# MA3202 Galois theory – spring 2015

## Lecturer

Karin Erdmann

Room 834, Sentralbygg II.

Telephone 73 59 xx xx.

E-mail: erdmann at maths.ox.ac.uk

Office hours Wednesdays 11-12

no office hour Wednesday 6 May

(there will be office hours the following weeks)

## Lectures and exam

Tuesday 08.15-10.00, M24 (note change)

Friday 08.15-10.00, M24

First lecture is Tuesday January 6

Exam: June 1 at 9.00-13.00

Reference group meetings: Thursday 5 Feb

Thursday 19 March (10am)

Easter break

We start again Tuesday 14th April

(ie no lecture on Friday 10th)

## Lecture Log

Week 1 first half of ch 11 Week 2 second half of ch11. Started ch 15 Week 3 ch.15 up to 3.2 Week 4 ch.15 up to 4.2 Week 5 ch.16 Sections 1 and 2 Week 6 ch.16 Section 5. From section 4: 4.6, 4.1, 4.3, 4.4, 5.1(b). Week 7 ch.17 up to 1.6 Week 8 ch.17 examples and 2.1 Week 9 ch.17 finite fields. Start on ch18.1 Week 10 ch.18 Sections 1 and 2 Week 11 ch.18 Start on Section 3 Week 12 ch.18 finishing Section 3 Week 13 ch.18 Section 5

## General information

## Textbook

P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul

*Basic Abstract Algebra*

Cambridge University Press
Second Edition
ISBN: 0-521-46629-6

## Syllabus

Contained in the chapters 11, 15, 16, 17, 18 in the textbook

## Exercises

Going over solutions: Fridays during the first hour

#### Exercise 1

Chapter 11.1: questions 1, 2, 3, 8

Chapter 11.3: questions 2, 4, 8

Problem (posed by Fermat)

Prove that the Diophantine equation y^2+2=x^3 has only the integer solutions
y=5 or -5 and x=3.

[Hint: Use that Z[\sqrt{-2}] is a Euclidean domain with
norm N(a+b\sqrt{-2}) = a^2+2b^2.]

#### Exercise 2

Chapter 15.1: 2, 4, 6(b)

Chapter 15.2: 2, 4

Chapter 15.3: 2, 4, 6, 10

Problem 4 (Continuation Exam August 2013)

#### Exercise 3 (different from previous year)

Construct splitting fields over Q for the polynomials
x^3-1, x^4+5x^2+6, x^6-8.

Find the degrees of these fields over Q.

Chapter 16.1: 3, 4, 8

Chapter 16.2: 2, 4

Exam May 2013 problems 2b), 3, 7.

#### Exercise 4

Do True-or-False exercise:
true-or-false.pdf

Continuation Exam August 2013: Problem 5

Exam, May 2013: Problems 1, 2a, 6.

#### Exercise 5

Exam May 2009 Problem 3

Cont Exam Aug 2013 Problem 2

Exam May 2013 Problem 5

Exam May 2012 Problem 5

Exam May 2011 Problem 2

Exam May 2010 Problems 1, 5

Exam May 2009 Problem 2.

#### Exercise 6

Cont Exam Aug 2013 Problem 3

Exam 2012 Problems 1, 4

Exam 2011 Problems 1, 3, 4

Exam 2009 Problem 5

Exam 2014 Problems 4, 5, 6.

#### Exercise 7

Exam May 2010 Problems 3,4,6

Exam 2006 Problems 1, 5

Exam 2004 Problem 5

Rest of Exam 2014

## Old exams

#### Some lecture notes

On Ch 15
ch15variation.pdf

Ch 16, Splitting fields
ch16-splittingfields.pdf

Ch. 16, Separable extensions
ch16-_separable.pdf

Some comments on ch 15 and ch 16
somecomments-ch15-16.pdf

Finite fieldsfinite-field.pdf

#### Summary

#### Vocabulary

Norwegian-Englishvocabulary-galoistheory.pdf