Mat 313 (Fall '10)

Department of Mathematics
SUNY at Stony Brook

Abstract Algebra

Mat 313, Fall 2010

Time and Place : TueTh 11:20-12:40; Physics P124

Instructor : Radu Laza

Office : Math Tower 4-121
Email : rlaza@math.sunysb.edu
Class Homepage : http://www.math.sunysb/~rlaza/algebra10.htm

Office Hours: Thr 2-3

Grader: Jan Gutt

Quick Links

Schedule
HW10 (due Dec 9)
HW11 (due Dec 14)
Sample Final

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. The course is mostly self-contained, but due to the abstract nature of the material it requires some familiarity with math at college level.

Announcements

Welcome! This is the main page for Abstract Algebra (Mat 313, Fall 2010).
Please check frequently this webpage for HW assignments, schedule, and announcements.
The first midterm will be in class on Oct. 12th (Tuesday). To prepare for the midterm review the notes (including the textbook, but pay special attention to the examples discussed in class), the HW assignments (esp. HW4), and the Sample Midterm (last year midterm). The material will cover the group chapters (Ch 1-11). You should understand well the notion of order, cyclic group and abelian group (including structural results). We will have a review session on Oct 7.
The second midterm will be in class on Nov. 16th (Tuesday). It will cover exclusively the chapters on rings. Review the midterm from last year and the current HW.

Grading

There will be 2 midterms (in class) and a final. There will be approximately 10 homework assignments.
The exams count for 80% of the final grade. The division is roughly: 40% for the final and 20% for each midterm. The remaining 20% will be for the homework assignments.

Schedule

Lecture	Day	Topic	Chapter	Homework Assignments
1	Aug 31	Introduction to abstract algebra	Ch. 0, 1
2	Sept 2	Groups	Ch. 2
3	Sept 7	Subgroups	Ch. 3	HW1 (due Sept 16)
-	Sept 9	no class
4	Sept 14	Cyclic groups, Permutation groups	Ch. 4, 5
5	Sept 16	Isomorphisms	Ch. 6	HW2 (due Sept 23)
6	Sept 21	Cosets, Lagrange Theorem	Ch. 7
7	Sept 23	External direct product	Ch. 8	HW3 (due Sept 30)
8	Sept 28	Normal subgroups and Factor groups	Ch. 9
9	Sept 30	Group Homorphisms	Ch. 10	HW4 (due Oct 7)
10	Oct 5	Fundamental Theorem of finite abelian groups	Ch 11
11	Oct 7	Review groups	Part 2
12	Oct 12	Midterm 1 (covering group theory)
13	Oct 14	Rings	Ch. 12
14	Oct 19	Integral domains	Ch 13	HW5 (due Oct 28)
15	Oct 21	no class
16	Oct 26	Ideals and Factor rings	Ch. 14
17	Oct 28	Ring Homomorphisms	Ch. 15	HW6 (due Nov 4)
18	Nov 2	Polynomial Rings	Ch. 16
19	Nov 4	Factorization of Polynomials	Ch. 17	HW7/8 (due Nov 16)
20	Nov 9	Divisibility in integral domains	Ch. 18
21	Nov 11	Review rings	Part 3
22	Nov 16	Midterm 2 (covering ring theory)
23	Nov 18	Vector Spaces	Ch. 19
24	Nov 23	Extension Fields	Ch. 20	HW9 (due Dec 2)
-	Nov 25	Thanksgiving
25	Nov 30	Algebraic Extensions	Ch. 21
26	Dec 2	Finite Fields	Ch. 22	HW10 (due Dec 9)
27	Dec 7	Further topics fields	Part 4
28	Dec 9	Review		HW11 (Dec 14)
	Dec 14	Final (2:15-4:45 in Phys 124)

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