Number Theory and Group Theory

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Office hours:

Time: 9am – 10am Mondays.

Location: Office 2.16, 2^nd Floor, Howard House, Queens Avenue.

You may have problems getting into the 2^nd floor of Howard House, so drop me an email at sean.prendiville@bris.ac.uk to let me know you’re coming.

Lecture notes.

Part 1. Number Theory (last update 19/11/12).

Part 2. Group Theory (all sections)

Group Theory Section 1

Group Theory Section 2

Group Theory Section 3

Group Theory Section 4

Group Theory Section 5

Group Theory Section 6

Group Theory Section 7

Group Theory Section 8

Exercises.

Number Theory:

Exercise Sheet 1

Solution Sheet 1

Exercise Sheet 2

Solution Sheet 2

Exercise Sheet 3

Solution Sheet 3

Exercise Sheet 4

Solution Sheet 4

Exercise Sheet 5

Solution Sheet 5

Homework 10/10/12: Questions 1, 2, 3, 5 and 6 of Sheet 1.

Homework 17/10/12: Questions 7 and 8 of Sheet 1, Questions 1 and 4 of Sheet 2.

Homework 25/10/12: Question 2 of Sheet 2, Questions 1, 3 and 4 of Sheet 3.

Homework 31/10/12: Question 5 of Sheet 3, Questions 1 and 3 of Sheet 4.

Homework 07/11/12: Questions 1, 2, 3 and 4 of Sheet 5.

Group Theory:

Exercises for Section 1

Solutions for Section 1

Exercises for Sections 2 and 3

Solutions for Sections 2 and 3

Exercises for Sections 4 and 5

Solutions for Sections 4 and 5

Exercises for Section 6

Solutions for Section 6

Exercises for Section 7

Solutions for Section 7

Exercises for Section 8

Solutions for Section 8

Homework 14/11/12: Questions 1, 2, 3, 4 of the Exercises for Section 1.

Homework 21/11/12: Questions 5, 6, 7, 9 of the Exercises for Section 1.

Homework 28/11/12: Questions 1, 3, 4, 7, 8 of the Exercises for Sections 2 and 3.

Homework 05/12/12: Questions 1, 2, 3, 6 of the Exercises for Sections 4 and 5.

Homework 12/12/12: Questions 1, 2, 5, 6, 7, 8 of the Exercises for Section 6.

Homework 16/01/13: Questions 2, 3, 4, 5 of the Exercises for Section 7.

Homework 23/01/13: Questions 1, 2, 3, 6, 7 of the Exercises for Section 8.

Useful/interesting resources.

- Chapters 10, 11, 13 and 14 of Martin Liebeck’s book A Concise Introduction to Pure Mathematics serve as an excellent reference for the number theory part of the course.

- Chapters 1 and 2 of Davenport’s ‘Higher Arithmetic’ are also useful.

- Arthur Chatters’ lecture notes from previous years. The material is almost the same, but the order may differ.

- Peter Cameron’s lecture notes on Mathematical Structures.

- Tim Gowers on the language and grammar of mathematics, an excerpt from The Princeton Companion to Mathematics.

- Kevin Houston on 10 Ways to Think Like a Mathematician and How to Write Mathematics.

- Ben Green’s excellent talk on Patterns in the Prime Numbers.

- Melvyn Bragg’s In Our Time recently discussed Fermat’s last theorem.