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Mathematics for Social Scientists

Mathematics for Social Scientists

October 2015 | 408 pages | SAGE Publications, Inc
Written for social science students who will be working with or conducting research, Mathematics for Social Scientists offers a non-intimidating approach to learning or reviewing math skills essential in quantitative research methods. The text is designed to build students’ confidence by presenting material in a conversational tone and using a wealth of clear and applied examples. Author Jonathan Kropko argues that mastering these concepts will break students’ reliance on using basic models in statistical software, allowing them to engage with research data beyond simple software calculations.

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1. Algebra Review





Summations and Products

Solving Equations and Inequalities

2. Sets and Functions
Set Notation


Venn Diagrams



3. Probability
Events and Sample Spaces

Properties and Probability Functions

Counting Theory

Sampling Problems

Conditional Probability

Bayes' Rule

4. Limits and Derivatives
What is a Limit?

Continuity and Asymptotes

Solving Limits

The Number e

Point Estimates and Comparative Statics

Definitions of the Derivative


Shortcuts for Finding Derivatives

The Chain Rule

5. Optimization

Finding Maxima and Minima

The Newton-Raphson Method

6. Integration
Informal Definitions of an Integral

Riemann Sums

Integral Notation

Solving Integrals

Advanced Techniques for Solving Integrals

Probability Density Functions


7. Multivariate Calculus
Multivariate Functions

Multivariate Limits

Partial Derivatives

Multiple Integrals

8. Matrix Notation and Arithmetic
Matrix Notation

Types of Matrices

Matrix Arithmetic

Matrix Multiplication

Geometric Representation of Vectors and Transformation Matrices

Elementary Row and Column Operations

9. Matrix Inverses, Singularity, and Rank
Inverse of a (2 x 2) Matrix

Inverse of a Larger Square Matrix

Multiple Regression and the Ordinary Least Squares Estimator

Singularity, Rank, and Linear Dependency

10. Linear Systems of Equations and Eigenvalues
Nonsingular Coefficient Matrices

Singular Coefficient Matrices

Homogeneous Systems

Eigenvalues and Eigenvectors

Statistical Measurement Models



Student Study Site
Use the Student Study Site to get the most out of your course!

The companion website includes solutions to the practice problems in the book. 

“Students in the social and behavioral sciences increasingly need a solid foundation of mathematical knowledge to be able to contribute to the research literature and be able to keep themselves current on new methodology. Unfortunately, math department classes really are not tailored to their needs. Mathematics for Social Scientists, on the other hand, is clearly aimed at what students need to be able to advance in subsequent methodology courses and in their future careers. It is written in an inviting and clear manner, without ever sacrificing rigor.”

Jay Verkuilen
The City University of New York

“Many students entering higher-level statistics classes have somehow forgotten their basic statistics or were never properly exposed to more than a cookbook explanation. More often than not, a student will leave the course without an understanding of probability, random variables, basic distribution theory and concepts etc. Without some background, it proves difficult for students to catch up with these ideas when they are introduced (or assumed to be known) in more advanced courses. This gap is especially pronounced between those students who were exposed to basic probability in a previous course and those who were not. Mathematics for Social Scientists will be a great resource for an instructor wishing to add this content to a basic statistics course as well as for the motivated self-learner.”

Dan Powers
University of Texas at Austin

This is a required texbook for understanding advanced univariate and multivariate statistics. I use this book as complementary book in my courses.

Dr Amin Mousavi
Educational Psychology , University Of Saskatchewan
December 12, 2015

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