Textbook in PDF format

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.
Acknowledgments
About the Author
Introduction
Algebra, Precalculus, and Probability
Algebra Review
Numbers
Fractions
Addition and Subtraction
Multiplication
Division
Exponents
Roots
Logarithms
Summations and Products
Solving Equations and Inequalities
Isolating a Variable
Distribution and Factoring
Solving Quadratic Equations
Solving Inequalities
Exercises
Sets and Functions
Set Notation
Intervals
Venn Diagrams
Functions
Function Compositions and Inverses
Graphs
Domain and Range
Polynomials
Linear Functions and Linear Graphs
Higher-Order Polynomials
Linear Regression
Exercises
Probability
Events and Sample Spaces
Properties of Probability Functions
Equally Likely Outcomes
Unions of Events
Independent Events
Complement Events
Counting Theory
Multiplication
Factorials
Combinations and Permutations
Sampling Problems
Sampling Without Replacement
Sampling With Replacement
Conditional Probability
Bayes’ Rule
Exercises
Calculus
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
Exercises
Optimization
Terminology
Finding Maxima and Minima
The Newton-Raphson Method
Exercises
Integration
Informal Definitions of an Integral
Riemann Sums
Integral Notation
Solving Integrals
Solving Indefinite Integrals
Solving Definite Integrals
Advanced Techniques for Solving Integrals
u-Substitution
Integration by Parts
Improper Integrals
Probability Density Functions
Moments
Exercises
Multivariate Calculus
Multivariate Functions
Multivariate Limits
Partial Derivatives
Definition and Notation
Gradients and Hessians
Optimization
Finding the Best-Fit Line for Linear Regression
Lagrange Multipliers
Multiple Integrals
Notation
Solving Multiple, Definite Integrals
Solving Multiple, Indefinite Integrals
Joint Probability Distributions and Moments
Exercises
Linear Algebra
Matrix Notation and Arithmetic
Matrix Notation
Types of Matrices
Matrix Arithmetic
Transpose
Trace
Addition and Subtraction
Scalar Multiplication
Kronecker Product
Vector Multiplication
Matrix Multiplication
Checking Conformability
Computing the Product
Geometric Representation of Vectors and Transformation Matrices
Elementary Row and Column Operations
Exercises
Matrix Inverses, Singularity, and Rank
Inverse of a (2 2) Matrix
Inverse of a Larger Square Matrix
The Adjoint Matrix
Determinants
Multiple Regression and the Ordinary Least Squares Estimator
Singularity, Rank, and Linear Dependency
Singularity
Linear Dependency
Rank
Exercises
Linear Systems of Equations and Eigenvalues
Nonsingular Coefficient Matrices
Solving by Taking a Matrix Inverse
Solving by Using Elementary Row Operations
Singular Coefficient Matrices
Systems With No Solution
Systems With Infinitely Many Solutions
Homogeneous Systems
Eigenvalues and Eigenvectors
Finding Eigenvalues
Positive-Definite and Negative-Definite Matrices
Finding Eigenvectors
Statistical Measurement Models
[id=JK]PrincipalPrinciple Components Analysis
Correspondence Analysis
Exercises
Conclusion: Taking the Math With You As You Proceed Through
Your Program
Index