PROGRAMME OUTCOMES, PROGRAMME SPECIFIC OUTCOMES AND COURSE

OUTCOMES

NAME OF PROGRAMME: UG MATHEMATICS

CBCSS-FIRST DEGREE PROGRAMME - BSc DEGREE COURSE

PROGRAMME OUTCOME(CORE) PO 1: Student will be able to demonstrate in-depth knowledge in one of the foundational areas of the Mathematical Sciences. PO 2: Enhanced skills of reasoning, analytical and problem solving. PO 3: Students become capable to pursue further studies in Mathematics and research. PO 4: Students become capable to teach the Mathematics curriculum at the secondary level. PO 5: Communicate Mathematics effectively by oral, written, computing and graphical means. PO 6: Demonstrate skills in the use of computers for control, data acquisition, and data analysis in experimental investigations.

PROGRAMME SPECIFIC OUTCOMES(CORE)

PSO 1: A thorough knowledge of fundamental mathematical facts PSO 2: Students will be able to formulate, analyze, and solve problems through analytical and Computational techniques and apply them to other disciplines when appropriate. PSO 3:Uphold scientific integrity and objectivity in professional endeavors PSO 4:Students should attain the needed written and oral communication skills to translate their degree into a viable career path.

Semester1

Paper Code:MM 1141 Name of Paper:Methods of Mathematics

Total Teaching Hours for Semester: 72 No of Lecture Hours/Week:4

Max Marks:80 Credits:4

COURSE OUTCOME

CO1 : Gain practice in writing algebraic proofs. Intuitive idea on the methods of Induction and

Principle of Well Ordering. Study Euclid’s Algorithm and the Fundamental Theorem on Arithmetic

CO2 : Approximate solutions to problems through graphical methods. Use of computers in plotting

graphs should be demonstrated, using Open Source Software such as GeoGebra or Gnuplot CO3 : A complete characterization of graphs of second degree equations in two variables, thus getting

an algebraically unified description of conics.

Semester2

Paper Code:MM 1221 Name of Paper:Foundations Of Mathematics

Total Teaching Hours for Semester: 72 No of Lecture Hours/Week:4

Max Marks:80 Credits:3

COURSE OUTCOME

CO1 : Study more properties and applications of the idea of congruence. Getting ideas on Fermat’s and Euler’s Theorems. Apply congruence on Round Robin Tournament, RSA codes etc. CO2 : Solve problems in a range of mathematical applications using the derivative or the integral. CO3: Apply calculus to analyze rectilinear motion, solving various applied optimization problems

and practical problems.

CO4: Demonstrate areas in polar coordinates and do basic Astronomical Computation using conic

section in polar co-ordinates.

Semester3

Paper Code:MM1341 Name of Paper: Algebra and Calculus I

Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5

Max Marks:80 Credits:4

COURSE OUTCOME

CO1 : Critically study the units of the ring of congruence classes leading to the definition of an abstract group, which culminates in the Abstract Fermat’s Theorem. CO2: Detailed study of Chinese Remainder Theorem which will enable them to study Cryptography. CO3 Study the origin of the concept of vectors in physics and engineering. CO4: extend the operations of differentiation and integration to vector valued functions of a real variable, with emphasis on Geometry and Physics

Semester4

Paper Code:MM 1441 Name of Paper:Algebra and Calculus-II Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5 Max Marks:80 Credits:4

COURSE OUTCOME

CO 1 : Students will be able to understand the properties of polynomials over commutative ring.

CO 2 : student will be able to calculate limits and derivatives of functions of two or more

variables

CO 3 : Students could compute definite integrals of functions of two or three variables and

evaluate double and triple integrals for area and volume.

Semester5

Paper Code:MM 1541 Name of Paper:Real Analysis-I Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5 Max Marks:80 Credits:4

COURSE OUTCOME CO 1 : Students will be able to describe the real line as a complete, ordered field . CO 2 : student will be able to use the definitions of convergence as they apply to

sequences,series,and functions. CO 3 : Students could produce rigorous proofs of results that arise in the context of real

analysis.

