 Jessica Claridge graduated from Queen Mary, University of London with an MSci in Mathematics in 2012. She then went on to complete a PhD in Mathematics at Royal Holloway, University of London in 2017. She joined the University of Essex in 2016, and is currently a Lecturer in Mathematics. Her research interests include Network Coding, Combinatorics and Finite Fields.

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.

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.

Linear Algebra a Modern Introduction, 4th Edition by David Poole, published by Cengage
2015. ISBN 9781285463247

Students entering the course should be familiar with the basic ideas of arithmetic and algebra (addition, subtraction, multiplication, division, use of brackets, positive negative and fractional powers, and the solution of simple equations) as described, for example, in Haeussler, E.F., Paul, R.S. and Wood,R., Mathematical Analysis for Business, Economics and the Life and Social Sciences, 11th ed., Pearson (pp. 2-19, 30-34 and 147-151). Students should possess a basic scientific calculator. Students may take any or all of the three Parts of the course, but anyone taking Parts 2 or 3 will be presumed to be familiar with the material covered in the preceding Parts.

Lecture 1: Operations on vectors.

Lecture 2: Linear Independence and vector spaces.

Lecture 3: Geometric Interpretation of Matrices.

Lecture 4: Gaussian Elimination and Systems of Linear Equations.

Lecture 5: Matrix Inverse and Solutions of Linear Equations

Lecture 6: Linear Least Squares.

Lectures 7: Multiple Regression Problems.

Lectures 8: Eigenvalues, Eigenvectors and Symmetric Matrices.

Lectures 9: General Singular Value Decomposition (SVD) and applications

Lectures 10: Overview and Plenary Session