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MAT-20049 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

For academic year: 2026/27 Last Updated: 17 March 2026

MAT-20049 - Real Analysis
Coordinator: Peter Fletcher Room: MAC2.36 Tel: +44 1782 7 33260
Lecture Time: See Timetable...
Level: Level 5
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2026/27

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

None

Barred Combinations

None

Description for 2026/27

This module provides a rigorous mathematical framework for real analysis justifying the previously studied methods of calculus for functions of a single variable. The module will study infinite series, limits of functions, continuity and differentiation from a rigorous point of view. The results covered enable calculus to be placed on a secure theoretical footing. An understanding of the core techniques in analysis is advantageous when studying certain level 6 modules.

Aims
The aim of this module is to provide students with core knowledge of real analysis, which provides rigorous mathematical justification to methods studied previously in calculus. In particular, the module is concerned with infinite series, limits of functions, continuity and differentiation.

Intended Learning Outcomes

state clearly the key definitions and theorems of real analysis related to infinite series, limits of functions, continuity and differentiation: 1,2,3
prove and apply the key theorems of real analysis related to infinite series, limits of functions, continuity and differentiation: 1,2,3
use the concepts and theory covered in the module to develop mathematical and logical arguments: 1,2,3
use the concepts and theory covered in the module to make judgements and to evaluate different approaches to solving problems: 1,2,3

Study hours

48 hours of scheduled classes, including lectures and tutorials
20 hours preparing to assessment
80 hours independent study
2 hours unseen examination

School Rules

None

Description of Module Assessment

1: Exam weighted 70%
Examination
2-hour closed-book end of module examination, containing no less than five and no more than eight questions.

2: Class Test weighted 15%
Class test
40-min class test on limits. Students are expected to spend about 10 hours in preparation.

3: Class Test weighted 15%
Class test
40-min class test on real analysis for functions of one variable. Students are expected to spend about 10 hours in preparation.

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: 17 March 2026