Linear Algebra and Calculus: Mathematical Foundations for Social Science Statistics

This course is designed to provide critical mathematical background for applications in quantitative social science research. The course will provide an overview of the essential concepts and language required for competent analysis using quantitative approaches in social science. It can also serve as a good refresher of relevant material before participation in a main course for those with an existing mathematical background. The topics focus on dimensions of linear algebra, calculus, and probability theory that are most commonly applied in social science research. Therefore instead of a comprehensive mathematical approach, the course will focus on the most critical concepts and approaches needed for deeper understanding of tools like multivariate regression, logistic regression, principle component analysis, structural equation modeling, and other statistical methods. The examples are taken from social science and the instructor will emphasize the areas of applied research where each concept is used as it is presented. The material will be introduced through interactive lectures with opportunities for participants to engage with the material during the sessions and through exercises between the sessions.

The planned structure will include:

• A brief introduction to important mathematical functions and notation
  • Mathematical properties of and equations for functions
  • Polynomial functions
  • Logarithms
  • Limits
  • Sequences and series
• Calculus
  • Derivatives
  • Integrals
  • Applications: identifying minimum and maximum points, optimization, convergence and divergence of series, …
• Linear algebra
  • Working with vectors and matrices
  • Simultaneous linear equations
  • Eigenvalues and eigenvectors
  • Applications and notation for regression analysis
• Probability theory
  • Permutations, combinations
  • Random variables
  • Probability distributions: Normal, Binomial, Poisson
  • Conditional probability and Bayes Law
  • Odds

Please inform the instructor of the main courses that you will participate in, as the content may be adapted accordingly.

Basic algebra (secondary school level)