SUNY at Stony Brook
Department of Mathematics
SUNY at Stony Brook

Abstract Algebra

 Mat 313, Fall 2009


Time and Place : TueTh 12:50-2:10 pm; Harriman Hall 111

Instructor : Radu Laza

Office : Math Tower 4-121
Email :  rlaza@math.sunysb.edu
Class Homepage :   http://www.math.lsa.umich.edu/~rlaza/algebra09.htm

Office Hours: Tue 2:10-4; by appointment

Grader: Tsung-Yin Lin


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Course Description

Prerequisite : Math 310, 312, 318, or permission of the instructor.

Textbook : Comtemporary Abstract Algebra , 7th edition, by Joseph A. Gallian.

This course introduces students to the key concepts of the modern (i.e. abstract) algebra. We will spend most of the semester discussing the concepts of group, ring and field (Parts 2-4 in the textbook) and the main results concerning those. Time permiting, we will cover also some of the special topics of Part 5 (the selection of topics will depend on the interest of the participants). The course is mostly self-contained, but due to the abstract nature of the material it requires some familiarity with math at college level.

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Grading


Schedule

Lecture Day Topic Chapter Homework Assignments
1 Sept 1 The integers / Introduction to abstract algebra Ch. 0, 1
2 Sept 3 Groups and subgroups Ch. 2, 3 HW1 (due Sept 15)
3 Sept 8 Cyclic groups Ch. 4
4 Sept 10 Permutation groups Ch. 5
5 Sept 15 Isomorphisms, External direct prodcut Ch. 6, 8 HW2 (due Sept 24)
6 Sept 17 Cosets, Lagrange Theorem Ch. 7
7 Sept 22 Normal subgroups and Factor groups Ch. 9
8 Sept 24 Group Homorphisms Ch. 10 HW3 (due Oct 1)
- Sept 29 no class (Monday schedule)
9 Oct 1 Fundamental Theorem of finite abelian groups Ch. 11 HW4 (due Oct 8)
10 Oct 6 Review groups Part 2
11 Oct 8 Midterm 1 (covering group theory) Part 2
12 Oct 13 Further topics groups
13 Oct 15 Rings Ch. 12, 13 HW5 (due Oct 22)
14 Oct 20 Integral domains Ch. 13
15 Oct 22 Ideals and Factor rings Ch. 14 HW6 (due Nov 3)
16 Oct 27 Ring Homomorphisms Ch. 15
17 Oct 29 Polynomial Rings Ch. 16 HW7 (due Nov 10)
18 Nov 3 Factorization of Polynomials Ch. 17
19 Nov 5 Midterm 2 (covering ring theory) Part 3
20 Nov 10 Divisibility in integral domains Ch. 18 HW8 (due Nov 17)
21 Nov 12 Vector Spaces Ch. 19
22 Nov 17 Extension Fields Ch. 20 HW9 (due Nov 24)
23 Nov 19 Algebraic Extensions Ch. 21
24 Nov 24 Finite Fields
- Nov 26 Thanksgiving
25 Dec 1 Further topics on Fields HW10 (due Dec 10)
26 Dec 3 Topics HW 11 (due Dec 10)
27 Dec 8 Review
28 Dec 10 Final

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