpose of improving the educational practice.


understand criteria for determining atypical psychological and behavioral functioning and

recognize deviations from normal psychological development in childhood and

adolescence;

differentiate and describe the main characteristic of the most common psychological and

developmental disorders in childhood and adolescence;

explain the role of different factors contributing to onset of psychological and

developmental disorders;

understand and apply the main principles of interventions for adapting instruction to meet

the needs of students with disabilities;

identify the adjustment problems of students with disabilities in real-life situations;

understand the need for providing support for to the students with psychological and

developmental disorders in collaboration with the school expert team.

125

By its content, teching and evaluation methods, the course contributes to the following learning



1. Characteristics of scientific educational research. The purpose of scientific research:

description, explanation, prediction and control of the researched problem. Advancement

of education through research.

2. Phases of educational research. Selecting and defining the research problem, choice of

research design, sample selection and measurement, testing research hypotheses,

publishing research results.

3. Descriptive and inferential statistics. The difference between the correlation method and

causal-comparative methods. Bivariate and multivariate statistics. How to interpret a

correlation?

4. Qualitative educational research. Methods of qualitative research. Advantages and

disadvantages of the qualitative and quantitative approach. Validity of qualitative methods.

5. Evaluation research in education. Quantitative and qualitative models of evaluation.

Formative and summative evaluation. Evaluation and educational needs analysis.

6. Research and the development of education. R & DE as strategies for improving

educational practice R & DE as a process of development and validation of educational

„products“ (programmes, methods, textbooks, educational techniques, etc.). The

relationship between educational research and the R & DE processes.

7. Ethical principles in educational research. Voluntarism, confidentiality and data protection,

areas where subject “cheating” is allowed, desensitising of subjects. Legal limitations.


The course consists of 30 hours of lectures and independent studying of selected readings. Classes

are carried out as lectures, discussions in seminars and by studying the selected reading.

Knowledge is assessed throughout the semester by means of written assignments and through

discussions with the students in seminars. The exam is oral.

PREREQUISITES: Didactics 2 - Teaching and educational system

READING LIST:

1. Američko udruženje za istraživanje u obrazovanju, Američko udruženje psihologa, Nacionalno

vijeće za mjerenje u obrazovanju, Standardi za pedagoško i psihološko testiranje, Educa,

Zagreb, 1992.

2. V. Mužić, Uvod u metodologiju istraživanja odgoja i obrazovanja, Educa, 1999.

3. B. Petz, Osnovne statističke metode za nematematičare, Liber, Zagreb, 1985.

ADDITIONAL READING:

1. W. R. Borg, M. D. Gall, Educational Research, Longman Scientific Publishers, 1989.

2. N. Gronlund, Measurement and Evaluation in Teaching, Macmillan Publishing Company,

Collier Macmillan Publishers, 1985.

126

COURSE TITLE: Set theory

PROPOSED BY:

Mladen Vuković, PhD, Associate Professor, Faculty of Science, Department of Mathematics,


PROGRAMME:

BSc in Mathematics




TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 Lecturer


Seminars 0 -

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: The course is divided into two parts. Naive set theory is

studied in the first part. The notions of countable and uncountable sets are considered and the

notions related to ordered sets are defined. The main aim of the first part is to motivate

introduction of axioms. In the second part is considered Zermelo-Fraenkel set theory. The notions

of ordinal and cardinal numbers are defined, and the enumeration theorem is proved. At the end

the axiom of choice is studied.


define notions of finite, infinite, countable and uncountable sets;

determine cardinality of some subsets of the set of reals;

prove that the set of reals is uncountable;

formulate and apply Cantor, Schroeder, Bernstein theorem;

formulate and apply ordering characterization theorems of the sets Q and R;

define the sets of numbers (N, Z, Q and R);

calculate with ordinal numbers;

formulate axiom of choice and apply Zorn lemma.



127


Naïve set theory

1. Introduction. History of set theory. Axiom of extensionality. Russell’s paradox.

Axiom of choice. Idea of cumulative hierarchy. Axiom of empty set and pairing

axiom. Ordered pair. Definitions of relation and function. Union axiom and powerset

axiom.

2. Equipotent sets. Finite and infinite sets. Countable sets.

3. Countable union of countable sets is countable set (application of axiom of choice). Set

of rational numbers is countable. Every infinite set consists a countable subset

(application of axiom of choice).

4. Uncountable sets. Set of reals is uncountable. Cardinal numbers (naive approach).

Basic Cantor theorem. Arithmetic of cardinal numbers.

5. Knaster - Tarski fixed point theorem. Banach’s lemma. Cantor – Bernstein - Schröder

theorem.

6. Binary relations: reflexive, ireflexive, symmetric, antisymmetric and transitive.

Equivalence relations. Partial order sets. Comparable elements. Chain, maximum and

minimum, the greatest and the least elements, upper bound, supremum and infimum.

Linear order sets. Order-preserving functions. Isomorphism.

7. Dense partial order sets. Cuts. Dedekind-style continuity. Theorems on ordered

characteristics of sets Q i R.

8. Wellorder sets. Basics properties of wellorder sets. Principle of transfinite induction.

Axiom of foundation.

Axiomatic set theory

1. Set of natural numbers: inductive set, natural numbers, axiom of infinity, axiom

schema of separation. Axiom of induction. Transitive sets. Basics properties. Every

natural number is transitive set. Dedekind recursion theorem.

2. The sets of numbers: integers, rational and real numbers. Von Neumann definition of

ordinals.

3. Basics properties of ordinal numbers. The enumeration theorem.

4. The ordering of ordinal numbers. Successor and limit ordinal. Recursion theorem. The

addition and multiplication of ordinal numbers. Theorem on subtraction.

5. Ordinal exponentiation. Normal form theorem for ordinal numbers. Cantor normal

form. Goodstein theorem.

6. Cardinal numbers. Arithmetic of cardinal numbers. König’s lemma. Alephs. Axiom

schema of replacement.

7. Axiom of choice. Cartesian product. Russell’s axiom. Zorn’s lemma. Hausdorff’s

maximal principle. Teichmüller - Tukey lemma. Zermelo’s theorem. Hartog’s

theorem. Proofs of simple equivalences. Banach - Tarski paradox.


128






successful elaboration of homework, grades for mid-term exams and final examination grade

PREREQUISITES: None

READING LIST:

1. W. Just, M. Weese, Discovering Modern Set Theory 1, AMS, 1996.

2. P. Papić, Uvod u teoriju skupova, HMD, Zagreb, 2000.

ADDITIONAL READING:

1. K. J. Devlin, Fundamentals of Contemporary Set Theory, Springer-Verlag, 1980.

2. F. R. Drake, D. Singh, Intermediate Set Theory, John Wiley & Sons, 1996.

3. J. M. Henle, An Outline of Set Theory, Springer, 1986.

4. T. Jech, Set Theory, Academic Press, 1997.

5. J.-L. Krivine, Aksiomatička teorija skupova, Školska knjiga, Zagreb, 1978.

6. M. D. Potter, Mengentheorie, Spektrum Akademischer Verlag, 1990.

7. J. Shoenfield, Axioms of Set Theory, Handbook of Math.Logic, J. Barwise (ed.), North-

Holland, 1985.

129

COURSE TITLE: Social aspects of information and communication technologies

PROPOSED BY:



Mladen Mauher, PhD, High School Professor, Polytechnics of Zagreb, Zagreb

PROGRAMME:



YEAR OF STUDY: second (elective)


TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 1

lecturer*

* Since it covers a wide range of topics, it is

suggested that this course be taught in part usinf

presentations by invited guest speakers - field

experts for some specific professional issues

Tutorials 0 -

Seminars 2 lecturer

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: This course aims to introduce students to legal, ethical,

business, professional and other social aspects of information and communication technology

(ICT) and professional software engineering practice.


critically evaluate the structure and the dynamics of interactions of society developments

and ICT;

identify tendencies and horizons of ICT developments and its interactions with societal and

individual challanges;

analyze ICT as primary driver of the business, administrative, public and professionally-

ethical change;

recognise appearances of the new and emerging ICT infrastructure models;

explore and present the phenomenon of ICT developments in the given domain.


outcomes at the level of the study programme: I-3, II-4, IV.


130

The following topics will be considered:

1. The Software Engineering Profession. The structure of the software engineering profession,

both in Croatia and abroad. Professional organisations and their importance. The most

significant international professional organisations (ACM and IEEE).

2. Software companies. Organisation and structure. ICT management. Project and team

management. Feasibility study of ICT projects. Manager communication.

3. E-commerce. Information economy. Foundations and basic aspects of e - commerce.

4. E-government. Contexts for governing in the information age. Re-engineering the government

machine: new technologies and organizational change.

5. ICT ethics. Professional ethics. Professional codes of conduct and codes of practice. Codes of

ethics of professional associations (ACM Software Engineering Code of Ethics and

Professional Practice). Ethics and the Internet. Ethics On-line.

6. Intellectual property related to ICT. Computers and intellectual property. The law relating to

different types of intellectual property (confidential information, copyright, data bases, e-

publishing, information society, trade marks, patents) and the relevance of each type to the

software industry. International implications.

7. Computer contracts. Software accreditation, certification and licensing. E-signature.

8. Computer abuse, misuse and computer criminal. The history of computer crime. The nature

and scope of computer crime (hacking, computer system attacks, communication interception,

fraud, forgery, denial of service attack, software, audio and audiovisual piracy, copyright

infringement, trademarks violations, theft of computer source code, etc.). Prevention. Data

protection.

9. Health and safety at work. The notion of ICT ergonomics. Standards: ISO 9241, EN 29241.

Hardware ergonomics. Workplace ergonomics. Software ergonomics. Human - computer

interaction (HCI). Principles of HCI. Human - computer interfaces. Building a graphical user

interface (GUI). Health risks of using ICT.

10. Other relevant issues related to social aspects of ICT. Topics proposed by the lecturer or

students.

Seminars consist of student individual oral presentations (supported by ICT, 45 minutes per person

in length) of assigned topics, followed up by a group discussion and related case studies.


Students are expected to follow lectures and seminars regularly, with an active participation in

group disscusions and case studies. Each student will be assigned to write an essay focused on a

selected topic related to the course syllabus and prepare an oral presentation of the main findings

of this independent research.

A student's grade will be determined according to the following distribution: written essay (40%),

its oral presentation (20%), and final oral exam (40%) . To achieve a pass students should gain a

minimum of 50% in each of the mentioned three elements.


READING LIST:

1. F. Bott, A. Coleman, J. Eaton, and D. Rowland, Professional Issues in Software Engineering,

131

3rd edition, Taylor & Francis, 2000.

ADDITIONAL READING:

1. R. Ayres, Essence of Professional Issues in Computing, Prentice Hall, 1999.

2. D. G. Johnson, Computer Ethics, Prentice Hall, 2003.

3. D. Bainbridge, Introduction to Computer Law, Longman Scientific Publisher, 2004.

4. Ž. Panian, Izazovi elektroničkog poslovanja, Narodne novine, Zagreb, 2002.

5. D. Amor, The E-Bussiness (R)evolution, Hewlett-Packard Professional Books/Prentice Hall,

2000.

6. C. Bellamy, J. A. Taylor, Governing in the Information Age, Open University Press, 1998.

7. C. J. Alexander, L. A. Pal, Digitalna demokracija, politike i politika u umreženom svijetu,

Panliber, Zagreb, 2001.

8. ***, eEurope – An Information Society for All,

http://www.europa.eu.int/comm/information_society/europe/index_en.htm

9. ***, Strategija razvitka Republike Hrvatske – Hrvatska u 21. stoljeću: Strategija razvoja

informacijske i komunikacijske tehnologije, http://www.hrvatska21.hr

10. D. Parker, Fighting Computer Crime – A New Framework for Protecting Information, John

Wiley & Sons, 1998.

11. D. Dragičević, Kompjutorski kriminalitet i informacijski sustavi, Informator, Zagreb, 1999.

12. ACM/IEEE-CS Joint Task Force on Software Engineering Ethics and Professional Practices,

Software Engineering Code of Ethics and Professional Practice (Version 5.2),

http://www.acm.org/serving/se/code.htm, September 1998.