Paper Code:MM 1542 Name of Paper:Complex Analysis I Total Teaching Hours for Semester: No of Lecture Hours/Week:4 Max Marks:80 Credits:3

COURSE OUTCOME CO 1 :Students will be able to define and analyse limits and continuity

forcomplexfunctionsaswellas consequences of continuity.

CO 2 : student will be able to apply the concept and consequences of analyticity and the Cauchy-

Riemann equations and of results on harmonic and entire functions.

CO 3 : Students could evaluate integral of complex functions along C.

Paper Code:MM 1543 Name of Paper:Differential Equations Total Teaching Hours for Semester: 54 No of Lecture Hours/Week:3 Max Marks:80 Credits:3

COURSE OUTCOME CO 1 :Students will be able to solve differential equations of first order using

graphical,numerical

and analytical methods and Solve and apply linear differential equations of second order .

CO 2 : Student will be able to demonstrate their understanding of how physical phenomena are

modelled by differential equations and dynamical systems.

Paper Code:MM 1544 Name of Paper:Vector Analysis Total Teaching Hours for Semester: 54 No of Lecture Hours/Week:3 Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 :Students will be able to differentiate vector fields and determine gradient vector fields and

find potential functions.

CO 2 :Student will be able to evaluate line integrals directly and evaluate surface and volume

integrals.

CO 3 : Students could apply Gauss’s Theorem and Stoke’s Theorem to solve numerous practical

problems.

Paper Code:MM 1545 Name of Paper:Abstract Algebra I Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5 Max Marks:80 Credits:4

COURSE OUTCOME

CO 1 :Students will be able to assess properties implied by the definitions of groups.

CO 2 :Student will be able to use various canonical types of groups including cyclic groups

andgroups of permutations CO 3 :Students could produce rigorous proofs of propositions arising in the context of abstract

algebra.

Paper Code:MM1551.1 Name of Paper:Operations Research Total Teaching Hours for Semester: 54 No of Lecture Hours/Week:3 Max Marks:80 Credits:2

COURSE OUTCOME CO1: Student will be able to formulate a given physical problem to a mathematical linear

programming problem.

CO2: Students will be able to transport items from ware houses to destination with minimum

cost.

CO3:They can assign jobs to machines with minimum completion time.

CO4: Project managements can be done using PERT and CPM.

Semester6

Paper Code: MM 1641 Name of Paper:Real Analysis-II Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5 Max Marks:80 Credits:4

COURSE OUTCOME

CO 1 : Students will be able to determine the continuity, differentiability, and integrability of

functions defined on subsets of the real line.

CO 2 : Student will be able determine the Riemann integrability of a bounded function and prove

a

selection of theorems concerning integration.

CO 3 : Students will be able to write solutions to problems and proofs of theorems that meet

rigorous

standards based on content, organization and coherence, argument and support, and style and

mechanics.

Paper Code:MM 1642 Name of Paper:Linear Algebra Total Teaching Hours for Semester: 72 No of Lecture Hours/Week:4 Max Marks:80 Credits:3

COURSE OUTCOME CO 1 :Students will be able to Solve systems of linear equations.

CO 2 :Students will be able to analyse vectors in R n geometrically and algebraically.

CO 3 : Students will be able to use matrix algebra and the related matrices to linear

transformations.

Paper Code:MM 1643 Name of Paper:Complex Analysis II Total Teaching Hours for Semester: 54 No of Lecture Hours/Week:3 Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 :Students will be able to analyse sequences and series of analytic functions and types of

convergence.

CO 2 :Students will be able to represent functions as Taylor, power and Laurent series, classify

singularities and poles, find residues and evaluate complex integrals using the residue theorem.

CO3: Students will be able to find difficult improper real integrals using residue theorem simply.

Also they can estimate the infinite sum in a better way

Paper Code:MM 1644 Name of Paper:Abstract Algebra II Total Teaching Hours for Semester: 54 No of Lecture Hours/Week:3 Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 :Students will be able to analyse and demonstrate examples of normal subgroups, factor

groups, ideals and factor rings.

CO 2 :Students will be able to use the concepts of isomorphism and homomorphism for groups

and rings.

CO 3 :Students will be able to produce rigorous proofs of propositions arising in the context of

abstract algebra.

