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Mathematics for Social Scientists

Mathematics for Social Scientists

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September 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
October 11, 2016
Key features


  • Comprehensive coverage of material includes game theory, statistics, probability, pre-calculus, calculus, and matrix algebra, unlike most math texts that only cover one of these areas.
  • Applications to real methods in social science methodology answer the common student question, “what will I use this for later in my career?”
  • End-of-chapter exercises effectively challenge readers through applications in politics, sociology, economics, psychology, and others.
  • A conversational tone throughout makes the material accessible without compromising the rigor of the presentation.

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