132

COURSE TITLE: Students’ competitions in mathematics

PROPOSED BY:

Matija Kazalicki, PhD, assistant professor, Faculty of Science, Department of Mathematics,


Vjekoslav Kovač, PhD, assistant professor, Faculty of Science, Department of Mathematics,


PROGRAMME: All undergraduate and graduate programs at Department of Mathematics

YEAR OF STUDY: All (facultative course)

SEMESTER: Spring

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer

Tutorials 0 -

Seminars 0 -

ECTS CREDITS: 3

COURSE AIMS AND OBJECTIVES: The main aim of the course is preparing students for

international competitions in mathematics. In addition to reviewing the undergraduate material, the

participants will gain familiarity with a variety of techniques, ideas and certain tricks for solving

original mathematical problems. Other objectives of the course are: promoting the general

mathematical culture to interested students, introducing better students to the scientific research,

and encouraging students for self-guided study and practice.


work on solving competition-type problems individually and in a team;

independently analyse the official (published) solutions to the problems posed at the

competitions “Vojtěch Jarník IMC" and "International Mathematics Competition for

University Students" over the previous years;

write down the solution to a given mathematical problem that satisfies the criteria for the

maximal number of points on the previously mentioned student competitions, assuming

that he/she knows the idea of the solution;

apply the basic results from the fields of algebra, analysis, number theory, and

combinatorics to the solving of competition-type problems;

relate parts of mathematics that are learned as separate theories throughout the studies.



COURSE DESCRIPTION AND SYLLABUS: The actual topics vary from year to year,

133

depending on the structure and interests of the audience and the actuality of the topics themselves.

1. The minimal polynomial and other tricks from linear algebra

2. Divide and conquer, project and conquer

3. Quadratic residues

4. Algebraic combinatorics

5. Iterative dynamical systems

6. The probabilistic method in combinatorics and graph theory

7. The classification of two-dimensional manifolds

8. Group actions and Burnside's lemma

9. The Riemann zeta function

10. Estimation and the asymptotic calculus in mathematical analysis

11. Elliptic curves

12. Applications of the Fourier analysis on finite abelian groups

13. The Hamel bases and applications

14. Introduction to algebraic topology

15. Ultrametric spaces

16. The Baire category theorem

17. Partially ordered sets

18. Tilings and the Gröbner bases


lectures and take-home assignments will be given in class regularly. Students will be graded

through take-home assignments only. In order to pass the course a student has to fulfil the minimal

requirements for at least half of the assignments.


READING LIST:

1. International Mathematics Competition for University Students, http://www.imc-math.org.uk/

2. Vojtěch Jarník International Mathematical Competition, http://vjimc.osu.cz/

ADDITIONAL READING:

1. R. Gelca, T. Andreescu, Putnam and beyond, Springer, 2007.

2. G. J. Szekely, Contests in Higher Mathematics: Miklos Schweitzer Competitions 1962-1991,

Springer, 1996.

134

COURSE TITLE: Teachers education in Europe

PROPOSED BY:

Vlatka Domović, PhD, Assistant Professor, Department of The Pedagogical, Psychological and

Didactic Education of Subject Area Teachers, Teacher Education Academy, University of Zagreb

PROGRAMME:



MSc in Mathematics and Physic Education


SEMESTER: second (fall)

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 1 Lecturer

Tutorials 0 -

Seminars 1 Lecturer

ECTS CREDITS: 3


Students will become acquainted with structure of the educational system and the system of

teacher education in Europe and the processes and problems of harmonising the Croatian system

of teacher education with the European one. Students will be able to conduct contrastive analyses

and understand main tendencies in the development of teacher education systems.



1. The system of teacher education – lifelong teacher education. Pre – service teacher

education, probation, in-service, continuing professional development. Models of initial

teacher education for primary, compulsory and secondary education. Institutions and

programmes for teacher education. Professionalization.

2. Educational systems in the European Union member countries (e.g. Scandinavian

countries, Great Britain, Germany, Austria, France, Slovenia) and countries in transition.

The educational system in the Republic of Croatia. A comparison with the educational

systems of other European countries.

3. Teacher education systems in Europe (e.g. Scandinavian countries, Great Britain,

Germany, Austria, France, Slovenia) and countries in transition - reforms and trends in

135

development.

4. The teacher education system in the Republic of Croatia (pre-school teachers, primary

school and secondary school teachers, probation and continuing professional

development). Comparison with other European countries.

5. Goals in teacher education – new key teacher competences (analysis of the European

Union documents on teacher education).

6. Students' achievements – international research (e.g. Programme for International Student

Assessment PISA – 2000. and 2003.) and the role of the teacher.


Classes will be conducted as lectures and seminars. Students are required to attend lessons and

prepare for each seminar topic by reading the required literature, and to prepare one term paper.

The exam is oral.

PREREQUISITES: None

READING LIST:

1. K. Mazurek, M. A. Winzer, C. Majorek, Education in a global society: a comparative

perspective, Allyn and Bacon, 1999. (selected chapters)

2. V. Domović, M. Matijević (eds.), Changes in Education of Teachers in Europe, Metodika

(special issue), University of Zagreb, Teacher Education Academy, Zagreb, 2002. (selected

chapters)

3. Structures of the education, initial training and adult education systems in Europe, 2003.

http://www.eurydice.org.

4. F. Buchberger, B. P. Campos, D. Kallos, J. Stephenson (eds.), Green Paper on Teacher

Education in Europe, 2000.

5. http://www.ibe.unesco.org/Regional/SEE/SEEpdf/Buchberger.pdf

6. Implementation of Education and Training 2010 - Work Programme. Working group

Improving Education of Teachers and Trainers – Progress Report, 2003.

http://europa.eu.int/comm/education/policies/2010/doc/working-group-report en.pdf

7. Međunarodna standardna klasifikacija obrazovanja - ISCED 1997, Državni zavod za

statistiku, Zagreb.

8. Prema društvu koje uči: poučavanje i učenje - Bijeli dokument o obrazovanju, Educa, Zagreb,

1995.

9. V. Domović, Z. Godler, Suvremeno obrazovanje učitelja u Europi i/ili moguća budućnost

obrazovanja učitelja u Republici Hrvatskoj, Metodika, 6 (4) (2003), 49 – 60.

ADDITIONAL READING:

1. E. Thomas, Teacher Education – Dilemmas and Prospects, Kogan Page, 2002.

2. R. Biermann (ed.), Europe at Schools in South Eastern Europe – Country Profiles, Zentrum für

Europäische Integrationsforschung. Rheinishe Friedrich – Wilhelms – Universität Bonn, 2003.

3. V. Luburić (ed.), Osposobljavanje strukovnih nastavnika i stručnih učitelja – istraživački

projekt, Nacionalni opservatorij za strukovno obrazovanje i osposobljavanje, Zagreb, 2002.

4. The teaching profession in Europe: Profile, trends and concerns, Report 1: Initial training and

136

transition to working life of teachers in general lower secondary education, 2002.

http://www.eurydice.org

http://www.eurydice.org/

137

COURSE TITLE: Using technology in mathematics teaching

PROPOSED BY:



Maja Starčević, PhD, assistant professor, Faculty of Science, Department of Mathematics,


PROGRAMME:






TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 1 Lecturer


Seminars 0

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: The goal of the course is to educate students / future

teachers how to apply Information and communication technologies (ICT) in preparing and

delivering their forthcoming lectures, as well as in their own growth and research.


independently plan mathematics lessons being held using computers;

choose lessons in which using computers makes the teaching more qualitative;

combine the traditional way of teaching with a modern approach;

use various computer tools in preparing the lessons, as well as in giving the lessons;

organize the lessons in accordance with technical capabilities of the classrooms;

choose adequate teaching means and programme support and create his own ones.


outcomes at the level of the study programme: I-1, I-2, II-1, II-3, II-4, II-5, III, IV.


I Concepts of ICT applications in mathematics education

1. Introduction. Standards of modern mathematics education. Organization of teaching

mathematics with regard to available equipment (classrooms equipped with calculators,

138

LCD projectors, one or more computers ... ).

2. Principles, planning and presentation of lectures. Choosing topics and problems in

mathematics, convenient to be explored and presented using ICT.

3. Software tools. Types of tools that can be used in teaching and their features: general tools

(spreadsheets, presentation software), specialized tools (graphical calculators, dynamic

geometry programmes, professional mathematical programme systems). Multimedia.

Advanced ICT applications (digital tutorials, distance education).

II Mathematical topics presented using ICT

1. Elementary functions. Analysis of graphs. Visualizing solutions of equations and

inequations.

2. Differential and integral calculus. Giving motivation and illustration of basic concepts in

differential and integral calculus.

3. Visualization of proofs in geometry. Performing proofs (Pythagora’s theorem, Euler’s line,

Nine-point circle, etc.) using animations.

4. Geometry constructions. Euclidean constructions. Dependence on given elements.

Animation of constructions. Geometric place. Second order curves. Solving challenging

problems using computers.

5. Vector. Vector definition and vectors operations using computers.

6. Plane transformations. Isometries (rotation, translation, reflection), homothety, similarity.

7. Stereometry. Intersections of solids (polyhedra, oval solids) with lines, planes and other

solids. Conic curves as intersections of cones with planes.

8. Analytical geometry in plane and space. Drawing curves and surfaces.

9. Polar coordinates. Drawing curves and surfaces in polar coordinate system.

10. Data analysis. Drawing data in a suitable way. Elements of probability and statistics.

11. Research and experimenting using computers. Solving various problems in mathematics

using ICT.

TEACHING AND ASSESSMENT METHODS: Students should attend 70% of all lectures and

tutorials, pass all mid-term exams and submit results of all take-home assignments and projects.

PREREQUISITES: Methods in teaching mathematics 1

READING LIST:

1. A. J. Oldknow, R. Taylor, Teaching Mathematics with ICT, Continuum, London, 2002.

ADDITIONAL READING:

1. M. Serra, Discovering Geometry: An Inductive Approach, Quizzes, Tests and Exams, Key


2. M. Serra, Discovering Geometry: An Inductive Approach, Teacher's Resource Book, Key


3. J. Murdock, E. Kamischke, E. Kamischke, Discovering Algebra: An Investigative Approach,

139

Teaching and Worksheet Masters, Key Curriculum Press, 2000.

4. J. Murdock, E. Kamischke, E. Kamischke, Advanced Algebra Through Data Exploration,

Constructive Assessment in Maths: Practical Steps for Classroom Teachers, Key Curriculum

Press, 2001.

5. T. D. Gray, J. Glynn, Exploring Mathematics with Mathematica, Addison-Wesley, New

York, 1991.

6. E.Don, Schaum’s Outline of Theory and Problems of Mathematica, McGraw-Hill, New York,

2001.

7. User manuals for software products being used in tutorials.

140

COURSE TITLE: Vector spaces

PROPOSED BY:

Damir Bakić, PhD, Professor, Faculty of Science, Department of Mathematics, University of

Zagreb

Goran Muić, PhD, Professor, Faculty of Science, Department of Mathematics, University of

Zagreb

Ozren Perše, PhD, Assistant Professor, Faculty of Science, Department of Mathematics,


Mirko Primc, PhD, Professor, Faculty of Science, Department of Mathematics, University of

Zagreb

PROGRAMME:

BSc in Mathematics


MSc in Mathematics and Computer ScienceEducation


SEMESTER: first (spring)

TYPES OF

INSTRUCTION

CONTACT HRS


Lectures 2 lecturer


Seminars 0

ECTS CREDITS: 5

COURSE AIMS AND OBJECTIVES: To explain basic results about linear operators on finite

dimensional vector spaces (Jordan form, functional calculus, operators on inner product spaces).



1. Linear operators on finite dimensional spaces

2. Dual spaces

3. Spectrum, characteristic and minimal polynomial

4. Nilpotent operators

5. Fitting decomposition

6. Jordan form

141

7. Functional calculus

8. Resolvent

9. Geometry of inner product spaces

10. The adjoint operator

11. Normal operators

12. Normal operators on real inner product spaces

13. Selfadjoint operators, Positive operators and polar decomposition

TEACHING AND ASSESSMENT METHODS: There will be 3-4 20-minute quizes and at the

end of the course written and oral exams.

