# Number Theory and Geometry

For an overview of the module, including aims and learning outcomes, click here.

Course materials for this module will be placed on this page once they become available. The Number Theory part is being taught by Manuel Breuning; the Geometry part is being taught by Sarah Hart.

All lectures are in room B20 (Malet Street), 6-9pm. Lecture dates:

Number Theory | 12, 19 and 26 October 2012; 2, 16, 23 and 30 November 2012; 7 December 2012. |

Geometry | 18, 25 Jan; 1, 8 Feb; 1, 8, 15, 22 March 2013. |

Revision lectures | Number Theory: 26 April 2013 |

### Geometry Notes and Resources are on .

### Additional Information for the Number Theory Part

Lecturer contact details:

Email: manuel.breuning@gmail.com

### Lecture Notes

Number Theory notes, Corrections to the Number Theory notes

Solutions to the exercises in the Number Theory notes

Quiz, 19/10/2012, Quiz, 16/11/2012, Solutions to the quizzes

### Assignments

Each assignment is worth 5% of the marks for this module. Marks for late submissions are capped at 40% for undergraduate programmes and 50% for postgraduate programmes, and submissions that are more than 14 days late will receive 0.

- Assignment 1 (due date: Monday 26 November 2012)
- Solutions to Assignment 1
- Assignment 2 (due date: Friday 18 January 2013)
- Solutions to Assignment 2

### Revision Lecture

Revision Quiz, Solutions to the revision quiz

Additional Revision Questions (discussed in the revision lecture)

### Additional Materials

J.W. Bruce, *A Really Trivial Proof of the Lucas-Lehmer Test. *The American Mathematical Monthly, 100(4): 370-371, 1993. * *

CrypTool (Free software for exploring cryptography.)

### Past Exam Papers

- sample paper page 1: Z
^{+}is the set of positive integers which this year was denoted by N - sample paper page 4, Question 9.(a) i): should be 3 (mod 4)
- sample paper page 4, Question 10.(d): should be (5/151)=1

exam paper 2011 solutions to the Number Theory questions

- exam paper page 1: Z
^{+}is the set of positive integers which this year was denoted by N