Math 25700: Basic Algebra Autumn 2016
All reading and homework is from Dummit and Foote. The information below is extremely preliminary, so make a point to check the assignment problems are up to date before completing them!

The listed exercises should be handed in on the first Monday following the date they are listed unless otherwise indicated.

# Assignments Last updated: September 26, 2016

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Lec # Date Topic(s) Sections Homework; exercises due in lecture on following Monday
1 Mon 9/26 Introduction. Shuffling. 0.1 Read Chapter 0; Extra Problem Due WED.
2 Wed 9/28 The Basic Axioms. 1.1 5, 6, 7
3 Fri 9/30 The Basic Axioms, Integers Modulo n. 1.1, 0.3 1.1: 11, 12, 17, 25, 28, 30, 31, 32, 34
4 Mon 10/3 Symmetric Groups I 1.3 Extra Problem Due WED.
5 Wed 10/5 Symmetric Groups II 1.3 1, 2, 7, 9a
6 Fri 10/7 Symmetric Groups III 1.3 12, 14, 15, 16
Extra Reading Dihedral Groups 1.2 1b, 5, 9, Extra Problem Due WED.
7 Mon 10/10 Homomorphisms, Subgroups generated by Subsets of a Group 1.6 1.4: 1,7 and 1.6: 2, 4, 8, 14, 17, and 2.4:6, 7, 8, 11, 14(d)
8 Wed 10/12 Cyclic Groups, Generators and Relations 2.3 2.1: 4, 6
HT Fri 10/14 Midterm I of II
9 Mon 10/17 Quotient Groups 3.1 2.3: 3, 9
10 Wed 10/19 Quotient Groups 3.1 22, 24, 26,42
11 Fri 10/21 Lagrange's Theorem 3.2 8, 14, 15
12 Mon 10/24 Alternating Group 3.5 3.3: 3, 8
13 Wed 10/26 Alternating Group II 3.5 2,12
14 Fri 10/28 Alternating Group III
15 Mon 10/31 Group Actions 1.7, 2.2 1.7: 4, 14-16, 2.2:4, for S_3
16 Wed 11/02 Problem Session   Extra Problem Due Monday.
HT Fri 11/04 Midterm II of II
Extra Reading Centralizers, Normalizers, et. al. 3.5, 1.7, 2.2
17 Mon 11/07 Permutation Representations, Cayley's Theorem 4.1, 4.2 4.1: 2, 3 4.2: 8, 9
18 Wed 11/09 Group Actions on coset spaces
19 Fri 11/11 Conjugacy classes, Class equation 4.3 2c, 7, 10, 22
20 Mon 11/14 Sylow Theorems 4.5
21 Wed 11/16 Sylow Theorems II 4.5 6, 7, 8, 19, 21, 33, 34
22 Fri 11/18 Sylow Theorems III 4.5
23 Mon 11/21 Simple Groups 3.4
24 Mon 11/28 Imprimitive Groups 5.5
25 Wed 11/30 Simple Groups of Order at most 100
Review To be determined Review session TBA
FINAL Mon 12/5 10:30-12:30 Final Exam at some location

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