PREREQUISITES: None

READING LIST:

1. S. Kurepa, Konačnodimenzionalni vektorski prostori i primjene, Liber, Zagreb, 1979

ADDITIONAL READING:

1. P.R.Halmos, Finite dimensional vector spaces, Van Nostrand, 1958

142

3.3. Course structure, rhythm of studying and student's obligations

Duration of the Graduate University Programme in Mathematics and Computer Science

Education is two academic years, i.e. four semesters, where each semester has 15 teaching weeks.

For each year of studies, classes are organized in semesters and all subjects are one semester in

length. Student teaching load in each of the first three semesters varies from 20 to 22 contact hours

per week. In the final fourth semester the teaching load is reduced to 18 contact hours per week,

while the remaining time is intended for completion of the master’s thesis, i.e. for the necessary

individual work and communication with the mentor. The practical class work in elementary and

in secondary school, is also counted as 4 hours of teaching load per week during the whole second

year.

The goal of this graduate programme is to give the students all the professional, didactical,

pedagogical and psychological competences necessary for successful realization of all teaching

programmes in mathematics and information and communication technologies at elementary and

in secondary school level. According to this, the core of the programme is formed by subjects and

methods closely related to the educational system and teaching of mathematics in secondary

schools (ISCED 2 and ISCD 3 levels). Primarily this is the compulsory core of subjects aimed at

introducing the didactics of mathematics (Didactics of Mathematics 1, 2, 3, 4, Using Computers in

Teaching Mathematics, Methods of teaching computer science 1, 2), and educational system and

general didactics (Didactics 1 — Curriculum Approach, Didactics 2 — Teaching and Educational

System), as well as practical implementation through Mathematics and Computer Science teaching

practice in middle and secondary school. The rest of the fixed part of the program are computer

courses: Computer architecture, Computer networks and Operating systems. These courses require

expert knowledge and a certain computer competence associated with the organization and

effective planning computer science lessons, and equipping and maintenance of computer

classrooms in elementary and secondary schools.

The variable part of the programme consists of one elective course in psychology and two in

pedagogy, as well as one elective mathematical module and two elective computer science

courses. Each elective mathematical module consists of two subjects chosen from the respective

lists, introducing students to some details of classical and recent results in selected basic

mathematical areas. The students have a choice of three standard elective modules (Algebra and

fundamentals of mathematics, Analysis, Geometry and topology). Since the same standard elective

modules appear also in the third year of the Undergraduate University Programme in Mathematics

Education (from which students have to choose two), the students have to choose one of the two

modules they have not taken as undergraduates. Two optional computer courses at the second year

of the study (one in fall and one in spring semester) provide advanced theoretical and

computational concepts and students are introduced to selected areas of computer science

(theoretical computer science, software engineering, information systems, etc.).

Finally, during the fourth semester, students prepare their individual written master's thesis

in which they individually elaborate, from the professional and didactical aspects, a mathematical

or computer science entity which can be applied when teaching mathematics in elementary or

secondary school. It is foreseen that a master’s thesis will be completed during the fourth semester.

The studies are completed by defending the master's thesis, final examination consisting of oral

presentation and defence of the thesis and questions concerning the general mathematical,

computer science and pedagogical-psychological-didactical knowledge and areas of student

master’s thesis in particular.

143

Graduate University Programme in Mathematics and Computer Science Education totals 120

ECTS credits, i.e. for each academic year 60 ECTS credits or for each semester 30 ECTS credits.

Each course earns an appropriate number of ECTS credits while the master's thesis earns 7 ECTS

credits. Required mathematics courses cover for 84 ECTS credits (70%), and elective courses

cover for 29 ECTS credits (24%). Since the students are free to choose the advisor and the topic of

their master’s thesis, the elective contents total 36 ECTS credits, i.e. 30% of the total ECTS

credits. On the other hand, mathematical courses earn 51 ECTS credits (42.5%), computer science

courses earn 45 ECTS credits (37.5%) and the pedagogical courses earn 17 ECTS credits (14.2%).

The most important, didactical component earns 78 ECTS credits (65%) in the whole programme.

The value of 1 ECTS credit has been determined as 25 active working hours of a student in

fulfilling his/her obligations. This means that for mastering a course with 5 ECTS credits and 3

contact hours during one semester, an average student needs 125255 working hours. Out of

that, 45153 working hours refers to class attendance of the particular course (lectures and

tutorials), 6 hours for mid-term exams, presenting the seminar topic or case study, or final

examination, and the remaining 74 hours (i.e. the total of 9 working days) for individual work of

the student and individual contacts with teachers and assistants on the particular course.

The study is organised according to semesters, i.e. the students enrol in a single term (either

winter or summer term). In doing so, they also register for all other student responsibilities for the

semester as determined by the programme of study in accordance with the Regulations of

Undergraduate and Graduate Studies at the Faculty of Science, University of Zagreb.

Requirements for enrolling in a particular course (the so-called precursors of a course), the

responsibilities and obligations of students as well as manners of taking exams are given in the

Execution Plan. As a rule, students are required to attend classes, to make homework assignments

and/or seminars and to take mid-term and final exams. The following minimum requirements for

obtaining signature should be taken into account: the presence of student in class at least 70

percent at the lectures and 70 percent during exercises, to deal with homework (at least 70 percent

by default) and have a passing grade on the mid-term examinations.

3.4. List of elective courses from other studies

The following courses from the Graduate University Programme in Mathematics and

Computer Science Education are common to other programmes:

Methods of teaching mathematics 1, 2, 3, 4, Using Technology in Mathematics Teaching,

Mathematics Teaching Practice in Middle School, Mathematics Teaching Practice in

Secondary School, Educational psychology - theories of learning and teaching mathematics

— common to: Graduate University Programme in Mathematics Education, Integrated

Undergraduate and Graduate University Programme in Mathematics and Physics Education

Didactics 1 – Curriculum Approach, Didactics 2 – Teaching and Educational System,

Evaluation in Education, Psychopathology in childhood and adolescence, Teachers education

in Europe, Research methods in education, Antisocial behavior, Intelligent systems in

teaching — common to other education studies at University of Zagreb;

Computer architecture, Computer networks, Operating systems, Vector spaces, Algebraic

structures, Metric spaces, Complex analysis, Euclidean spaces, Models of geometry, Design

and analysis of algorithms, Computer graphics, Combinatorics, Cryptography and network

security, Multimedia systems, Social aspects of information and communication

technologies, Object-oriented programming (C++), Mathematical software, Advanced

databases, Machine learning, Natural language processing — common to at least one of the

following programmes: Undergraduate University Programme in Mathematics,

Undergraduate University Programme in Mathematics Education, Integrated Undergraduate

144

and Graduate University Programme in Mathematics and Physics Education, Graduate

University Programme in Theoretical Mathematics, Graduate University Programme in

Applied Mathematics, Graduate University Programme in Mathematical Statistics, Graduate

University Programme in Financial and Business Mathematics, Graduate University

Programme in Computer Science and Mathematics, Graduate University Programme in

Mathematics Education.

3.5. List of courses to be taken in foreign language

All courses foreseen in the programme may be taken in English.

3.6. Criteria and conditions for transfer of ECTS credits from other studies

The transfer of ECTS credits from other studies at the University of Zagreb, as well as

from other universities in the Republic of Croatia and abroad, is envisaged. Transfer of credits is

based on comparison of study programmes. The Department of Mathematics appoints an ECTS

coordinator and a commission for credits transfer approval.

3.7. Completion of studies

The studies at the graduate programme are finished upon successful completion of all study

obligations foreseen by the programme. These obligations are: successful passing of examinations

from all required and elective courses as foreseen by the programme, completion of master’s thesis

and successful passing of the final exam. In other words, the studies are completed upon

acquisition of 120 ECTS credits in compliance with the programme. The final examination

consists of oral presentation and defence of the thesis and questions concerning the general

mathematical, computer science and pedagogical-psychological-didactical knowledge and areas of

the thesis in particular.

3.8. Requirements for continuation of interrupted studies

Students who have interrupted their studies are allowed to continue their studies in

compliance with the actual programme and the recognition of achieved ECTS credits before the

interruption. Students who have lost the right to study at Graduate University Programme in

Mathematics and Computer Science Education at the Faculty of Science, Department of

Mathematics, University of Zagreb are not allowed to continue their studies. They may continue

the studies at other graduate programmes offered by the Department of Mathematics and their

achieved ECTS credits will be recognised after comparison of study programmes.

145

4. CONDITIONS FOR REALIZATION OF THE PROGRAMME

4.1. Place of realization of the study programme

All teaching activities of the Graduate University Programme in Mathematics and Computer

Science Education takes place at work premises (classic, multimedia and computer classrooms,

library, and reading-room) of the Faculty of Science, Department of Mathematics, University of

Zagreb, Bijenička cesta 30, Zagreb, and at work premises (classic and computer classrooms) in

primary and secondary schools in the City of Zagreb, selected for conduction of teaching practice.

4.2. Information on premises and equipment envisioned for studies

The building of the Department of Mathematics at 30 Bijenička cesta, Zagreb, with the total

area of 8400 m2, was constructed in 1991, and extended in 2013. There are 21 classrooms, one

seating 200 persons, 11 classrooms for 70-90 persons, while the others have 30-50 seats. Seven

largest rooms are lecture theatres, equipped with multimedia equipment (sound system, LCD

projectors and computers), while other premises are equipped with LCD projectors, screens and

computers.

Student computers are distributed in 6 computer classrooms with the total of 90 working

places. Also, at the Department of Mathematics there is a modern teleconference room with a

“smart board” and HD equipment for distance online learning and work. In the computing centre

there are 19 servers for various purposes out of which 2 Linux servers and 2 Windows servers are

available to students. All student computers are connected to 100 Mbit local network with

permanent 1 Gbit connection to CARNet, and Internet. All necessary software is installed on

computers, from operating systems (MS Windows, Linux) through programming languages (C,

C++, Java), data base systems (MS SQL Server, MySQL), office packages (MS Office,

OpenOffice), to special mathematical tools (LaTeX, MATLAB, SAS Statistical Software, StatSoft

Statistica, WinEdit). The software included in MSDN AA subscription is freely available to

students.

Central library is also available and open to students, with the largest collection of literature

on mathematics in Croatia as well as student reading-room with 70 seats and connections to

computer network.

Department of Mathematics is integrated into the Croatian Higher Education Information

System (ISVU) which means that the entire studying process is supported by information

technology, so that students have the possibility to perform many of their activities online.

4.3. Teachers and collaborators to participate in execution of studies

The proposed Graduate University Programme in Mathematics and Computer Science

Education has been realised by teachers and assistants from the Faculty of Science, Department of

Mathematics, University of Zagreb and external collaborates for courses in pedagogy and

psychology, some computer science courses, and for taking care of Mathematics Teaching Practice

in Middle and Secondary School.

For these subjects a permanent collaboration will be established with the following

institutions, members of University of Zagreb: Faculty of Teacher Education — Department of

The Pedagogical, Psychological and Didactic Education of Subject Area Teachers (Didactics 1 –

Curriculum Approach, Didactics 2 – Teaching and Educational System and elective pedagogical

and psychological courses), Institute for social research - Zagreb, Centre for educational research

146

and development (Evaluation in education), Faculty of Philosophy (Educational psychology -

theories of learning and teaching) and Faculty of Electrical Engineering and Computing

(Computer Architecture, Operating Systems, Computer graphics). The Mathematics Teaching

Practice in Middle and Secondary School is organized in collaboration with a number of

elementary and secondary schools in Zagreb, and will be carried out by experienced practising

teachers of mathematics and computer science in those schools.

The precise teachers course assignments will be made according to realization plan for

each academic year. Since it is planned to enrol not more than 60 students in each year, the

compulsory course lectures will be performed for the whole group, for tutorials and seminars the

students will be divided into two groups, and for practical didactic class work into twelve groups

of 5 students. This principle applies to the teaching of elective courses with the exception of

special cases when more than 60 students enrol a particular subject (i.e. courses that are common

to a number of graduate and undergraduate studies, which are performed by visiting professors and

taught for only one academic year, and the like). In such cases, according to the needs and

possibilities (human and physical) additional round of exercises is formed.

