Introduction

Overview

Examination and evaluation

Syllabus

Homework

News

Homework 6 due December 18

Class is cancelled this week 3/4 Dec due to sickness. There is, however, Homework due December 11

Homework 4 due December 3

Syllabus for Part I: Groups

Nov 4: Lecture 1. Chapter 1.1–1.2(p.25)

Introduction to groups.

Nov 7: Exercises

Suggested exercises: Chapter 1.1: 1,5,7,9,11,20,22,28,34
Chapter 1.2: 10

Nov 11: Lecture 2. Chapter 1.2–1.4

Dihedral groups, symmetric groups, matrix groups.

Nov 14: Exercises

Suggested exercises: Chapter 1.2: 3,7,15
Chapter 1.3: 1,3,6,9,11,15
Chapter 1.4: 2,7

Nov 20: Lecture 3. Chapter 1.6,2.1–2.2, 2.4–2.5

Homomorphisms and isomorphisms, subgroups, centralizers, normalizers, generation.

Nov 21: Exercises

Suggested exercises: Chapter 1.6: 2,4,9,17
Chapter 2.1: 1,3,6,8
Chapter 2.2: 10,14
Chapter 2.4: 3,8,13

Nov 25: Lecture 4. Chapter 2.3, 3.1

Cyclic groups. Cosets, normal subgroups and quotient groups.

Nov 28: Exercises

Suggested exercises: Chapter 2.3: 23
Chapter 2.3: 1,3
Chapter 3.1: 1,3,8,10,21

Dec 3: Lecture 5. Chapter 3.2, 1.7, 2.2 (p.51–52)

Group actions and Lagrange's theorem

Dec 4: Exercises

Suggested exercises: Chapter 3.1: 24,29,33,36
Chapter 2.2: 7,13
Chapter 3.2: 1,2,16

Dec 10: Lecture 6. Chapter 3.3, 4.2, 4.3

Isomorphism theorems, orbits and stabilizers, the class equation

Dec 11: Exercises

Suggested Exercises: Chapter 3.3: 1,3
Chapter 4.2: 2,8
Chapter 4.3: 2,3,5,6,10,13,25,30

Dec 18: Lecture 7. Chapter 4.4–4.5

The Sylow theorems and applications.

Dec 19: Exercises

Syllabus for Part II: Rings

to be announces

Exam

to be announced