Paper Code:MM 1645 Name of Paper:Computer Programming

(Practical ) Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5 Max Marks:80 Credits:4

COURSE OUTCOME CO 1 :Students will be able to use LaTeX to create documents and presentations.

CO 2 :Students will be able to exhibit facility with a Linux command line environment.

CO 3 :Students will be able to write code in Python to perform mathematical calculations and

scientific simulations.

CO4: Improve their logical ability to create more programmes to evaluate time cosuming

calculations.

Paper Code:MM 1661.1 Name of Paper:Graph Theory (Elective) Total Teaching Hours for Semester: 54 No of Lecture Hours/Week:3 Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 :Students will be able to understand the basic definitions and concepts of Graph theory

CO 2 :Students will be able to be able to formulate problems in graph theoretic terms.

CO 3 :Students will be able to carry out complete proofs for results from the course curriculum

(counting arguments, induction, indirect proofs, algorithmic proofs).

Paper Code:MM 1646 Name of Paper:Project Total Teaching Hours for Semester: 36 No of Lecture Hours/Week:2 Max Marks:80 Credits:4

COURSE OUTCOME CO 1 :Students will be able to articulate a clear research question or problem and formulate a

hypothesis

CO 2 :Students will be able to use library and other tools to search for existing body of research relevant to their topic.

CO 3 :Students will be able to articulate the relevance of their research to their coursework and

professional future, synthesizing their research, academic, and professional interests and

goals.

PROGRAMME OUTCOME(COMPLEMENTARY FOR PHYSICS) PO 1: Apply mathematical tools and methods for understanding the theory of Physics and develop the capability of applying the same in solving problems in Physics

. PO 2: Student will be able to demonstrate in-depth knowledge in foundational areas of the Mathematical Sciences. PO 3: Students become capable to pursue further studies in research. PO 4: Demonstrate a range of appropriate Mathematical and logical skills including IT competency. PO 5: Provide a systematic understanding of the concepts and theories of mathematics and their

application in the real world – to an advanced level, and enhance career prospects in a huge array of fields.

PO 6: Demonstrate skills in data acquisition, and data analysis in experimental investigations.

PROGRAMME SPECIFIC OUTCOMES(COMPLEMENTARY FOR PHYSICS)

PSO 1: Students should attain an ability to communicate reasoned arguments of a mathematical nature in both written and oral form. PSO 2: Students will be able to formulate, analyze, and solve problems through analytical and Computational techniques and apply them to other disciplines when appropriate. PSO 3:Uphold scientific integrity and objectivity in professional endeavors PSO 4: Develop proficiency in the analysis of complex physical problems and the use of mathematical or other appropriate techniques to solve them.

Paper Code:MM 1131 Name of Paper: Differentiation and Analytic

Geometry Total Teaching Hours for Semester: 72 No of Lecture Hours/Week:4 Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 : Students will be able to compute limits and derivatives of algebraic,trigonometric, and

piece-wise defined functions.

CO 2 :Students will be able to Solve problems in a range of mathematical applications in the field

of physics using the derivative .

CO 3 :Students will be able to understand the equations of different type of conic sections in

cartesian and polar coordinate systems and their applications in physics

Paper Code: MM 1231.1 Name of Paper: Integration and Vectors Total Teaching Hours for Semester: 72 No of Lecture Hours/Week:4 Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 : Students will be able to compute definite and indefinite integrals of algebraic and

trigonometric functions using formulas and substitution.

CO 2 :Students will be able to evaluate double & triple integrals for area and volume and

Solve problems in a range of mathematical applications in the field of Physics.

CO 3 : Students will be able to differentiate vector fields and determine gradient vector fields and

find potential functions.

CO 4 : Students could apply Gauss’s Theorem and Stoke’s Theorem to solve numerous

practicalproblems.

Paper Code:MM 1331.1 Name of Paper Differential Equations, Theory

of Equations and Theory of Matrices

Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5 Max Marks:80 Credits:4

COURSE OUTCOME

CO 1 : Students will be able to solve differential equations of first order using graphical

andanalytical methods and solve and apply linear differential equations of second order .