Additional shifts for lectures and tutorials, i.e. the improvement of the teaching quality by

reducing the number of students in a particular group is brought in line with the growth dynamics

of personnel and space potentials of the Department of Mathematics, as foreseen by 2003

Development Strategic Plan. Our aim is to achieve the standard of maximum of 30 students in one

audio tutorials shift and the maximum of 15 students in one shift of laboratory tutorials (computer

classroom sessions).

Below is the list of teachers who shall participate in the realization of the Graduate

University Programme in Mathematics and Computer Science Education, but without the list of

mentors and schools where students will do their practical classroom work, since these are

reconsidered each academic year (according to capabilities of particular schools).

Faculty of Science, Department of Mathematics:

Dražen Adamović, PhD, professor

Ljiljana Arambašić, PhD, associate professor

Tina Bosner, PhD, assistant professor

Zvonimir Bujanović, PhD, assistant professor

Aleksandra Čižmešija, PhD, professor

Andrej Dujella, PhD, professor

Zrinka Franušić, PhD, assistant professor

Goran Igaly, PhD, senior lecturer

Zvonko Iljazović, PhD, assistant professor

Mladen Jurak¸ PhD, professor

Matija Kazalicki, PhD, assistant professor

Vjekoslav Kovač, PhD, assistant professor

Vedran Krčadinac, PhD, associate professor

Robert Manger¸ PhD, professor

Eduard Marušić – Paloka, PhD, professor

Željka Milin Šipuš, PhD, associate professor

Goran Muić, PhD, professor

Ivica Nakić, PhD, assistant professor

Goranka Nogo, PhD, assistant professor

Ozren Perše, PhD, assistant professor

Mirko Polonijo, PhD, professor

147

Mirko Primc, PhD, professor

Saša Singer, PhD, associate professor

Siniša Slijepčević, PhD, professor

Maja Starčević, PhD, assistant professor

Dragutin Svrtan, PhD, professor

Juraj Šiftar, PhD, professor

Hrvoje Šikić, PhD, professor

Boris Širola, PhD, professor

Sanja Varošanec, PhD, professor

Vladimir Volenec, PhD, professor

Marko Vrdoljak, PhD, assistant professor

Mladen Vuković, PhD, associate professor

Faculty of Philosophy:

Vesna Vlahović – Štetić, PhD, professor

Faculty of Electrical Engineering and Computing: Leonardo Jelenković, PhD, assistant professor

Slobodan Ribarić, PhD, professor

Faculty of Teacher Education:

Tajana Ljubin Golub, PhD, associate professor

Dubravka Miljković, PhD, associate professor

Siniša Opić, PhD, assistant professor

Daria Rovan, PhD, assistant professor

Daria Tot, PhD, assistant professor

Ruđer Bošković Institute: Tomislav Šmuc, PhD

Polytechnics of Zagreb

Mladen Mauher, PhD

148

4.4. Data about each of the engaged teachers

NAME: Dražen Adamović, PhD

JOB TITLE: Professor

DATE OF LAST PROMOTION: 19th June 2012

ACADEMIC INSTITUTION: Faculty of Science, Department of Mathematics, University

of Zagreb

E-MAIL: [email protected]

URL: http://www.math.hr/~adamovic/

SHORT CURRICULUM VITAE:

Dražen Adamović was born in Osijek, Croatia on January 13, 1967. He studied

Mathematics at the University of Zagreb where he obtained his B.Sc. and M.Sc. degrees in

Mathematics in 1992 and 1995, respectively. In 1996 he obtained his Ph.D. in Mathematics

at the same university. The title of the thesis was ‘‘Representation of vertex algebras at half-

integer level associated to symplectic affine Lie algebra’’ (adviser prof. dr. Mirko Primc). He

was Teaching Assistant ( 1992-1998), Assistant Professor (1998-2002), Associate Professor

(2002-2007) and at the Department of Mathematics, University of Zagreb. He was promoted

to Professor in 2007. He lectured 10 undergraduate courses and 4 graduate courses.. He was

supervisor of 20 Diploma Thesis, one Master’s Thesis and two PhD dissertation. He is a

organizer of the Algebra Seminar at the Department of Mathematics. From 2003-2006 , he

was the chair of Scientific Section and Scientific Colloquium of Croatian Mathematical

Society. He is editor in Central European Journal of Mathematics (since 2004), Mathematical

Communications (since 2008). Since 2012. he is Managing Edotor of Glasnik Matematicki.

He was a leader of domestic project “Vertex-algebras” and Croatian-Hungarian research

project “Algebraic methods in mathematical physics”. He was organizer of the conferences

Functional Analysis X and Representation Theory XI, XII organized in Dubrovnik 2008.,

2009. and 2011 , and workshopa Algebraic methods in Mathematical Physics organized in

Zagreb in 2011.

His current research interests include vertex operator algebras, conformal field theory,

representation theory and infinite-dimensional Lie algebras and superalgebras. He published

30 research articles about these subjects (23 indexed in CC and SCI). According to SCI, his

papers are cited over 150 times and in some monographs on vertex algebras. He was invited

speaker at more than 20 mathematical conferences in Europa, USA, India and China. He

visited TIFR and Harish-Chandra Institute, in India, and the Erwin-Schroedinger institute in

Austria. He also visited universities Albany (USA), Lund (Sweden) and Budapest (Hungary).

He is a reviewer of Mathematical Reviews and Zentrablatt fur Mathematik. He is a member of

the Croatian Mathematical Society and the American Mathematical Society. He received

National Science Award for 2009.

mailto:[email protected]

http://www.math.hr/~adamovic/

149

NAME: Ljiljana Arambašić, PhD

JOB TITLE: Associate Professor

DATE OF LAST PROMOTION: 17th May 2011

ACADEMIC INSTITUTION: Faculty of Science, Department of Mathematics, University of

Zagreb


URL: http://www.math.hr/~ljsekul/

SHORT CURRICULUM VITA

Education: B.Sc. 1995, University of Zagreb, Department of Mathematics, M.Sc. 1999,

University of Zagreb, Department of Mathematics, Ph.D. 2005, University of Zagreb, Department

of Mathematics, thesis advisor: Damir Bakić.

Teaching: University of Zagreb, several mathematical courses; advisor for 11 B.Sc. thesis.

Research interests: operator theory, C*-algebras, Hilbert C*-modules, frame theory,

wavelet theory.

150

NAME: Tina Bosner, PhD

JOB TITLE: Assistant Professor

DATE OF LAST PROMOTION: 27th October 2009


Zagreb


URL: web.math.pmf.unizg.hr/~tinab/


She was born in Zagreb in 1973., where she obtained her B. Sc. in 1997. at the Department

of Mathematics of the University of Zagreb under the supervision of Prof. D. Svrtan. In the same

year and at the same institution she started her graduate studies. She received M. Sc. in 2002. and

Ph. D. in 2006. with the thesis „Knot insertion algorithms for Chebyshev splines“. The Ph. D.

advisor was Prof. M.Rogina.

Since 1998. she works as a teaching assistant at the Department of Mathematics of the

University of Zagreb, and since 2009. as an assistant professor. She taught several courses for

math and non-math students including Numerical methods in physics, Scientific computing and

Practicum in numerical methods of statistics.

Her research interest is Chebyshev theory for spline functions and development of

numerically stable algorithms for calculating with certain splines which can be applied to CAGD

or for solving singularly perturbed boundary value problems.

151

NAME: Aleksandra Čižmešija, PhD




Zagreb


URL:


Born in Čakovec, Croatia, on August 16th 1968. Graduated from Department of

Mathematics, University of Zagreb with major in mathematical informatics and statistics.

Obtained MSc degree in 1994 and PhD in 1999. PhD thesis title was Mixed Means and

Inequalities of Hardy and Carleman Type (supervisor: Croatian Academy member Josip Pečarić).

She has been employed at the University of Zagreb, Department of Mathematics, since

1990, first as an assistant, senior assistant (1999), assistant professor (2001) and associate

professor (2006). She was a vice-dean for education (2002 - 2005). She is a member of the

Division of Computer Science and the Chair of Didactics of Mathematics and ICT.

Areas of her scientific and professional interest are: mathematical analysis (functional

spaces and theory of inequalities) and didactics of mathematics. She authored 29 scientific papers

(20 of them listed in SCIE), 2 compilations of mathematical competitions and 20 didactical and

popularization papers.

She is member of the editorial boards of the following journals: Journal of Mathematical

Inequalities, Croatian Journal of Education (scientific journals listed in SCIE / SSCI), Matka and

Math-e (popularization journals).

152

NAME: Andrej Dujella, PhD


DATE OF LAST PROMOTION: 14th July 2009


Zagreb


URL: http://web.math.hr/~duje/


Andrej Dujella was born on May 21, 1966. in Pula. He completed primary and secondary

education in Novigrad and Zadar, and graduated from the Department of Mathematics, University

of Zagreb in 1990. He received his M.Sc. in 1993 and Ph.D. in 1996 at the same faculty. From

1997 he works at the same faculty as Assistant Professor, from 2000 as Associate Professor, and

from 2004 as Professor. During that period, he gave lectures on 10 undergraduate and 5 graduate

courses. He was visiting professor at Technische Universität Graz (2001), University of Debrecen

(2007) and Basque Center for Applied Mathematics Bilbao (2011).

The main fields of his research interest are Diophantine equations and elliptic curves. The

most important scientific results are related to the theory of Diophantine m-tuples. His list of

publication contains 77 research papers and 3 books. Supervisor of 10 Ph.D. dissertation, 8

Master's thesis and 160 graduation thesis. Editor-in-Chief of the scientific journal Glasnik

Matematicki since 2012. In 2000 received Croatian Mathematical Society Award for Scientific

Achievements in Mathematics, in 2004 received Award of the Croatian Academy of Sciences and

Arts, and in 2006 received State annual award for science. Leader of 10 scientific projects (8 of

them are international). Married, father of three children.


153

NAME: Zrinka Franušić, PhD


DATE OF LAST PROMOTION: 19rd February 2013.


Zagreb


URL: http:// web.math.pmf.unizg.hr/~fran/


Zrinka Franušić was born on January 2, 1972 in Zagreb. She completed primary and

secondary education in Zagreb. She received B.Sc. in 1995, M.Sc. in 2000 and Ph.D. degrees in

2005, all in Mathematics at Department of Mathematics, University of Zagreb. In 1995 she

started as Teaching Assistant at Department of Mathematics in Zagreb. At the present has position

of Assistant Professor at the same department.

She taught several courses in mathematics (recitations for Linear algebra, Elementary

mathematics, Euclidean spaces, Calculus, etc., lectures for Analytic geometry, Elementary number

theory, Cryptography) for math and non-math students. She was a supervisor of 15 graduation

thesis.

The main fields of her research interest is the theory of Diophantine m-tuples and

diophantine equations.

Married, mother of four children.


154

NAME: Goran Igaly, PhD

JOB TITLE: senior lecturer



Zagreb


URL: http://web.math.pmf.unizg.hr/~igaly/


Education: Born in Zagreb, Croatia, on March 29th 1963. Graduated from Department of

Mathematics, University of Zagreb with major in mathematical informatics and statistics.

Obtained MSc degree in 1992 and PhD in 1997

Teaching:1988—2012 At Department of Mathematics, University of Zagreb. G. Igaly was

the lecturer of about 35 courses.

Research interests: Combinatorics (formal languages, enumerative combinatorics).


155

NAME: Zvonko Iljazović, PhD


DATE OF LAST PROMOTION: 26th January 2011


Zagreb


URL:


Education: B.S. (2001., University of Zagreb), M.S. (2005., University of Zagreb), PhD

(2010., University of Zagreb)

Research interests: computable analysis, computable topology


157

NAME: Leonardo Jelenković, PhD



ACADEMIC INSTITUTION: Faculty of electrical engineering and computing, University of

Zagreb


URL: http://www.fer.unizg.hr/leonardo.jelenkovic


Leonardo Jelenković was born 1973. in Pazin, Croatia. He received the BS degree in Electrical

Engineering in 1996., and MS degree (2001) and PhD degree (2005) in Computer Science, all at

University of Zagreb Faculty of Electrical Engineering and Computing. He joined the Department

of Electronics, Microlelectronics, Computer and Intelligent Systems in 1997, and still works there

as assistant professor.

