Algebra II

Calendar

SES #	TOPICS	KEY DATES
Group Representations
1	Group representations
2	Unitary representations	Problem set 1 out
3	Characters
4	One-dimensional characters
5	The regular representation	Problem set 1 due Problem set 2 out
6	Characters (cont.)
Rings: Basic Definitions
7	Rings, ring homomorphisms	Problem set 2 due
8	Ideals, quotient rings, correspondence theorem
9	Maximal ideals, prime ideals, fractions	Problem set 3 out
Rings: Factoring
10	Gauss’ Lemma
11	Unique factorization
12	Factoring integer polynomials	Problem set 3 due
13	First quiz
Quadratic Imaginary Integers
14	Gauss primes	Problem set 4 out
15	Quadratic integers
16	Ideal factorization
17	Prime ideals	Problem set 4 due Problem set 5 out
18	Ideal classes
Linear Algebra over a Ring
19	Integer matrices
20	Free modules
21	Presenting modules	Problem set 5 due
22	Hilbert Basis Theorem	Problem set 6 out
23	Structure of abelian groups
24	Linear Operators
25	Second quiz
Fields: Field Extensions
26	Algebraic elements, degree
27	Ruler and compass	Problem set 6 due
28	Adjoining elements
29	Finite fields	Problem set 7 out
30	Primitive elements
Fields: Galois Theory
31	Symmetric functions, discriminant	Problem set 7 due Problem set 8 out
32	Splitting fields, the Galois group
33	Fixed fields, Galois extensions
34	The main theorem	Problem set 8 due Problem set 9 out
35	Cubic and quartic equations
36	Quartic equations (cont.)
37	Third quiz
38	Roots of unity, Kummer extensions
39	Quintic equations	Problem set 9 due