Abstract Algebra

Instructor: Yifan Yang

Fall 2006

Instructor: Yifan Yang Abstract Algebra

Information

1 Venue: SA215.2 Time: 1:30–3:20 Mondays (lectures), 9:00–9:50

Wednesdays (lectures), 12:30–1:30 Fridays (quizzes).3 Textbook: A first course in abstract algebra, 7th ed., by

John B. Fraleigh.4 Course webpage: http://e3.nctu.edu.tw.5 Instructor: Yifan Yang.

1 Office: SA338.2 Phone: 56419.3 Email: [email protected] Office hour: Walk-in or by appointment.

6 Teaching assistants: Ms. Fang-Ting Tu and Mr. Yao-HanChen.

1 Emails: ??? and [email protected] Tutorial time/place: TBA.

Information

Grading policy

1 Weekly homework: 15%, due on each Monday.2 Weekly quizzes: 20%, 12:30–1:30 each Friday.3 Midterm: 30%, 9:00am, November 5 (Saturday), covers

Sections 0–6 and 8–11.4 Final: 30%, 9:00am, January 7 (Saturday), covers Sections

13–17 and 34–37.5 Classroom participation: 10%.

Important: The passing grade is 58 (after rounding up to thenearest integer). Absolutely no score adjustment.

Grading policy

How the class works

1 We will use slides heavily in class. The slides for eachsection are available for download before that section istaught.

2 During classes, we have in-class exercises. Typicalproblems are: find examples that satisfy a given definition,do some easy computation, and fill out missing steps inproofs. This activity constitutes 10% of the final grade(classroom participation).

3 Homework assignments are given at the end of eachsection. There are usually 7–10 problems for each section.You are required to turn in your homework for a section onthe Monday after that section is finished in class. (Thus, insome weeks, you may need to do up to 20 problems.)

How the class works

1 No late submission of homeworks is allowed since TA’s willpost the solutions to the homework on Wednesday of thesame week.

2 On Fridays, quizzes will be given. They cover the samesections as the homeworks you turn in on Monday of thesame week.

3 Homeworks are not graded upon the correctness of yoursolutions, but upon how much effort you put in. You canstill get perfect scores even if you can not solve anyproblems, provided that you explain in details thedifficulties you encounter.

How the class works

1 Do not copy other people’s homework. Every time you arecaught doing this, 5 points will be deducted from your finalscore.

2 You are expected to spend at least 4–5 hours a week,besides the lectures, on this course. (No complain please,as the instructor and the TA’s spend much more time thanyou do.)

How the class works

1 Do not copy other people’s homework. Every time you arecaught doing this, 5 points will be deducted from your finalscore.

2 You are expected to spend at least 4–5 hours a week,besides the lectures, on this course. (No complain please,as the instructor and the TA’s spend much more time thanyou do.)

What is Abstract Algebra?

According to Wikipedia, Abstract algebra is a branch ofmathematics concerning the study of structure, relation andquantity. Rather than working directly with numbers, onecan work with symbols, variables, or elements of some set.Addition and multiplication are viewed as general operations,and their precise definitions lead to structures such as groups,rings and fields.Together with geometry and analysis, algebra is one of thethree main branches of mathematics.

Why should you study abstract algebra?

1 In mathematics, groups, rings, and fields are everywhere inany serious mathematics.

2 In chemistry and material science, group theory is used toclassified crystal structures, regular polyhedra, and thesymmetry of molecules.

3 In physics, groups are used to describe the symmetrieswhich the laws of physics seem to obey, such as relativity,quantum mechanics, and particle physics.

4 In cryptography and coding theory, ring and field theory isessential. (In other words, whenever you are listening toyour CD albums, you are using field theory. Whenever youare using secured internet transmission, you are using fieldtheory as well.)

5 Finally, it is beautiful.

Abstract Algebra

Documents

Transcript of Abstract Algebra