Thesis of his master degree was “Evaluation and analysis of Stewart parallel manipulators” in

which he designed algorithms for workspace calculation and analysis (kinematic properties, error

analysis). In his doctorate “Multithreaded embedded systems based on monitors”, he proposed

particular monitors (synchronization primitives) as basic building block for embedded systems

with severe hardware constraints. Mentor for BS, MS and PhD was prof. Leo Budin.

Leonardo Jelenković is involved in several courses on PhD studies (Scheduling algorithms,

Algorithms in embedded computer systems), graduate studies (Real time systems, Operating

systems for embedded computers) and undergraduate studies (Operating systems), all on

University of Zagreb Faculty of Electrical Engineering and Computing. He also teaches an course

(Operating systems) on University of Zagreb Faculty of Science. He had mentored 37 students so

far.

Research interests of Leonardo Jelenković include: operating system concepts, designs and

implementations (particularly for embedded and real-time systems), multithreading

(parallelization, scheduling, RT communication and synchronization), representation of previous

systems, methods and problems for students. He has published 13 papers in conference

proceedings and one paper in journal. He is co-author of two books (in Croatian): “Operating

Systems” (Operacijski sustavi) and “System software” (Sustavna programska potpora). He has

prepared teaching materials for his graduate courses.

Leonardo Jelenković is IEEE member. He is also secretary for AMAC-Alumni FER (alumni

association of University of Zagreb Faculty of Electrical Engineering and Computing).


http://www.fer.unizg.hr/leonardo.jelenkovic

158

NAME: Vedran Krčadinac, PhD




of Zagreb


URL: http://www.math.hr/~krcko/


Born on the 26th November 1973 in Zagreb. Attended elementary school in Zagreb and in

Hamburg (Germany), and secondary school in Zagreb (XV. Gymnasium – MIOC). BSc

degree in December 1996, MSc degree in October 1999, and PhD degree in May 2004 at the

Department of Mathematics, Faculty of Science, University of Zagreb, under the supervision

of prof. Juraj Šiftar.

From April 1997 teaching assistant and young researcher at the Department of Mathematics.

From December 2005 assistant professor, and from June 2011 associate professor in

mathematics. Since 2005 lecturer in 10 undergraduate courses, 2 graduate courses and one

postgraduate course. Supervisor of 26 masters theses and co-supervisor of one doctoral

dissertation.

Researcher on the scientific projects Combinatorial designs and finite geometries and Non-

associative algebraic structures and their applications. Published 7 scientific papers related

to the first project; research topics are combinatorial and geometric-combinatorial structures,

in particular existence and classification problems about them. Published 5 scientific papers

related to the second project; research topics are special classes of quasigroups with

applications in geometry. Also published 6 professional papers, 4 of which co-authored by

students.

Head of the Geometry Section and active member of the Seminar for Geometry at the

Department of Mathematics. Seven contributed presentations at international conferences and

one invited plenary lecture. Member of the Croatian Mathematical Society.


http://www.math.hr/~krcko/

159

NAME: Tajana Ljubin Golub, PhD


DATE OF LAST PROMOTION: 24th November 2010

ACADEMIC INSTITUTION: Faculty of Teacher Education, University of Zagreb


URL:


Tajana Ljubin Golub received her degrees from University of Zagreb, Department of

Psychology. For several years she was working as a clinical psychologist (1990-1997). She was

senior lecturer at Police College of Ministry of Interior (2003-2009) teaching subjects in

psychology, and also served in the same institution as a vice dean (2003-2008).

Currently she is Associate Professor of Applied Psychology at Faculty of Teacher

Education where she teaches several courses on the educational psychology (e.g. Psychology of

Learning and Teaching) and applied psychology (e.g. Forensic Psychology, Prevention of Abuse

and Risk Behaviors). She has published around 40 papers and book chapters on topics related to

applied psychology. In 2007 she get an award „Marulić: Fiat Psychologia“ for her contribution to

the development of applied psychology in Croatia.

160

NAME: Robert Manger, PhD


DATE OF LAST PROMOTION: 13th March 2012


Zagreb


URL: http://www.math.hr/~manger


Robert Manger was born in Zagreb in 1957. He received the BSc (1979), MSc (1982), and

PhD (1990) degrees in mathematics, all from the University of Zagreb. For more than ten years he

worked in industry, where he obtained practical experience in programming, computing, and

designing information systems. In the period between 2000 and 2003 he also served at the

Croatian Ministry of Science and Technology as a deputy minister responsible for ICT.

Dr Manger is presently a full professor at the Department of Mathematics. He teaches

undergraduate and postgraduate courses dealing with data structures and algorithms, database

systems, software engineering, and NP-hard combinatorial optimization problems. He is the leader

of the scientific project 037-0362980-2774 “Distributed algorithms for finding optimal paths in

graphs” financed by the Croatian Ministry of Science, Education and Sports.

His current research interests include: combinatorial optimization, design and analysis of

algorithms, meta-heuristics, parallel and distributed processing.

Dr Manger has published 22 papers in international scientific journals, 30 scientific papers

in conference proceedings, 10 professional papers, and 4 course materials. He acted as a mentor

for more than 100 undergraduate, 5 postgraduate and 4 doctoral students. He is also a co-author of

the strategic document “Croatia in the 21st Century – Information and Communication

Technology”, which has been adopted by the Croatian parliament.

Dr Manger is a member of the Croatian Mathematical Society, Croatian Society for

Operations Research and IEEE Computer Society.

161

NAME: Eduard Marusic-Paloka, PhD




Zagreb


URL: www.math.hr/~emarusic


He received his BSc at the University of Zagreb (1989), Msc at the University of Zagreb

(1992), and Phd at the Universite de St-Etienne in 1995.

He taught several courses, including Analytical mechanics, and Mathematical analysis 3, 4,

Methods of mathematical physics, Applied analysis, Introduction to analysis, Mathematical

methods of fluid mechanics, Introduction to Sobolev spaces.

His research interests include Partial differential equations, mathematical models in

continuum mechanics (fluid mechanics) and homogenization.

He has published 57 papers, 44 of them in journals covered by the Current Contents. His

papers are cited more then 230 times according to the WOS, so far. He is member of the editorial

bord of „Glasnik matematički“, „Differential equations and applications“ and „ISRN

Mathematical analysis“. In 2005 he has received Croatian state award for science. He was

principal investigator of 3 scientific projects financed by MZOŠ. He was researcher on one french

and one EU project.

He was the head of the Division for applied mathematics 2003./2004. i 2004./2005. of the

Department of mathematic. He is deputy head in charge of the research of the Department of

mathematics from 2007. until now.

162

NAME: Mladen Mauher, PhD

JOB TITLE: High School Professor

DATE OF LAST PROMOTION: 20th April 2010

ACADEMIC INSTITUTION: Polytechnics of Zagreb, Zagreb (1st November 2011)

E-MAIL: [email protected], [email protected]

URL: http://www.tvz.hr


Graduated on Faculty of economic sciences, Zagreb. Master's degree from the area of economy

(economy of automations) on University in Zagreb; doctor's degree on Faculty of organization and

informatics in Varaždin, University in Zagreb.

ICT professional and management career („Chromos“, „Jugobanka Zagreb“, „Zagrebačka banka“).

Scientific and professional work in Institute of traffic sciences and Zagreb University Computing

Centre. Strategic management positions in „Jugobanka Zagreb“ and „Zagrebačka banka“ banks.

Adviser in ICT projects for „Privredna banka Zagreb “ and „Croatia insurance“, and some SME

business systems.

Head of Government Office for the internetization. Author, co-author and participant in e-

Government documents (healthcare, education, court and justice, culture, election; acts and

regulations of information society). Participated in ICT project management unit in healthcare.

Member is CARNet Management board (2002/2003). Keynote speaker on Microsoft e-

Government Leader's Conference in Seattle. Participant of Croatian delegation on World Summit

On Information Society, Geneve.

Lectured „Computer programming“ at Faculty of transportation sciences, „Banking Technology“

at DSM at Faculty of Electrical engineering and computing, „Information management

technologies“ at Master of Business Administration and „Organization and management“ (Faculty

of Economics). Lectures „Electronic government“ on Management in Informatics of Postgraduate

Studies (Faculty of Economics) and „Electronic Business Systems“ at Polytechnic graduate

professional study programme. Chosen for lecturer on PDS for Economic Theory.

Lectures on Polytechnic of Zagreb (Electronic business systems, Software engineering and

information systems, Physical Asset Management System), High school for Applied Computing

Zagreb (Software Engineering, Business Information Systems), Faculty of Science-Department of

Mathematics (Social aspects of ICT, Software Project Management).

Member of Croatian society for simulation modeling; Croatian society for operations research;

Organization board of Information Technology Interfaces Conference; Program board of „Journal

of Computing and Information Technology“ - national edition; Organization board of 5.

Symposium „Computer Science in Sport”. Member of the MIPRO International Program

Committee.

Has published more than 40 scientific and professional papers at international and domestic

conferences and journals.



http://www.tvz.hr/

163

NAME: Željka Milin Šipuš, PhD


DATE OF LAST PROMOTION: 21nd January 2014


Zagreb


URL:


She received her B. sc. In 1987 with the thesis “Radon transform”, supervised by prof.

dr.sc. Mirko Primc, at the Department of Mathematics, University of Zagreb. She received her M.

sc. 1991. with the thesis “Elliptic operators and Hodge theory”, supervised by prof. dr.sc. Mirko

Primc, at the Department of Mathematics, University of Zagreb. She received her Ph. D. in 1998

with the thesis “Multidimensional isotropic spaces”, University of Zagreb, supervised by prof. dr.

sc. Boris Pavković.

She lectured the following undergraduate courses at Department of Mathematics,

University of Zagreb: Introduction to differential geometry, Analytic geometry, Geometry of

surfaces, Linear Algebra, Riemannian geometry, ICT in mathematics education, Methods of

teaching mathematics, and post-graduate courses Geometry and topology, Mathematics education

research and Semi-Riemannian geometry; and at Department of Mathematics, University of

Osijek: Introduction to differential geometry.

Her research interests include differential geometry in semi-Riemannian spaces, geometry

of Cayley-Klein spaces and mathematics education. She authored 16 research papers

published/accepted for publication in international journals. She collaborated in several scientific

projects, like: Geometries and algebraic-geometrical structures (prof. dr. sc. Vladimir Volenec),

Didactical standards in mathematics education (prof. dr. sc. Zdravko Kurnik), Differential

geometry of spaces with indefinite and degenerate metrics (prof. dr. sc. Blaženka Divjak) and

Educational research in Physics and Mathematics (dr. sc. Maja Planinić).


164

NAME: Dubravka Miljkovic, PhD


DATE OF LAST PROMOTION: 3rd March 2009



URL


Born on 28th September, 1953. in Zagreb. Graduated in Psychology and Pedagogy at the

Faculty of Philosophy, University of Zagreb in 1975. In 1986 obtained MA in Psychology with a

thesis on the area of reading and in 1990 a Ph.D. in Education with the theme in the field of

general education. Additional trainings were in the field of NGO Management, Human Resource

Management and Transactional Analysis.

After graduation she worked as a school psychologist and teacher at primary school, at

educational center and grammar school, where she taught psychology. At Croatian Studies she was

a lecturer in Educational Psychology, Psychology Teaching Methods and Positive Psychology.

She was the member of the Governing Council of the University of Applied Sciences Vern, where

she also founded several courses in the area of business and organizational psychology. Since May

2005 she has been permanently employed at Faculty of Teacher Education in the Department of

Educational Studies. From 2007 – 2009 she was the head of this department and the head of

pedagogical and psychological training course. She has been teaching Pedagogy, Didactics,

Classroom Management (at the graduate and doctoral studies), Communication in Education,

Educational Theory and Evaluation in Education.

