Module manager: Robert Barham
Email: R.J.Barham@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2024/25
Grade B in A-level Mathematics or equivalent.
| MATH1005 | Core Mathematics |
| MATH1010 | Mathematics 1 |
| MATH1012 | Mathematics 2 |
| MATH1331 | Linear Algebra with Applications |
This module is approved as a discovery module
Linear Algebra is the formal, detailed theory which covers the ideas involved in solving simultaneous equations, and using matrices and determinants. This course starts by treating simultaneous equations in full generality, and introduces the notions involved in matrices and vector spaces. These basic ideas will be used and expanded in a wide variety of further mathematics modules, and are essential for understanding much of numerical computing. Hence this (or an equivalent) is an essential module for all students of mathematics and many others.
A first introduction to Linear Algebra, and in particular to the use of matrices.
On completion of this module, students should be able to:
(a) solve systems of linear equations
(b) perform elementary matrix algebra
(c) solve simple eigenvalue problems.
1. General systems of linear equations: Reduction by elementary row operations to echelon form; solution from echelon form by back substitution.
2. Matrices and matrix algebra: Elementary matrices and inverse of a matrix.
3. Determinants: Definition by expansion, effect of elementary operations, evaluation.
4. Concrete vector spaces and subspaces: Definitions of span and linear combination; linear dependence. Basis and dimensions of a vector space. Rank. Linear maps.
4. Eigenvalues and eigenvectors: Characteristic polynomial for eigenvalues. Eigenvalues and eigenvectors of symmetric matrices. Classification of critical points of multivariate maps.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 22 | 1 | 22 |
| Tutorial | 5 | 1 | 5 |
| Private study hours | 73 | ||
| Total Contact hours | 27 | ||
| Total hours (100hr per 10 credits) | 100 | ||
Studying and revising of course material.
Completing of assignments and assessments.
Regular example sheets.
!!! In order to pass the module, students must pass the examination. !!!
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 15 |
| Total percentage (Assessment Coursework) | 15 | |
There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 0 Mins | 85 |
| Total percentage (Assessment Exams) | 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 10/4/2023
Errors, omissions, failed links etc should be notified to the Catalogue Team