MA1LA: Linear Algebra

Module code: MA1LA

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: 4

When you’ll be taught: Semester 2

Module convenor: Dr Peter Chamberlain , email: p.g.chamberlain@reading.ac.uk

Pre-requisite module(s): Before taking this module, you must have at least a grade B in A-Level Mathematics grade B, or equivalent. (Open)

Co-requisite module(s): IN THE SAME YEAR AS TAKING THIS MODULE YOU MUST TAKE MA1CA (Compulsory)

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2025/6

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 12 May 2025

Overview

Module aims and purpose

To introduce the mathematics of linearity needed for other modules. Taking as our starting point the need to be able to solve systems of linear equations and determine eigenvalues and eigenvectors we develop the algebra of matrices which we use as a stepping stone to the more general theory of linear spaces. 

Module learning outcomes

By the end of the module, it is expected that students will be able to: 

1. Perform operations in matrix algebra. 
2. Prove statements in matrix algebra. 
3. Determine inverses, determinants, the solution of linear equations, eigenvalues and eigenvectors. 
4. Use the concepts of linear space, linear independence, dimension and linear mapping, to carry out appropriate calculations in a variety of contexts. 

Module content

Matrices feature in many areas of mathematics, particularly in applicable and numerical mathematics. The theory of matrices, their properties and application also play a key role in the sciences, engineering, social sciences, and computing. 

This module comprises both an introduction to matrix theory and its applications, and an introduction to the basic theory of vector spaces and linear transformations in a more abstract framework, which leads to simple, more transparent proofs of many results and provides further tools to treat problems in mathematics, engineering and physics. 

The abstract view of vector spaces is indispensable for infinite-dimensional spaces, which appear in other branches of mathematics (such as functional analysis and operator theory) and applications (such as the theory of differential equations and quantum physics). 

Structure

Teaching and learning methods

Lectures supported by problem sheets, and tutorials. 

Study hours

At least 54 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.