She is one of the founders and first president of the Association of Telephonic Emergency

Services in Croatia. She (co)wrote 34 books (of which 3 are university and 1 polytechnic

textbooks), chapters in several books, about 80 scientific papers and more than 300 professional

and popular articles for many newspapers and magazines and is the editor in chief of the

pedagogical journal Napredak. She participates in various radio and TV shows related to topics in

psychology and pedagogy, she is the member of the administrative committee of the Forum for

Freedom in Education and a member of Croatian Academy of Educational Sciences, Croatian

Psychological Society, Croatian Psychological Association and Croatian Pedagogical Literary

Society.

In 1997 she was awarded The Ramiro Bujas award by Croatian Psychological Society, for

the exceptional achievements in the promotion and popularization of psychology. She was

awarded the Annual National Award for popularizing psychology by Croatian Ministry of

Science. In 2009 she received The Zoran Bujas award for psychological book of the year.

165

NAME: Goran Muić, PhD




Zagreb


URL: http://web.math.pmf.unizg.hr/~gmuic/


Education: Diploma thesis 1993 (advisor M. Primc). Master degree thesis 1996 (advisor M.

Tadić). Ph. D. 1997 (advisor M. Tadić).

He taught several courses in pure mathematics and computer science: Mathematical

structures, Mathematics for chemistry I, II, Complex Analysis, Algebraic Curves, Vector Spaces,

Introduction into Mathematics, Elementary Mathematics II, Computer Science Lab I, II. He gave

6 graduate courses. He advised 26 defended diploma thesis, 3 master thesis, and 4 Ph.D. thesis.

Research interests: automorphic and modular forms. He visited and gave lectures on

several universities in USA, including a three year stay at the University o Utah, Paris, Berlin,

Vienna, Tel-Aviv, Jerusalem, Poitiers, Oberwolfach, Kyoto, Hong-Kong.

He authored 39 published/accepted research papers. He was awarded by the Croatian

Mathematical at the Third Croatian mathematical congress held in Split in the summer of 2004.

He was awarded by the Outstanding Instructorship Award for research and teaching at the

University of Utah in 1999.

166

NAME: Ivica Nakić, PhD


DATE OF LAST PROMOTION: 23th September 2014


of Zagreb


URL:


He obtained his B. Sc. in 1995. at the Department of Mathematics of the University of

Zagreb under the supervision of prof. B. Najman. In 1996. he started his graduate studies at

the Department of Mathematics. He recieved M. Sc. in 1998. In 2003 he obtained Ph. D.

thesis with the title Optimal damping of vibrational systems at the Fernuniversitaet Hagen,

Germany. The Ph. D. advisor was prof. K. Veselić.

He worked as a teaching assistent at the Department of Matematics of Univversity of

Zagreb during the following periods: 1996. -2000, 2002.-2003. From 2000 till 2002 he

worked as a Wissenschaftliche Mitarbeiter at the Fernuniversitaet Hagen in Germany. He

became assistant professor at the Department of Mathematics in 2003.

His research intersts cover systems theory, operator theory, vibrational systems and

semigroup theory, as well as various applications of aforementioned mathematical fields.

He organized two scientific conferences, and was to the main editor of the journal

math.e in the period 2009-2012.

167

NAME: Goranka Nogo, PhD




Zagreb


URL: web.math.hr/~nogo


She graduated from Department of Mathematics, University of Zagreb with major in

mathematical informatics and statistics. She obtained MSc degree in 1985 and PhD in 1998. PhD

thesis title was Parallel Algorithms for Network Flow Problems.

She has been employed at the University of Zagreb, Department of Mathematics, since

1982, first as an assistant, senior assistant, and assistant professor. She has been head of

Computing Centre. She is member of the Division for Computer Science and Chair of Didactics of

Mathematics and ICT.

Areas of her scientific and professional interest are: parallel algorithms, combinatorial

optimisation, and didactics of ICT. She authored 12 scientific papers and 16 didactical and

popularisation papers. She is also a co-author of two textbooks. She was associated in 5 scientific

projects, one technology project, and nine projects of ICT application.

She acted as a mentor for 16 undergraduate students.

168

NAME: Siniša Opić, PhD


DATE OF LAST PROMOTION: March 2009



URL


Siniša Opić was born on the 08th December 1973 in Pakrac. He graduated in 1996 at the Faculty

of Philosophy, Department of Pedagogical Science. That same year he enrolled in postgraduate

studies (mr.sc.) at the Faculty of Education and Rehabilitation Sciences, Department of Behave

Disorders. After passing the differential exams he got Masters (of science) in 1999.

In 2007 he got his doctorate at the University of Zagreb, Department of Pedagogy, where since

2006 he has been working as a lecturer (part time job).

Since 2009 he has been employed as an assistant professor (docent) at Faculty of Teacher

Education, University of Zagreb (full time job).

He is also is (or was) a lecturer at the Faculty of Science, Academy of Fine Arts, Faculty of

Teacher Education in Gospić (University of Rijeka).

He performs lecture at many courses, undergraduate, graduate and doctoral studies. The areas of

scientific interest are: research methodology (social science), trichotomy of behavior disorders,

pedagogy and didactics. He mentors a dozen students in the preparation of the master thesis.

He is a reviewer of several scientific journals and several international scientific conferences,

textbooks, the University Development Fund.

He is the author of many scientific papers, professional papers, invited lectures, presentations at

international and national scientific conferences.

Published articles; http://bib.irb.hr/lista-radova?autor=231642

169

NAME: Ozren Perše, PhD


DATE OF LAST PROMOTION: 19th February 2013


of Zagreb


URL:


Ozren Perše was born in Zagreb, Croatia on March 3rd, 1976. He studied

Mathematics at the University of Zagreb where he obtained his B.Sc. and M.Sc. degrees in

Mathematics in 1998 and 2003, respectively. In 2005 he obtained his Ph.D. in Mathematics

at the same university. The title of the thesis was ‘‘Vertex operator algebras associated to

affine Lie algebras of type A_l^1 and B_l^1 on admissible half-integer levels’’ (advisors:

Dražen Adamović and Mirko Primc). From 1999 to 2007 he was Teaching Assistant at the

Department of Mathematics, University of Zagreb.

He lectured the following undergraduate courses: Linear Algebra I, II; Elementary

Mathematics II and Vector spaces. He also lectured the graduate course ‘‘Kac-Moody

algebras’’. He was supervisor of 11 Diploma Thesis. He is a co-organizer of the Algebra

Seminar at the Department of Mathematics.

His current research interests include vertex operator algebras and representation

theory of infinite-dimensional Lie algebras. He published 7 research articles about these

subjects. Since 2007, he is an investigator in the research project ‘‘Vertex operator algebras

and infinite-dimensional Lie algebras’’ headed by Mirko Primc. He was a collaborator in the

Croatian-Hungarian bilateral research project “Algebraic methods in mathematical physics”

headed by Dražen Adamović and Gabriella Bohm. In 2008 he received the Croatian

Mathematical Society Award for young scientist. He attended many mathematical

conferences in Europe, USA and Asia. He is a reviewer for Mathematical Reviews and

Zentrablatt fur Mathematik. He is a member of the Croatian Mathematical Society and the

American Mathematical Society.


170

NAME: Mirko Polonijo, PhD




Zagreb


URL:


Education: Born in 1949 in Zagreb. Graduated in mathematics in 1975 from the Faculty of

Sciences (PMF) in Zagreb (Theory of Quaternars and Möbius's Geometry, thesis supervisor Prof.

Vladimir Volenec). Awarded doctor's degree in 1981 from the PMF in Zagreb (Geometry of

Totally Symmetric Medial Ternary Quasigroups, thesis supervisor Prof. Vladimir Volenec).

Teaching: Employed at the Department of Mathematics of PMF since 1972. Appointed

full professor at the Department of Mathematics of PMF in 1993. Head of the Geometry Section of

the Department of Mathematics. Head of the Geometry Seminar. Head of the Graduate Seminar in

Geometry. Elected head of the Department of Mathematics from 1989 until 1992.

Taught various undergraduate and graduate courses at the Department of Mathematics of

PMF, and teacher training colleges in Osijek and Maribor. Wrote and published (independently

and as co-author) over 60 elementary-school textbooks, work-books, reference books and books

from popular and recreational mathematics.

Research interests: Research interests focus on the theories of binary and n-ary quasigroups

and other algebraic structures, algebraic nets and functional equations, as well as their application

in geometry. Published 24 research papers and 13 scholarly papers. He Participated with papers in

numerous congresses, conferences, seminars and spent some time conducting research abroad.

Collaborator in the scientific project titled Geometries and Algebraic-geometric structures.

Awarded the Department of Mathematics Award for special scientific activity in 1985, together

with professor dr. M. Primc. National annual award for popularisation and promotion of science

(2007)


171

NAME: Mirko Primc, PhD




Zagreb


URL:


He was born in 1948 in Zagreb. He received his B.Sc. in 1971 at the University of Zagreb,

his MSc in 1974, and his PhD in 1995 at the same institution. He has been working at the

Department of Mathematics, University of Zagreb since 1971. He spent a year at the Institute for

Advanced Studies in Princeton as a visiting scientist in 1980/1981, a year in Berkeley in 1983/84,

and a year in Lund in 1991/92.

Her research interests include Representation theory of semisimple Lie groups, and Kac-

Moody algebras. He published 23 scientific papers. He received Ruđer Bošković prize for his

scientific contrubutions.

172

NAME: Slobodan Ribarić, PhD


DATE OF LAST PROMOTION: 1997

ACADEMIC INSTITUTION: Faculty of EE and Computing, University of Zagreb


URL: http://www.zemris.fer.hr/clan.php?clan=4&lang=1


Slobodan Ribarić, Ph.D., is a Full Professor at the Department of Electronics, Microelectronics,

Computer and Intelligent Systems, Faculty of Electrical Engineering and Computing, University of

Zagreb, Croatia. He teaches the following courses at the undergraduate, graduate level and

postgraduate levels: Computer Architecture II, Introduction to Pattern Recognition (undergraduate

level), Pattern Recognition and Computer Vision (graduate level), and Computer and Robot Vision,

and Biometric Security Systems (postgraduate level). S. Ribarić is a head of the Laboratory of

Pattern Recognition and Biometric Security Systems (RUBOISS). Slobodan Ribarić received the

B.S. degree in electronics, the M.S. degree in automatics, and the PhD. degree in electrical

engineering from the Faculty of Electrical Engineering, Ljubljana, Slovenia, in 1974, 1976, and

1982, respectively.

His research interests include Pattern Recognition, Artificial Intelligence, Biometrics, Computer

Architecture and Robot Vision. He has published more than one hundred and fifty papers on these

topics. Some articles have been published in the leading scientific journals such as IEEE

Transactions on Ind. Electronics, IEEE Transactions on Pattern Analysis and Machine Intelligence,

Microprocessing and Microprogramming, Int. Journal of Pattern Recognition and Artificial

Intelligence i IEEE Proceedings Vision, Image & Signal Processing. Ribarić is author of five

books: Microprocessor Architecture (1986, four editions), The Fifth Computer Generation

Architecture (1986.), Advanced Microprocessor Architectures (1990, two editions), CISC and

RISC Computer Architecture (1996), Computer Structures, Architecture and Organization of

Computer Systems (2011). The book CISC and RISC Computer Architecture was named as the best

scientific books in the field of information science of year 1996 (J. J. Strossmayer award). S.

Ribarić is co-author of the book An Introduction to Pattern Recognition (1988).

Professor Ribarić has held a series of invited lectures at universities and institutes in China,

Germany, Italy and Slovenia. He is a member of Editorial Board of IET Biometrics Journal and

CIT Journal.

Ribarić is a member of the IEEE and MIPRO.

173

NAME: Saša Singer, PhD

JOB TITLE: associate professor

DATE OF LAST PROMOTION: 28st September 2010


Zagreb


URL: http://web.math.hr/~singer/


Saša Singer obtained his BSc in mathematics, at the Department of Mathematics,

University of Zagreb in 1981, MSc in mathematics and PhD in mathematics, at the same

Department in 1988 and 1996, respectively. The title of the PhD thesis was ‘‘Complexity of the

Descent Functions for Polynomial Equations’’.

