Introduction

Overview

Examination and evaluation

Syllabus

Homework

News

This class is over. Next course start: November 2014.

Makeup exam (Solutions)

Makeup exam (resit) on May 21, 2pm-7pm in E53

Final exam (Solutions)

Exam March 19 2pm-7pm. Ah-Ka: Q26; Kj-Wi: Q31

Syllabus for Part I: Groups

Nov 5: Lecture 1. Chapter 1.1–1.2(p.25)

Introduction to groups.

Nov 8: Exercises

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

Nov 12: Lecture 2. Chapter 1.2–1.4

Dihedral groups, symmetric groups, matrix groups.

Nov 15: Exercises

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

Nov 21: Lecture 3. Chapter 1.6,2.1–2.3, 2.5

Homomorphisms and isomorphisms, subgroups, centralizers, normalizers, cyclic groups.

Nov 22: Exercises

Suggested exercises: Chapter 1.6: 2,4,9,17
Chapter 2.1: 1,3,6,8
Chapter 2.2: 10,14
Chapter 2.3: 1,3

Nov 26: Lecture 4. Chapter 2.3–2.4, 3.1

Continuation on cyclic groups, generation. Cosets, normal subgroups and quotient groups.

Nov 29: Exercises

Suggested exercises: Chapter 2.3: 23
Chapter 2.4: 3,8,13
Chapter 3.1: 1,3,8,10,21

Dec 4: Lecture 5. Chapter 3.2, 1.7, 2.2 (p.51–52)

Group actions and Lagrange's theorem

Dec 5: Exercises

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

Dec 11: Lecture 6. Chapter 3.3, 4.2, 4.3

Isomorphism theorems, orbits and stabilizers, the class equation

Dec 12: 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 19: Lecture 7. Chapter 4.4–4.5

The Sylow theorems and applications.

Syllabus for Part II: Rings

Jan 20: Lecture 8. Chapter 7.1–7.2, 9.1

Rings, integral domains, fields. Examples

Jan 24: Exercises

Suggested exercises: Chapter 4.5: 6,7,13,14,16,18,23
Chapter 7.1: 5,6,7,8,11,16
Chapter 7.2: 1,3,5

Jan 27: Lecture 9. Chapter 7.3–7.4

Homomorphisms, ideals, quotient rings, maximal ideals and prime ideals.

Jan 30: Exercises

Suggested exercises: Chapter 7.3: 4,6,8,13,17,19,29
Chapter 7.4: 5,7,8,10,15,17

Feb 3: Lecture 10. Chapter 7.5–7.6

Rings of fractions. The Chinese Remainder Theorem.

Feb 6: Exercises

Suggested exercises: Chapter 7.5: 2,3
Chapter 7.6: 5,6,7

Feb 10: Lecture 11. Chapter 8.1–8.3

Euclidean domains, principal ideal domains, unique factorization domains.

Feb 13: Exercises

Suggested exercises: Chapter 8.1: 5,6,7,9
Chapter 8.2: 5
Chapter 8.3: 5,10
Chapter 9.2: 3,9

Feb 17: Lecture 12. Chapter 9.2–9.4

More about polynomial rings and irreducibility.

Feb 20: Exercises

Feb 24: Lecture 13. Chapter 10.1–10.3; notes

Modules, homomorphisms, quotient modules.

Feb 27: Exercises

Mar 3: Lecture 14. Chapter 12.1, 12.3; notes

Modules over principal ideal domains. The Jordan normal form

Mar 6: Exercises

Exam

Wed Mar 19, 14:00-19:00, Q26, Q31