ECPR

Install the app

Install this application on your home screen for quick and easy access when you’re on the go.

Just tap Share then “Add to Home Screen”

ECPR

Install the app

Install this application on your home screen for quick and easy access when you’re on the go.

Just tap Share then “Add to Home Screen”

Linear Algebra and Calculus: Mathematical Foundations for Social Science Statistics

Kristin Makszin
kristin.makszin@gmail.com

Central European University

Course Dates and Times

Thursday 28 - Saturday 30 July

10:00-12:00 and 14:00-17:00

15 hours over 3 days

Prerequisite Knowledge

Basic algebra (secondary school level)


Short Outline

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 mathematical language and approaches 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. The examples are taken from social science and the instructor will emphasize the areas of applied research where each concept is used. 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.


Long Course Outline

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.

Day Topic Details
Thursday Calculus (~3 hours)

Calculus:

  • Derivatives
  • Integrals

Applications: identifying minimum and maximum points, optimization, convergence and divergence of series, …

Friday Linear algebra

Linear algebra

  • Working with vectors and matrices
  • Simultaneous linear equations
  • Eigenvalues and eigenvectors

Applications and notation for regression analysis

Thursday Functions and Notation (~2 hours)

Functions and notation

  • Mathematical properties of and equations for functions
  • Polynomial functions
  • Logarithms
  • Limits
  • Sequences and series
Saturday Probability theory

Probability theory

  • Permutations, combinations
  • Random variables
  • Probability distributions: Normal, Binomial, Poisson
  • Conditional probability and Bayes Law
  • Odds
Day Readings
Thursday

Timothy M. Hagle, Basic Math for Social Scientists: Concepts, Quantitative Applications in the Social Sciences 108 (Thousand Oaks, Calif: Sage, 1996), chapter 1.

 

Gudmund R. Iversen, Calculus, Quantitative Applications in the Social Sciences 110 (Thousand Oaks, Calif: Sage Publications, 1996), chapters 2 and 3.

Friday

Krishnan Namboodiri, Matrix Algebra: An Introduction, Quantitative Applications in the Social Sciences 38 (Beverly Hills: Sage Publications, 1984), pages 7-38.

 

Jeff Gill, Essential Mathematics for Political and Social Research, Analytical Methods for Social Research (Cambridge ; New York: Cambridge University Press, 2006), chapters 3 and 4.

Saturday

Jeff Gill, Essential Mathematics for Political and Social Research, Analytical Methods for Social Research (Cambridge ; New York: Cambridge University Press, 2006), chapters 7 and 8.

 

Tamás Rudas, Probability Theory: A Primer, Quantitative Applications in the Social Sciences 142 (Thousand Oaks, CA: Sage, 2004).

Software Requirements

None

Hardware Requirements

None

Literature

See online sources and recommended readings on the course website.


Additional Information

Disclaimer

This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc). Registered participants will be informed at the time of change.

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, please contact us before registering.