Number Theory

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 function.

Additional outcomes:

Outline content:
Number theory is a subject which has been studied for well over two thousand years. It deals with the integers and has the feature that the questions are easy to understand, but often surprisingly difficult to answer - many of the properties of prime numbers have this feature, for example. The main topics are the ideas of divisibility, prime numbers, factorisation and congruences, with applications, and 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

Summative Assessment Methods:

Written exam 100%

Other information on summative assessment:
One examination paper.

Formative assessment methods:
Problem sheets

Penalties for late submission:
The Module Convener 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 40% overall.