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MAT-10071 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

For academic year: 2025/26 Last Updated: 04 December 2025

MAT-10071 - Sets, Functions and Proofs
Coordinator: Amirreza Khodadadian
Lecture Time: See Timetable...
Level: Level 4
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2025/26

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

None

Barred Combinations

None


Description for 2025/26

The aim of this module is to support your progress from the methods-based
approach to the higher levels of understanding and rigour present in degree level Mathematics. You will encounter mathematical statements, the meaning of proof, and some proof strategies. You will also gain experience of working with fundamental Mathematical objects including sets and functions. All of these techniques and ideas will be illustrated in action through an exploration of number theory.

Aims
To enable students to develop fluency in working with formal mathematical statements, arguments, and proofs, and with fundamental mathematical objects including sets, functions, and various families of numbers. To introduce topics in number theory including factorisation of integers, prime numbers, and modular arithmetic. To provide students with experience of solving problems involving these concepts.

Intended Learning Outcomes

interpret, critique and construct formal mathematical arguments concerning fundamental mathematical objects including sets, functions, and integers: 1,2,3
make judgements and evaluate different approaches to solving problems involving sets, functions, divisibility, and modular arithmetic: 2,3
state key definitions and properties of fundamental mathematical objects including sets, functions, and integers: 1,3
prove elementary theorems concerning sets, functions, divisibility, and modular arithmetic: 2,3

Study hours

36 hours lectures
12 hours Examples Classes
10 hours coursework preparation
92 hours private study

School Rules

None

Description of Module Assessment

1: Class Test weighted 20%
Proof comprehension class test
A multiple choice 40-minute class test. This consists of a set of questions with 4 possible solutions. Students will be graded for identifying the correct solutions, and also for giving reasoning why the other three are not correct.

2: Assignment weighted 20%
Take-home, written assignment.
A take-home assignment comprising approximately 5 questions designed to assess students' progress towards the ILOs relating to problem solving. Solutions will be uploaded to the KLE. Students should expect to spend 10 hours on the assessment.

3: Exam weighted 60%
Two hour examination
The examination paper will consist of no less than five and no more than eight questions all of which will be compulsory. The examination will be closed book

The University undertakes a continuous review of its teaching and research provision to ensure programmes are of a high quality and changes may be made to modules where it is necessary and reasonable to do so. Please be aware that minor changes to modules, such as a change to an individual assessment, can occur up until enrolment, although we endeavour to give you as much notice as possible of any changes. Details about the circumstance in which changes are made to programmes can be found in the Student Agreement, available at: https://www.keele.ac.uk/legalgovernancecompliance/governance/actcharterstatutesordinancesandregulations/studenttermsconditions/

Last Updated: 04 December 2025