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

Course Info

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assignment Problem Sets