**3A Mathematics for Social Scientists, Part 3 **

Dr Dan Brawn, University of Essex

8 - 19 August (two week course / 15 hrs)

**Dan Brawn** is a Lecturer in the Department of Mathematical Sciences.

### Course Content

- This component of the course focuses on solving systems of linear equations by Gaussian elimination; inverse matrices and singularity; vector spaces and subspaces; linear dependence, dimension, and rank; matrix eigenvalues and eigenvectors. It also considers the application of these topics to the linear regression problem. Finally, the course considers the method of linear algebra called ’Singular Value Decomposition’ (SVD) which lies at the heart of many useful applications.

### Course Objectives

- To provide participants with the essentials of linear algebra required for the study of multivariate analysis. Emphasis is placed on the relationship between the algebra and geometry.

### Course Prerequisites

- For participants who have not taken the second half of Mathematics for Social Scientists, Part 2, some familiarity with matrix arithmetic is helpful. However, there is a short summary of basic matrix arithmetic at the end of the part 3 course notes which is adequate for this component of the course and which will be briefly reviewed.

### Background Reading

- For a review of the concepts listed in the prerequisites we recommend the Matrices and Vectors quick reference leaflets which can be found by following the leaflets link from http://www.mathscentre.ac.uk/students.php. Note that the site also has learning resources available for these and other basic mathematical topics.

### Representative Background Reading

- G. Farin and D. Hansford, Practical Linear Algebra (A Geometry Toolbox) Third Edition 9781466579569 CRC press Taylor and Francis group
- Haeussler, E.F., Paul, R.S., and, Wood, R. 2004. Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences. Prentice Hall.
- Any suitable texts or online sources.