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Mathematics for Social Scientists
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Mathematics for Social Scientists

October 2015 | 408 pages | SAGE Publications, Inc
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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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Part I: ALGEBRA, PRECALCULUS, AND PROBABILITY
 
1. Algebra Review
Numbers

 
Fractions

 
Exponents

 
Roots

 
Logarithms

 
Summations and Products

 
Solving Equations and Inequalities

 
 
2. Sets and Functions
Set Notation

 
Intervals

 
Venn Diagrams

 
Functions

 
Polynomials

 
 
3. Probability
Events and Sample Spaces

 
Properties and Probability Functions

 
Counting Theory

 
Sampling Problems

 
Conditional Probability

 
Bayes' Rule

 
 
PART II: CALCULUS
 
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

 
Notation

 
Shortcuts for Finding Derivatives

 
The Chain Rule

 
 
5. Optimization
Terminology

 
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

 
Moments

 
 
7. Multivariate Calculus
Multivariate Functions

 
Multivariate Limits

 
Partial Derivatives

 
Multiple Integrals

 
 
PART III: LINEAR ALGEBRA
 
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

 

Supplements

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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