## MA4Z7-Number Theory

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Autumn term module
Pre-requisites: MA1RA1 Real Analysis I or MA1AN1 Analysis I or MA2RA1 Real Analysis I and MA1ALG Algebra I or MA2ALG Algebra I
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3Z7 Number Theory
Module version for: 2017/8

Module Convenor: Dr Chris Daw

Summary module description:

This module covers the theory of numbers.

Aims:

To put on a rigorous basis some fundamental facts about the integers that are familiar to all students at an intuitive level; to introduce topics which are easily appreciated, but whose solutions are much less easy.

Assessable learning outcomes:

By the end of the module students are expected to be able to:

•    use the ideas of factorisation, prime numbers and congruence of numbers,

•    solve appropriate problems in these areas.

•    manipulate arithmetical functions.

•    manipulate Dirichlet series

•    make some elementary estimates of the average of arithmetical functions.

This module will be assessed to a greater depth than the excluded module MA3Z7.

Outline content:

The main topics are:

• divisibility and prime numbers;

• congruences and modular arithmetic;

• a study of arithmetical functions.

For the latter we introduce their Dirichlet generating functions and use these to obtain their average behaviour.

Brief description of teaching and learning methods:

Lectures supported by problem sheets.

Contact hours:
 Autumn Spring Summer Lectures 20 Guided independent study 80 Total hours by term 100.00 Total hours for module 100.00

Summative Assessment Methods:
 Method Percentage Written exam 100

Other information on summative assessment:

Formative assessment methods:

Problem sheets.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Length of examination:

2 hours.

Requirements for a pass:

A mark of 50% overall.

Reassessment arrangements:

One examination paper of 2 hours duration in August/September.