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MA222 Half Unit

Further Mathematical Methods (Linear Algebra)

**This information is for the 2022/23 session.**

**Teacher responsible**

Dr James Ward

**Availability**

This course is compulsory on the BSc in Data Science. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

**Pre-requisites**

Students should ideally have taken the course Mathematical Methods (MA100) or equivalent, entailing intermediate-level knowledge of linear algebra, linear independence, eigenvalues and diagonalisation.

**Course content**

This course develops ideas first presented in MA100. It consists of the linear algebra part of MA212, covering the following topics: Vector spaces and dimension. Linear transformations, kernel and image. Real inner products. Orthogonal matrices, and the transformations they represent. Complex matrices, diagonalisation, special types of matrix and their properties. Jordan normal form, with applications to the solutions of differential and difference equations. Singular values, and the singular values decomposition. Direct sums, orthogonal projections, least square approximations, Fourier series. Right and left inverses and generalized inverses.

**Teaching**

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours in the Lent Term.

**Formative coursework**

Written answers to set problems will be expected on a weekly basis.

**Indicative reading**

The following is a useful background text:

- Martin Anthony and Michele Harvey, Linear Algebra: Concepts and Methods (Cambridge University Press 2012).

**Assessment**

Exam (100%, duration: 1 hour and 30 minutes) in the summer exam period.

** Key facts **

Department: Mathematics

Total students 2021/22: Unavailable

Average class size 2021/22: Unavailable

Capped 2021/22: No

Value: Half Unit

**Course selection videos**

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

**Personal development skills**

- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills