Keele Badge

MAT-10083 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

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

MAT-10083 - Algebra: from Sets to Spaces
Coordinator: Christian Bean
Lecture Time: See Timetable...
Level: Level 4
Credits: 30
Study Hours: 300
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 introduces you to the language of modern mathematics and the art of writing mathematical proofs. You will work with fundamental mathematical objects such as sets and functions, study the beautiful and elegant arguments of number theory, and explore algebraic and geometric perspectives on vectors in 2,3, or n-dimensional space. You will also learn how these concepts can be applied to develop strategies for solving a wide range of mathematical problems.

Aims
To develop students' command of formal mathematical language and to give them experience of reading and writing formal mathematical arguments (proofs).
To introduce fundamental mathematical objects such as sets, functions, integers, vectors, and matrices, which underpin all subsequent topics, and to begin to explore their properties and interconnections.
To use these objects to develop powerful methods for solving problems and exploring phenomena in mathematics.

Intended Learning Outcomes

Interpret and express ideas clearly and accurately using formal mathematical language including quantifiers, conditional statements, converses, and contrapositives;: 1
evaluate, critique, and construct formal mathematical proofs using a variety of approaches such as proof by contradiction and proof by induction;: 1
make judgements and evaluate different approaches to solve problems involving fundamental mathematical objects such as sets, functions, integers, vectors, and matrices;: 2,3
state key definitions and properties of fundamental mathematical objects and utilize these to construct arguments and solve problems;: 3
apply both algebraic and geometric approaches to questions concerning vectors, lines, and planes, and extend these concepts to n-dimensional vectors;: 3
select and apply suitable matrix methods to solve problems arising in vector algebra such as systems of simultaneous linear equations or eigenvalue/eigenvector problems.: 2,3

Study hours

72 hours Lectures
24 hours Example Classes (including 3 problem sheets)
12 hours Assignment completion
2 hours final examination
190 hours private study

School Rules

None

Description of Module Assessment

1: Problem Sheets weighted 40%
Proof Problems Sheets
Three problem sheets evenly spread out over the semester. These will be designed to try and help the students with the key threshold concept, namely reading and writing formal mathematics. There will be two types of problems with this in mind. The first type will be a multiple choice question which will give four potential proofs of a mathematical statement, and the student will be expected to identify the correct solution and also give reason as to why each of the other three are incorrect. This will help familiarise student with what is expected of mathematical writing and proof. The second type of problem will be more traditional where students will be asked to prove some statements using the concepts taught within the course. Students will be marked on both the correctness of their solutions as well as their ability to express this in formal mathematical language. Each proof problem sheet will be given out during one of the weekly examples classes and it should be possible for the student to complete it during the session.

2: Assignment weighted 20%
Vectors and Matrices Assignment
A take-home assignment comprising of 3 questions concerning vectors and matrices. The questions will be of a similar nature to those in the formative problem sheets that will be covered in the weekly examples classes. Students will be given at least one week to complete the assignment and are expected to upload their solutions as a pdf to the KLE. Students should expect to spend approximately 12 hours on the assignment.

3: Exam weighted 40%
Final examination - 2 hours
A 2 hour closed-book examination consisting of approximately 6 questions worth 100 marks, all of which are compulsory.

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