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Maths Refresher – FREE COURSE

Course Dates and Times

Monday 17 – Friday 21 February, 08:00–08:50
This is a FREE supplementary course. You must register and pay for a one-week or two-week course in order to take it. To book, please check the box when registering.

Susumu Shikano

susumu.shikano@uni-konstanz.de

Institution: Universität Konstanz

Quick maths refresher focusing on topics essential to better understand analytical tools in modern social scientific research.

Such tools include statistical models (e.g. linear regression, factor analysis), estimation techniques (e.g. least squares, maximum likelihood), measurement, formal modelling, and all kinds of inferences.

The course deals with:

logic
algebra
calculus
matrix
probability

Logic is essential for sound inferences as well as for theory formation. Algebra, calculus and matrices are essential for formal modelling and for better understanding statistical models and estimation techniques. Probability playes a crucial role in statistical models as well as measurement of theoretical concepts.

We won't be able to discuss individual topics thoroughly in such a short space of time. Instead, I will emphasise the relationship between mathematics and individual aspects of social science research.

After this course, you can extend your knowledge of maths through the recommended readings, depending on your areas of interest.

Instructor Bio

Susumu Shikano is Professor of Political Methodology at the University of Konstanz. His research interests are spatial models of politics and various topics in political behaviour.

His work has appeared in journals including Public Choice, Political Psychology, Party Politics, West European Politics, and the British Journal of Political Science.

@SusumuShikano

THIS IS THE WINTER SCHOOL 2019 OUTLINE

Basic algebra (secondary school level)

Day	Topic	Details
Monday	Logic	Basic concepts (connectives, predicates, quantifiers) Inference
Tuesday	Algebra	Variables Functions and Equations
Wednesday	Matrix algebra	Calculation with matrices Inverses of matrices A system of equations in matrix form Determinants
Thursday	Calculus	Differential calculus Partial derivatives Integration
Friday	Probability	Probability axioms Probability functions Random variables Joint and marginal distributions

Day	Readings
Monday	Patrick Suppes (1957) Introduction to Logic Chapters 1–4 Dover
Tuesday	Jeff Gill (2006) Essential Mathematics for Political and Social Research Chapter 1 Cambridge University Press
Wednesday	Jeff Gill (2006) Essential Mathematics for Political and Social Research Chapters 3–4 Cambridge University Press
Thursday	Jeff Gill (2006) Essential Mathematics for Political and Social Research Chapters 5–6 Cambridge University Press
Friday	Jeff Gill (2006) Essential Mathematics for Political and Social Research Chapters 7–8 Cambridge University Press

Software Requirements

None

Hardware Requirements

None

Literature

Austen-Smith, D.; Banks, J. S. (1999)
Positive Political Theory I: Collective Preference
University of Michigan Press

Austen-Smith, D.; Banks, J. S. (2005)
Positive Political Theory II: Strategy and Structure
University of Michigan Press

Gary King (1989)
Unifying Political Methodology: The Likelihood Theory of Statistical Inference
University of Michigan Press

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