Group Theory Spring 2020

Description

The course introduces the basic ideas of group theory, including symmetry groups, abelian, cyclic, and permutation groups. Also subgroups, normal subgroups, group homomorphisms, quotient groups, direct products, group actions on a set, and the Sylow theorems. The theory will be illustrated by examples from geometry, linear algebra and combinatorics, and we will discuss some applications. We will cover parts of preparatory chapters 1 and 2, then the chapters 3 and 7 of the text.

Textbook

We will follow Abstract Algebra (4rd edition) by John A. Beachy and William D. Blair

Class Notes

• Chapter 1: Integers

• Chapter 2: Functions

• Chapter 3: Groups I

• Chapter 3: Groups II

• Chapter 7: Structure of Groups

Homework

• HW1

• HW2

• HW3

• HW4

• HW5

• HW6

• HW7

• HW8

Tests and Final

• Review set for Test 1

• Test 1

• Review set for Test 2

• Test 2

• Review set for Test 3

• Test 3

• Final