He is author or co-author of 28 research articles in the fields of numerical linear algebra,

and the complexity and accuracy of the numerical algorithms. He attended over 50 international

meetings. He is a member of the Croatian Mathematical Society, SIAM, ACM and ILAS. His

current research interests include design, analysis and application of the efficient and accurate

numerical algorithms.

Saša Singer is author or co-author of 14 professional and popularization papers. He is also

a member of the editorial board of Matematičko-fizički list (mathematical-physical journal for the

secondary school students).

He currently lectures the following undergraduate courses: Programming 1 and

Programming 2, and Numerical Mathematics, and the graduate course The Design and Analysis of

Algorithms. In the past he lectured 17 other courses. He also lectured three postgraduate courses.

He was supervisor of 96 Diploma Thesis, and co-supervised one PhD Thesis. He co-authored the

lecture notes Parallel algorithms and web-book Numerical analysis.

http://web.math.hr/~singer/

174

NAME: Siniša Slijepčević, PhD


DATE OF LAST PROMOTION: 23th September 2014


Zagreb


URL:


He graduated in 1994. on Department of Mathematics, University of Zagreb, and obtained

PhD in University of Cambridge, Department of Applied Mathematics and Theoretical Physics,

UK, in 1999. The topic of his PhD is in the area of Dynamical Systems.

He was a teaching assistant between 1994 and 2000 on University of Zagreb and

University of Cambridge, where he taught Mathematical Analysis, and several courses in Applied

Mathematics and Probability and Statististics. Between 2000 and 2004 he worked as a consultant

and manager in McKinsey & Company, in Prague. Since 2004, he is an Assistant Professor and

Associate Professor in the Department of Mathematics.

His research interests cover Dynamical systems and Probability. He published original

results in Matematische Zeitschrift, Nonlinearity, Discrete and Continuous Dynamical Systems A,

Ergodic Theory and Dynamical Systems, J. Dynam. Differential Equations, Physica A, and others.

The paper with the highest number of citations up to day is on applications of dynamical systems

techniques to Parabolic Differential Equations: Th. Gallay, S. Slijepčević: Energy flow in formally

gradient partial differential equations on unbounded domains (2001.), J. Dynam. Differential

Equations.

The focus of research is ergodic theory, dynamical systems, and applications. In ergodic

theory, the focus is investigations of non-uniform hyperbolicity and applications. The applications

to partial differential equations are related to dissipative systems and energy flow. The applications

to number theory are related to the phenomena of recurrence and equivalent notions of difference

and van der Corput sets.

175

NAME: Tomislav Šmuc, PhD

JOB TITLE: Senior Research Associate

DATE OF LAST PROMOTION: 2006

ACADEMIC INSTITUTION: Ruđer Bošković Institute (permanent employment as scientist)


URL: http://www.irb.hr


Tomislav Smuc was born on 18 August 1961 in Zagreb. He graduated from the Faculty of

Electrical Engineering at the University of Zagreb in 1986. From 1986 he works at Ruder

Boskovic Institute where he obtained Master's degree in 1991 and defended a PhD thesis in 1994,

on the topic of heuristic optimization of nuclear reactor loading patterns. During 90-ties he spent

over two years as a visiting scientist at the nuclear research centers in United Kingdom, Finland,

Germany and The Netherlands. From the year 1999 he works mainly in the field of computer

science and computational modeling with applications in other fields of science. He is currently

the head of the Division Electronics at the Institute Rudjer Boskovic Institute.

From 2008 to 2010 he introduced teaching the subject of Artificial Intelligence and from 2010

Machine learning in the graduate studies of computer science and mathematics at the University of

Zagreb. From 2008 he has mentored two PhD theses and four master theses.

His fields of research are machine learning, knowledge discovery and data mining, and

applications of these techniques primarily in the bio-sciences. He has published over 50 scientific

papers in journals and peer-reviewed conference proceedings, some of them in the top quality

journals like PLoS Genetics, PloS One, Proteomics, Annals of Nuclear Energy. Currently he is PI

of the research project on machine learning methodologies for predictive modeling in

computational biology. He is a member of the IEEE Computer Society and European and Croatian

nuclear society.


http://www.irb.hr/

176

NAME: Maja Starčević, PhD


DATE OF LAST PROMOTION: 27th October 2009


Zagreb


URL:


Education: B.Sc. 1999 (Department of Mathematics, University of Zagreb), M.Sc. 2003

(Department of Mathematics, University of Zagreb), Ph.D. 2008 (Department of Mathematics,

University of Zagreb).

Teaching: held recitations for 9 courses and lectures for 5 undergraduate courses (Linear

algebra, Analytical mechanics, Systems of differential equations, Object oriented programming

(C++), .Net programming ...), supervisor of 6 B.Sc. thesis

Research interests: mathematical modelling if fluid mechanics, partial differential

equations


177

NAME: Dragutin Svrtan, PhD


DATE OF LAST PROMOTION: 11st March 2003


Zagreb


URL:


Date and place of birth: June 9,1950 - Kraljevec Gornji, Croatia

Graduation: Theoretical Mathematics at the University of Zagreb, Croatia , 1971

M.Sc., University of Zagreb, 1979, Ph.D., University of Zagreb, 1982

Languages: Croatian, English, German and Russian

Family status : married , two sons Miro and Damir

Research Possition:

1971-1982,1983-1985 Teaching Assistant, Department of Mathematics, University of Zagreb

1982-1983 Fulbright Research Scholar, Department of Mathematics, Berkeley, USA

1985-1990 Assistent Professor, Department of Mathematics, University of Zagreb

1990-1997 Associate Professor, Department of Mathematics, University of Zagreb

1997- Professor, Department of Mathematics, University of Zagreb.

2001(15.01-15.04) Visiting Professor , LMU, Munich , Germany.

Education:

1971 Graduated in Theoretical Mathematics at the University of Zagreb (Diploma Work:

"Elements of Morse theory")

1979 Obtained an M.Sc. degree at the University of Zagreb (M.Sc.thesis: "Surgery on

differentiable manifolds")

1982 Obtained an Ph.D. degree at the University of Zagreb (Ph.D.Thesis: "Contributions to the

theory of symmetric functions with applications to the Chern character of exterior powers")

Teaching: Differential Geometry, Concrete Mathematics, Number Theory,

Research interests: Differential Geometry and Topology (Chern Character, Atiyah Sutcliffe

conjectures), Algebraic Combinatorics (formal languages, polyomino enumerations,

noncommutative symmetric functions), Symbolic computation (cluster algebras, Robbins problem,

Sabitov theory), Quantum Algebra (multiparametric quon algebras ) .

Among other research results : Proofs of Scott's conjecture on permanents, Korbas conjecture on

Stieffel_Whitney classes of grassmannians, disproof of one-parametric and a multiparametric

extension of Zagier's conjecture, proof of some casses of Atiyah_Suttclife conjectures, solution of

a Robbins heptagon and octagon problem .

178

NAME: Juraj Šiftar, PhD


DATE OF LAST PROMOTION: 13th December 2011


Zagreb


URL:


Born in 1955. in Karlovac, Croatia. Living in Zagreb since 1967. Has two children.

Graduated (B.Sc.) in 1977. in Theoretical mathematics at the Mathematical Department of

Faculty of Natural Sciences and Mathematics in Zagreb. Since 1977/78. working as a teaching

assistant at the same department. Obtained M.Sc. degree in 1980. (thesis: "Groups of

perspectivities of finite translation planes"). In 1983/84. working on a Ph.D. thesis under

supervision of Prof. Z.Janko at the Mathematical Institute in Heidelberg. Obtained Ph.D. degree in

1985. in Zagreb (thesis "Finite 4-semiaffine linear spaces"). Elected to the position of assistant

professor in 1986, associate professor in 1993, professor in 2006 and tenured professor in 2011.

Teaching: courses in Linear algebra, Projective geometry, Set theory and Selected topics in

geometry for undergraduate students of mathematics, various mathematical courses for

undergraduate students of physics, electrical engineering etc at the University in Zagreb; 11

postgraduate courses mostly in the fields of finite geometries and coding theory. In 1993/94. gave

an elective course "Finite projective planes" as a visiting professor at the Institute for Geometry of

the Technical University in Graz, Austria. Supervised more than 50 diploma (B.Sc.) theses, four

M.Sc. theses and one Ph.D. thesis.

Publications: 17 research papers in the fields of finite geometries and quasigroup theory,

some of them with co-authors B.Shita, H.Zeitler and V.Krčadinac.

179

NAME: Hrvoje Šikić, PhD




Zagreb


URL:


Education: Diploma (Univ of Zagreb, 1982), Magister (Univ of Zagreb, 1986), PhD (Univ

of Florida, 1993)

Teaching: Lectures and exercise sections for more than twenty various courses in Croatia

and USA.

Research interests: Probability and stochastic processes, potential theory, wavelets.

180

NAME: Boris Širola, PhD


DATE OF LAST PROMOTION: 13th March, 2012


Zagreb


URL:


Boris Širola was born 1963 in Rijeka, Croatia. He completed both the elmentary and

secondary school in Zagreb, and then (acad. year 1983/84) enrolled on the study of mathematics at

PMF-MO. He received his B.Sc. in 1988. The same year he became an instructor and graduate

student of mathematics at PMF-MO. He received his M.Sc. in 1992, and his Ph.D. in 1996. In

October 2000 he became an assistant professor, in February 2006 an associate professor, and in

March 2012 a professor.

For many years he was teaching several courses: Algebraic structures, Elementary

mathematics 1 and 2, Mathematics 1 and 2 etc. He was also an instructor for numerous courses;

e.g., Mathematical analysis 3 and 4, Vector space, Chosen topics in algebra, Theory of analytic

functions etc. In the graduate school he lectured on 3 courses: Lie algebras and representation

theory, Commutative algebra and Riemann Zeta-function. He was an advisor for 6 graduate thesis.

His main research interest is in algebra: Lie algebras, algebraic groups and their

representations, noncommutative algebra and algebraic number theory. His publication list

consists of 18 papers; and one more paper has been accepted for publication. Some of renowned

journals where he has published papers are: Algebras and Representation Theory, Journal of

Algebra, Journal of Lie Theory, Proceedings of the Amer. Math. Soc., Transactions of the Amer.

Math. Soc. etc. He was the principal researcher of 3 scientific projects funded by the Ministry of

Science, Education and Sport, Reublic of Croatia. He is a co-founder and co-leader of the Seminar

for algebra. As a visiting scholar he spent an acad. year 1998/99 at the MIT (Cambridge, USA). In

shorter periods, of 3 to 4 weeks, he also visited the TIFR (Mumbai), Mathematische Institut,

Heinrich Heine Universitet (Dusseldorf) and University of Utah (Salt Lake City). He gave a

number of talks at international mathematical conferences and seminars, both at home and abroad.

He is a member of the Croatian Mathematical Sociey and American Mathematical Society.


181

NAME: Daria Tot, PhD


DATE OF LAST PROMOTION: 5th May 2010



URL:


She was born on 24 February 1964 in Odžak. She completed elementary and secondary school in

Rijeka, where she graduated from the Faculty of Education in 1997 and became Teacher of

Pedagogy. She completed her master thesis Continual Professional Training and Professional

Development of Teachers at the Faculty of Humanities and Social Sciences in Rijeka in 2006. She

obtained an MSc degree in the area of social sciences, field of educational sciences, and in 2009

she obtained a PhD degree, from the same institution, in social sciences, in the field of pedagogy,

branch of didactics, with the doctoral dissertation Self-evaluation of Teachers and the Quality of

Teaching.

After graduating from the Faculty of Humanities and Social Sciences , she was employed as an

expert associate of pedagogy in a private elementary school Grivica in Rijeka, in the kindergarten

Rijeka and in the elementary school Milan Brozović in Kastav. As an external associate teacher

she organized seminars and workshops at the courses School Pedagogy and Theory of Educational

System in School at the Department of Pedagogy at the Faculty of Humanities and Social Sciences

in Rijeka from 2006 to 2010 (form 2008 as an assistant).

At the beginning of May 2010 she was hired as a senior lecturer (docent), and since 25 May 2010

she has been working at the Faculty of Teacher Education in Zagreb.

