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MAT-20035 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

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

MAT-20035 - Exploring Algebra and Analysis
Coordinator: Paul Truman Room: MAC2.16 Tel: +44 1782 7 33246
Lecture Time: See Timetable...
Level: Level 5
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

MAT-10046 Calculus,
MAT-10047 Algebra.

Barred Combinations

None.

Description for 2025/26

Algebra and Analysis are two central areas of Pure Mathematics.
In Linear Algebra, you'll build on the vector and matrix algebra from Level 4 by exploring abstract vector spaces. You'll focus on using bases to describe elements within these spaces.
In Analysis, you'll dive into the study of the infinitely small and infinitely large, and explore the rigorous foundations of Calculus.
You will encounter new topics via guided investigations, develop the theory via lectures, and consolidate your knowledge via practice sessions.

Aims
This module will give students a grounding in Linear Algebra and Real Analysis, two of the major branches of Pure Mathematics. Topics will be introduced via guided investigations and developed more formally via lectures. In this way students will gain insight into the different styles of thinking required for each of these branches.

Intended Learning Outcomes

define and identify concepts from linear algebra such as vector spaces, subspaces, linearly independent sets, and dimension: 1,2
define and identify concepts from real analysis such as bounded, monotonic, or convergent sequences of real numbers: 2
state, prove and apply fundamental theorems of linear algebra related to abstract vector spaces and of real analysis related to sequences of real numbers: 2
select and apply appropriate concepts from linear algebra or real analysis to solve theoretical problems: 1,2
make judgements and evaluate different approaches to problem solving
: 1,2

Study hours

Active Learning Hours:
Exploration sessions: 12 hours
Lectures: 24 Hours
Practice sessions: 12 hours
Independent Study Hours:
Preparation for and completion of assignments: 12 hours
Consolidation of lecture material: 64 hours
Examination preparation: 24 hours
Final examination: 2 hours.

School Rules

None.

Description of Module Assessment

1: Assignment weighted 30%
Linear Algebra Assignment
An assignment comprising approximately 5 questions design to examine students' progress towards the ILOs concerning identifying and applying fundamental concepts of linear algebra. Solutions will be uploaded to the KLE. Students should expect to spend 12 hours on the assessment.

2: Exam weighted 70%
2-hour unseen examination
The examination paper will consist of no less than five and not more than eight questions all of which are 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