Dominik Duell is Lecturer for Applied Quantitative Methods in the Department of Government at the University of Essex and received his PhD in Politics from New York University in 2014. He studies voting behavior, political competition, and electoral accountability in representative democracies with a special focus on how social identity relationships influence citizens’ choices. His work lies at the intersection of Political Economy, Political Behavior, Experimental Methods, and Political Psychology. In his research, Dominik builds on strategic and behavioral theories of voting and implements laboratory, field, and survey experiments to analyze how individuals evaluate their politicians’ performance, when they discriminate in favor of their social group, how they make redistributive allocation decisions, or how they coordinate their choices with their peers when forming electoral coalitions. His work is published in the American Journal of Political Science and Comparative Political Studies and has been supported by a number of different academic and government institutions, including the U.S. National Science Foundation and the French National Research Agency (ANR).

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 as a Tutor and part-time Lecturer in Mathematics. As part of her role she is the Area Coordinator for the Further Mathematics Support Programme. 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.

**Recommended 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.

**Additional Reading:**

Linear Algebra a Modern Introduction, 4th Edition by David Poole, published by Cengage

2015. ISBN 9781285463247