As a member of teaching staff at the Department for Educational Sciences she gives lectures at the

following courses: Didactics 1: Curriculum Approach, Didactics 2: Teaching and Teacher's

Professional Activities, Pedagogy 1: Theory and Practice of Education and Pedagogy 2:

Educational System to students of teacher education studies at the Faculty of Science in Zagreb.

She teaches Didactics as part of the pedagogical-psychological and didactical program for subject

teachers at the Faculty of Teacher Education in Zagreb. As an external associate she teaches

Pedagogy in the (Trainer Education Department) at the Faculty of Kinesiology in Zagreb.

She participated in writing analyses and reviews for the Napredak magazine, as well as papers for

the conference on ECNSI advanced and systematic research. She is a member of Croatian

Pedagogical Society.

She is a researcher involved in a scientific project approved by the Ministry of Science, Education

and Sports of the Republic of Croatia (009-0000000-2489) led by Professor Anita Klapan, PhD.

Project title: "Perspectives of Adult Education in Croatia in the framework of lifelong learning".

She has worked as an external associate professor since 2007 on the scientific project of the

Ministry of Science, Education and Sports called "Analytical model of monitoring new

educational technologies in lifelong learning", Ministry of Science and Technology of the

Republic of Croatia (227-2271694-1699), led by Professor Vladimir Šimovic, PhD.

The field of her research are professional competences of teachers and subject teachers, their

professional development as well as evaluation and self-evaluation of their work. She proposed a


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model of professional development for teachers and subject teachers, and she also created a

hypothetical algorithmic model of teacher’s self-evaluation. She has published 15 scientific papers

and many academic papers, and has actively participated in the work of several national and

international professional and scientific conferences.

She actively participated in the organization of conferences at the Institute of Education of the

Republic of Croatia (Education and Teacher Training Agency). She is working on popularization

of science by giving lectures on pedagogy and didactics at the Primorsko Goranska County Expert

Council of pedagogues and the City of Zagreb as well as to giving lectures to teachers and subject

teachers in schools. She participated in the work of a dozen international scientific conferences.

183

NAME: Sanja Varošanec, PhD

JOB TITLE Professor

DATE OF LAST PROMOTION: 13th December 2011


Zagreb


URL:


She received her B.S.(Mathematics) 1986, Department of Mathematics, University of

Zagreb, her M.Sc. in Mathematics in 1990 at the Department of Mathematics, University of

Zagreb, and her Ph.D. in Mathematics in 1994 at the Department of Mathematics, University of

Zagreb

Title of her dissertation is Gauss' Type Inequalities, thesis adviser: Josip Pečarić. From

1987 untill 1996 she was an assistant at Dept. of Math., from 1996 she was an assistant professor,

from 2001 an associate professor, and from 2006 she has been a professor of mathematics at the

same Department.

She taught several courses including Mathematical Analysis I and II, Projective Geometry,

Introduction in Differential Geometry, Didactics of Mathematics I, II, III and IV, and Descriptive

Geometry.

Her main research interests are in mathematical analysis, especially in theory of

inequalities. She has published more than 50 scientific articles in the international mathematical

journals and proceedings. She took a part in seven projects funded by the Croatian Ministry of

Science. Now, she is a principal researcher of one of them, a co-leader of Seminar of Inequalities

and Applications. Since 2002 she has been a chair woman of Cathedra for mathematical education.

She also published several mathematical textbooks for secondary and primary schools

and wrote a number of articles with themes from elementary mathematics. She has been an

associate editor of Mathematical Inequalities and Applications and editor for Poučak and

Matematika i škola, journals for mathematics teachers.

184

NAME: Vesna Vlahović – Štetić, PhD



ACADEMIC INSTITUTION: Faculty of Philosophy, University of Zagreb


URL:


She was born in 1959 in Zagreb where she finished primary school and Mathematical grammar

school. She attended the study of psychology at the Department of Psychology, Faculty of

Philosophy, University of Zagreb, from where she graduated in 1982, receiving the MA degree in

1986 and the PhD in 1996 at the same institution.

From 1982 until 1987 she worked as an assistant at the Department of psychology of the Faculty

of arts and sciences in Zadar. She became an assistant at the Department of Psychology of the

Faculty of Philosophy in Zagreb in 1987 and a senior assistant in 1996. In 1998 she was promoted

to the position of assistant professor, in 2002 to associated professor, and in 2007 to full professor.

Since 2000 she has been the Chief of the Chair of Educational Psychology.

At the graduate program level she gives lectures in ‘’Educational psychology of gifted students’’,

‘’Methodology of teaching psychology’’ and ‘’Educational Psychology: learning and teaching’’ to

students of psychology, ‘’Psychology of learning and teaching mathematics’’ to psychology and

mathematics students, and ‘’Working with gifted students’’ to students of the Faculty of

Philosophy. Currently, she is the chief of the program Psychology of education at the postgraduate

doctoral studies while giving lectures in ‘’Cognitive models of learning: the example of

mathematics and natural sciences’’ on the same studies. She is also taking part in teaching at the

postgraduate programs of pedagogy and glotodidactics at the Faculty of Philosophy in Zagreb and

‘’Early upbringing and obligatory education’’ at the Faculty of Teacher Education. Besides

teaching at the University she has given numerous educations and lectures to teachers, principles,

psychologists and pedagogues in schools, CARNet lecturers, university assistants and professors.

Currently, she is the chief researcher on the scientific project Psychological factors of math

learning: performance, strategies, motivation and attitudes. She published over fifty scientific and

professional articles and co-authored five books (one of them is currently a university textbook

and one is university handbook). She has actively participated in more than twenty scientific

conventions in Croatia and abroad.

She has taken part in several projects of NGOs, UNICEF, UNESCO and the Institute for

education. She is the member of the Croatian psychological association, European Association for

Research on Learning and instruction (EARLI) and International School Psychology Association

(ISPA).

185

NAME: Vladimir Volenec, PhD




Zagreb


URL:


He was born in 1943 in Sređani Donji, near Daruvar. He received his B.Sc. in 1965 at the

University of Zagreb, his MSc in 1968, and his PhD in 1971 at the same institution. He has been

working at the Department of Mathematics, University of Zagreb since 1965.

He published 115 scientific papers, mostly in Geometry and Algebra. He also published

several secondary school teaching books. He received several local grants. He supervised 20 MSc

and PhD thesis, and authored 10 graduate courses. He participated in many international

conferences, and was a visiting scientist in Budapest, Graz and Prague.

186

NAME: Marko Vrdoljak, PhD

JOB TITLE: Associate professor



of Zagreb


URL:


Born in Tuzla, Bosnia and Herzegovina, on July 17th, 1972. Graduated from

Department of Mathematics, University of Zagreb in 1995 (Optimal control for the process of

heating of a rod, advisor M. Alić). Obtained MSc degree in 1999 (Homogenisation and its

applications to optimal shape design, advisor N. Antonić) and PhD in 2004 with the thesis On

some questions in relaxation theory for optimal design problems, supervised by N. Antonić.

From October 1999 till March 2000 he worked as a guest researcher at Max-Planck

Institute for Mathematics in the Sciences in Leipzig with research project titled Optimal

design and relaxation. Took a part in six scientific projects funded by the Croatian Ministry of

Science (leader of the project Mathematical modelling of geophysical phenomena and the

international project Functional analysis methods in mathematical modelling).

From 1996 to 2006 he was teaching assistent, and since 2006 he is assistant professor

at the Department of Matematics, University of Zagreb. Main areas of his scientific interest

are Partial Differential equations, Calculus of Variations and Optimal control.

187

NAME: Mladen Vuković, PhD

JOB TITLE: Associate professor

DATE OF LAST PROMOTION: 21th February 2012


Zagreb


URL: web.math.hr/~vukovic


Born in Varaždin, Croatia, on August 29th 1963. Graduated from Department of

Mathematics, Faculty of Science, University of Zagreb, with major in theoretical mathematics.

Obtained MSs degree in 1990 and PhD in 1996. PhD thesis title was Generalized Veltman models.

He has been employed at the University of Zagreb, Department of Mathematics since 1987,

first as an teaching assistant, senior assistant (1996), assistant professor (2000) and associate

professor (2012).

On the graduate study of mathematics in Zagreb he gave six courses. He taught over than

twenty undergraduate courses in pure mathematics and computer science (Mathematical Logic,

Computability, Complexity, Set Theory, Differential and Integral Calculus, Linear Algebra,

Incompleteness of Arithmetic, Mathematical Structures, …) He gave lectures on Faculty of

Transport and Traffic Sciences and Faculty of Electrical Engineering and Computing in Zagreb,

University of Osijek and University of Bihać. He was supervisor of 65 diploma thesis, two

master’s thesis and one PhD dissertation. He is the author of the book about mathematical logic.

Now, he is a head of the Seminar for mathematical logic and foundations of mathematics on the

graduate study of mathematics.

He is a member of the editorial board of Matematičko-fizički list journal and Math.e

electronic journal. For many years he has written reviews for Zentralblatt fur Mathematik and

Mathematical Reviews. From 2001 to 2005 he was head for undergraduate study of education of

Mathematics. From 2005 to 2010 he was head of integrated study Mathematics and Physics. From

2010 he is head of all undergraduate studies at Department of Mathematics.

The area of his research interest is mathematical logic, or precisely provability and

interpretability logics, and computability. He published twelve science articles and thirteen

didactical and popularization mathematical articles. His article are in the following journals:

Mathematical Logic Quarterly, Logic Journal of IGPL and Notre Dame Journal of Formal Logic.

He took a part on ten mathematical conferences. More than fifteen years he was a project

collaborator on the different science project, and he is head of a science project on mathematical

logic, now.

He is a member of the Croatian Mathematical Society and Association for mathematical

logic.


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4.5. List of teaching sites for practical teaching


provides mathematical and computer science teaching practice, with 60 hours of practice in

primary school and 60 hours of practice in high school for each student. Teaching practice is

conducted in selected primary and secondary schools in the City of Zagreb, in groups of up to 5

students (that is, in 12 groups). In the academic year 2011/12. the appointed schools were:

• primary schools: Primary School August Harambašić, Primary School August Šenoa, PS Dobriša

Cesarić, PS Fran Galović, PS Ivan Goran Kovačić, PS Malešnica, PS Gustav Krklec, PS Otok,

PS Pavlek Miškin, PS Prečko, PS Remete, PS Silvije Strahimir Kranjčević and PS Vrbani;

• high schools: II. Grammar school, V. Grammar school, IX. Grammar school, XI. Grammar

school, XV. Grammar School, Grammar School Titus Brezovacki, School of Natural Sciences

Vladimir Prelog, Technical School Ruder Boskovic.

List of schools for teaching practice will be updated for every academic year, in accordance with

designated mentors - math and computer science teachers in the appointed schools, and the needs

of this study.

4.6. Optimum number of students considering space, equipment and number of teachers

We foresee the registration of approximately 30 students in each year of studies.

4.7. Estimated costs of studies per student

Total costs of studies per student are estimated to 48 000 kn, i.e. 24 000 kn per year of

studies.

4.8. Methods for monitoring quality and performance of study programme execution

The Head of the Graduate University Programme in Mathematics and Computer Science

Education is appointed from the ranks of teachers from the faculty. His/her task is to organise

studies, coordinate its realisation and monitor the quality of courses and student performance

during each academic year.

The Council of Heads of Studies organises the performance of undergraduate and graduate

studies. In addition to heads of all undergraduate and graduate studies, the Council also includes

Assistant Head of Department, time-table coordinator, and assistant and student representatives. At

regular meetings of the Council, the student success and teaching process for the courses are

discussed.

Also, at the Department of Mathematics there is the Chair for Methods of Teaching

Mathematics and Computer Science whose objectives, among other things, are improvement and

ongoing concern about controlling the quality of teaching at the department, preparation,

implementation and evaluation of teaching, the analysis of classification procedure and student

efficiency at all study programmes.

All teachers and collaborators (assistants), for all courses they teach, have regular weekly

consultations at previously defined hours. Besides that, as support for each course, materials and

information for students are placed at web sites and students are able to discuss their courses and

studies with teachers, assistants and among themselves at appropriate Internet forums.

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Finally, in the last week of classes in each semester, the anonymous poll among students is

conducted in order to evaluate the quality of teaching for each course.

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