Modern Algebra (현대대수학2)

Class Info Class Number: MATH 414-001 Dates: Sep 01 2023 - Dec 20 2023 Room: NS 318 Meeting time: Tue 15:00 - 16:20 (7A) Thu 15:00 - 16:20 (7A) Prof: Mark Siggers Office Hours Text: John B. Fraleigh's "A First Course in Abstract Algebra (7th ed.)"

Links Class Infomation Classnotes Seminar Problems

Syllabus

This is a continuation of Algebra I, in which I assume you have become familiar with Groups, including such things as Cosets, Homomorphsims, and group actions. We will follow the text, and continue with basic Ring and Field theory. This covers such things as polynomial and quotient rings and ideals; extension fields, the Sylow theorems, UFDs and, if you are well behaved, Galois Theory. Here is an approximate schedule.

Week	Sections	Topics
1	18, 19	Rings and Fields
2	20, 21	Euler's Theorem, Quotient Fields
3	22, 23	Rings of polynomials and factorisation
4	26, 27	Ideals and Factor Rings
5	29, 30	Extension Fields
6	31, 33	Algebraic Extensions, Finite Fields
7	34	Isomorphism Theorems
8	Test 1
9	35, 36	Sylow Theorems
10	37, 45	UFD
11	46, 47	Factorization
12	48, 49	Isomorphism Extension Theorem
13	50, 51	Splitting Fields and Separable Extensions
14	53, 54	Galois Theory
15	-	Test 2

Homework.

There will be suggested homework problems each week. You do not have to hand them in, people will asked to present problems from among these in the seminar. These same problems will also appear on tests.

Attendence and participation

Your attendence will be based on participation in the seminar. We will only take attendence in lectures if attendence becomes a problem. (If you will be unable to attend regularly, please let me know.)

Tests

There will be two tests. The first will be on Oct 24 or 26, the second on Dec 14 or 19. We will decide the date of the exams at least 2 weeks before the exam.

Evaluation

Attendence: 10% Tests: 2 x 45%.