CO 2 : Students will be solve systems of linear equations and compute and use eigenvectors and

eigenvalues.

CO 3 : Students will be able to diagonalise a matrix and apply this technique in computing

matrix powers and solving system of equations.

CO 4 : Students will be able to solve polynomial equations of degree greater than two.

Paper Code:MM 1431.1 Name of Paper Complex Analysis, Fourier

Series and Fourier Transforms

Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5 Max Marks:80 Credits:4

COURSE OUTCOME

CO 1 :Students will be able to represent complex numbers algebraically and geometrically.

CO 2 : Students will be apply the concept and consequences of analyticity and the Cauchy-

Riemann equations and of results on harmonic and entire functions.

CO 3 :Students will be able to evaluate complex contour integrals directly and by the

fundamental theorem, apply the Cauchy integral theorem in its various versions, and the Cauchy

integral formula.

CO 4 : Students will be able to represent functions as Taylor, power and Laurent series, classify

singularities and poles, find residues and evaluate complex integrals using the residue theorem.

CO 5 : Students will be able to In-depth knowledge of Fourier analysis and its applications to

problems in physics.

PROGRAMME OUTCOME(COMPLEMENTARY FOR CHEMISTRY) PO 1: Apply mathematical tools and methods for understanding the theory of Chemistry and develop the capability of applying the same in solving problems in Chemistry. PO 2: Student will be able to demonstrate in-depth knowledge in foundational areas of the Mathematical Sciences. PO 3: Students become capable to pursue further studies in research. PO 4: Demonstrate a range of appropriate Mathematical and logical skills including IT competency. PO 5: Provide a systematic understanding of the concepts and theories of Mathematics and their

application in the real world – to an advanced level, and enhance career prospects in a huge array of fields.

PO 6: Demonstrate skills in data acquisition, and data analysis in experimental investigations.

PROGRAMME SPECIFIC OUTCOMES(COMPLEMENTARY FOR CHEMISTRY)

PSO 1: Students will be able to recognize the relationships between different areas of mathematics and the connections between mathematics and chemistry. PSO 2: Students will be able to formulate, analyze, and solve problems through analytical and Computational techniques and apply them to other disciplines when appropriate. PSO 3:Uphold scientific integrity and objectivity in professional endeavors PSO 4: Provide a systematic understanding of the concepts and theories of mathematics and their application in the real world – to an advanced level, and enhance career prospects in a huge array of fields.

Paper Code:MM 1131.2 Name of Paper Differentiation and Matrices

Total Teaching Hours for Semester: 72 No of Lecture Hours/Week:4

Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 : Students will be able to compute limits and derivatives of algebraic, trigonometric, and

piece-wise defined functions.

CO 2 :Students will be able to Solve problems in a range of mathematical applications in the field

of chemistry using the derivative .

CO 3 : Students will be solve systems of linear equations and compute and use eigenvectors and

eigenvalues.

CO 4 : Students will be able to diagonalise a matrix and apply this technique in computing

matrix powers and solving system of equations.

Paper Code:MM 1231.2 Name of Paper: Integration, Differential

Equations and Analytic Geometry

Total Teaching Hours for Semester: 72 No of Lecture Hours/Week:4

Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 : Students will be able to compute definite and indefinite integrals of algebraic and

trigonometric functions using formulas and substitution.

CO 2 :Students will be able to evaluate double & triple integrals for area and volume and

Solve problems in a range of mathematical applications in the field of Physics.

CO 3 : Students will be able to solve differential equations of first order using graphical

andanalytical methods and solve and apply linear differential equations of second order .

CO 4 : Students will be able to understand the equations of different type of conic sections

incartesian and polar coordinate systems and their applications.

Paper Code:MM 1331.2 Name of Paper: Vector Analysis and Theory of

Equations

Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5

Max Marks:80 Credits:4

COURSE OUTCOME

CO 1 : Students will be able to apply derivative concepts to find tangent lines to level curves.

CO 2 : Students will be able to differentiate vector fields and determine gradient vector fields

and find potential functions.

