Introductory description

This module allows students to develop a fluency with the algebra of matrices and vectors, and an understanding of topics related to linear transformations, in particular eigenvalues and eigenvectors, coordinate transformations, and matrix diagonalisation and its applications. This provides students with a deeper understanding of techniques used in mathematical economics and econometrics.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module will typically cover the following topics: Vector and matrix algebra; Vector spaces and coordinate systems; Linear transformations; Eigenvalues and eigenvectors; Simultaneous equations; Matrix diagonalisation; Inner products; Symmetric matrices; Quadratic forms.

Learning outcomes

By the end of the module, students should be able to:

• Subject knowledge and understanding: … demonstrate an understanding of symbolic logic, basic properties of number systems, vectors and matrices in R2, R3 and Rn, vector spaces, linear maps, quadratic forms and their applications to certain sorts of problems (solving systems of simultaneous equations, long-term behaviour of coupled recurrence relations, etc). The teaching and learning methods that enable students to achieve this learning outcome are: Lectures, tutorials, problem sheets and independent study. The assessment methods that measure the achievement of this learning outcome are: Problem sheets, online quizzes and unseen examination.
• Key skills: …understand formal mathematical definitions and theorems, and apply them to solve problems in linear algebra. The teaching and learning methods that enable students to achieve this learning outcome are: Lectures, tutorials, problem sheets, online quizzes and independent study. The assessment methods that measure the achievement of this learning outcome are: Problem sheets, online quizzes and unseen examination.

Indicative reading list

Please see Talis Aspire link for most up to date list.

View reading list on Talis Aspire

Subject specific skills

Students will have the opportunity to develop skills in:
Analytical thinking and communication
Analytical reasoning
Critical thinking
Problem-solving
Abstraction

Transferable skills

Students will have the opportunity to develop:
Numeracy and quantitative skills
Written communication skills
Oral communication skills
Mathematical, statistical and data-based research skills