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
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.
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 |