CO 3 : The integral ideas of the functions defined including line, surface and volume integrals –

both derivation and calculation in rectangular, cylindrical and spherical coordinate systems

CO 4 : Students could apply Gauss’s Theorem and Stoke’s Theorem to solve numerous practical

problems.

CO 5 : Students will be able to solve polynomial equations of degree greater than two.

Paper Code:MM 1431.2 Name of Paper: Abstsract Algebra and Linear

Transformations

Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5

Max Marks:80 Credits:4

COURSE OUTCOME

CO 1 : Students will be able to assess properties implied by the definitions of groups, rings and fields.

CO 2 : Student will be able to use various canonical types of groups (including cyclic groups and

groups of permutations). CO 3 :Students will be able to recognize the concepts of Linear independence of vectors, Linear

independence of Matrix columns.

CO 4 : Students will be able to use matrix algebra and the related matrices to linear

transformations such as rotation, reflection, projection etc. on the plane.

PROGRAMME OUTCOME(COMPLEMENTARY FOR STATISTICS) PO 1: Apply mathematical tools and methods for understanding the theory of Statistics and develop the capability of applying the same in solving problems in Statistics. PO 2: Student will be able to demonstrate in-depth knowledge in foundational areas of the Mathematical Sciences. PO 3: Students become capable to pursue further studies in research. PO 4: Demonstrate a range of appropriate Mathematical and logical skills including IT competency. PO 5: Provide a systematic understanding of the concepts and theories of Mathematics and their

application in the real world – to an advanced level, and enhance career prospects in a huge array of fields. PO 6: Demonstrate skills in data acquisition, and data analysis in experimental investigations. PO7: Evaluate hypotheses, theories, methods and evidence within their proper contexts.

PROGRAMME SPECIFIC OUTCOMES(COMPLEMENTARY FOR STATISTICS)

PSO 1: Solve complex problems by critical understanding, analysis and synthesis. PSO 2: Understand the relevance of multidisciplinary studies in developing a subject. PSO 3:Uphold scientific integrity and objectivity in professional endeavors PSO 4: Provide a systematic understanding of the concepts and theories of mathematics and their application in the real world – to an advanced level, and enhance career prospects in a huge array of fields.

Paper Code:MM 1131.4 Name of Paper: Theory of equations, Infinite

series and Analytic Geometry Total Teaching Hours for Semester: 72 No of Lecture Hours/Week:4 Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 : Students will be able to compute roots of given equation and numerical methods to find

approximate roots. CO 2 :They will be able to do vrious methods to check the existence of infinite series. CO 3 :Students will be able to understand the equations of different type of conic sections in

cartesian and polar coordinate systems and their applications in physics

Paper Code:MM 1231 .4 Name of Paper: Differential Calculus Total Teaching Hours for Semester: 72 No of Lecture Hours/Week:4 Max Marks:80 Credits:3

COURSE OUTCOME

CO 1 : Students will be able to use differentiation to statistics CO 2 :Students will be able to Solve problems to find maxima and minima CO 3 :Students will be able to use graphical analysis in statistics.

Paper Code:MM 1331.4 Name of Paper: Integration and Complex

numbers Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5 Max Marks:80 Credits:4

COURSE OUTCOME CO 1 : Students will be able to apply integration in rectilinear motion. CO 2 : Students will be able to use double and tripple integrals to find area of surfaces and

volume of solids. CO 3 : Students could apply De- Moivre’s theorem to find nth roots of unity. Separation of real

and imaginary parts of complex numbers .

Paper Code:MM 1431.4 Name of Paper: Linear Algebra Total Teaching Hours for Semester: 90 No of Lecture Hours/Week:5 Max Marks:80 Credits:4

COURSE OUTCOME

CO 1 : Students will be able to understand vector space ,orthogonality,eigen values and eigen

vectors and their relevance. CO 2 : Students will be able to do Gram Schmidt orthonormalization process. CO 3 :Students will be able to recognize the concepts of Linear independence of vectors, Linear independence of Matrix columns. CO 4 : Students will be able to use matrix algebra and the related matrices to linear transformations such as rotation, reflection, projection etc. on the plane. CO5: They can diagonalise the matrix of a linear transformation so that it is easy to handle the

transformation.