# 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
14 Gauss primes Problem set 4 out
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
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

#### Learning Resource Types

assignment Problem Sets