Module code: MAT2051

Module provider


Module Leader

FISHER D Dr (Maths)

Number of Credits


ECT Credits



FHEQ Level 5

JACs code

Module cap (Maximum number of students)


Module Availability

Semester 2

Overall student workload

Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION 80%
School-timetabled exam/test CLASS TESTS 20%

Alternative Assessment


Prerequisites / Co-requisites

MAT1031 Algebra

Module overview

This module introduces students to some aspects of number theory, combinatorics and set theory. It complements other pure mathematics modules by considering a variety of topics not encountered elsewhere.

Module aims

Learning outcomes

Attributes Developed

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

Indicative content includes:

Review of basics:Euclidean algorithm, prime factorization, congruences, Euler’s totient function.

Chinese Remainder Theorem, Fermat's Little Theorem, Wilson's Theorem.

RSA cryptography.

Arithmetic functions. Möbius inversion.

Quadratic residues. Quadratic reciprocity. Euler's criterion. The Legendre symbol.

Simple Diophantine equations.

Recurrence relations, generating functions, partitions.

Binomial identities and their application to combinatorial problems.

Axioms of set theory. Relations on sets.Ordered sets.The axiom of choice.

Countability.  Cardinal and ordinal numbers. 

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

Knowledge of the theory and practice of the topics covered.

Experience of the methods used to interpret, understand and solve problems in these areas.


The learning and teaching methods include:

Three 50-minute lectures per week for eleven weeks, some being used as problem classes.

Online notes supplemented by additional examples in lectures.

Two unassessed coursework assignments, marked and returned.

Personal assistance given to individuals and small groups in office hours.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to

construct and interpret mathematical arguments in the context of this module;

display subject knowledge by recalling key definitions and results;

apply the techniques learnt to both routine and unfamiliar problems.


Thus, the summative assessment for this module consists of:

One two-hour examination at the end of Semester 2, worth 80% of the module mark.

One class test, worth 20% of the module mark.


Formative assessment and feedback

Students receive written comments on their marked coursework assignments.  Verbal feedback is provided in lectures and office hours.


Reading list

Reading list for NUMBERS AND SETS :

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.