Mathematics Course for Political and Social Research

ISBN-10: 0691159173
ISBN-13: 9780691159171
Edition: 2013
List price: $31.95 Buy it from $24.53
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Description: Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a semester-long or yearlong course to acquire the  More...

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Book details

List price: $31.95
Copyright year: 2013
Publisher: Princeton University Press
Publication date: 9/6/2013
Binding: Paperback
Pages: 456
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 1.914
Language: English

Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a semester-long or yearlong course to acquire the necessary skills. The problem is that most available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts. A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices and a handy reference for seasoned researchers.The book begins with the fundamental building blocks of mathematics and basic algebra, then goes on to cover essential subjects such as calculus in one and more than one variable, including optimization, constrained optimization, and implicit functions; linear algebra, including Markov chains and eigenvectors; and probability. It describes the intermediate steps most other textbooks leave out, features numerous exercises throughout, and grounds all concepts by illustrating their use and importance in political science and sociology.Uniquely designed for students and researchers in political science and sociologyUses examples from political science and sociologyFeatures "Why Do I Care?" sections that explain why concepts are useful to practicing political scientists and sociologistsIncludes numerous exercisesComplete online solutions manual (available only to professors)Selected solutions available online to students

List of Figures
List of Tables
Preface
Building Blocks
Preliminaries
Variables and Constants
Sets
Operators
Relations
Level of Measurement
Notation
Proofs, or How Do We Know This?
Exercises
Algebra Review
Basic Properties of Arithmetic
Algebra Review
Computational Aids
Exercises
Functions, Relations, and Utility
Functions
Examples of Functions of One Variable
Preference Relations and Utility Functions
Exercises
Limits and Continuity, Sequences and Series, and More on Sets
Sequences and Series
Limits
Open, Closed, Compact, and Convex Sets
Continuous Functions
Exercises
Calculus in One Dimension
Introduction to Calculus and the Derivative
A Brief Introduction to Calculus
What Is the Derivative?
The Derivative, Formally
Summary
Exercises
The Rules of Differentiation
Rules for Differentiation
Derivatives of Functions
What the Rules Are, and When to Use Them
Exercises
The Integral
The Definite Integral as a Limit of Sums
Indefinite Integrals and the Fundamental Theorem of Calculus
Computing Integrals
Rules of Integration
Summary
Exercises
Extrema in One Dimension
Extrema
Higher-Order Derivatives, Concavity, and Convexity
Finding Extrema
Two Examples
Exercises
Probability
An Introduction to Probability
Basic Probability Theory
Computing Probabilities
Some Specific Measures of Probabilities
Exercises
Appendix
An Introduction to (Discrete) Distributions
The Distribution of a Single Concept (Variable)
Sample Distributions
Empirical Joint and Marginal Distributions
The Probability Mass Function
The Cumulative Distribution Function
Probability Distributions and Statistical Modeling
Expectations of Random Variables
Summary
Exercises
Appendix
Continuous Distributions
Continuous Random Variables
Expectations of Continuous Random Variables
Important Continuous Distributions for Statistical Modeling
Exercises
Appendix
Linear Algebra
Fun with Vectors and Matrices
Scalars
Vectors
Matrices
Properties of Vectors and Matrices
Matrix Illustration of OLS Estimation
Exercises
Vector Spaces and Systems of Equations
Vector Spaces
Solving Systems of Equations
Why Should I Care?
Exercises
Appendix
Eigenvalues and Markov Chains
Eigenvalues, Eigenvectors, and Matrix Decomposition
Markov Chains and Stochastic Processes
Exercises
Multivariate Calculus and Optimization
Multivariate Calculus
Functions of Several Variables
Calculus in Several Dimensions
Concavity and Convexity Redux
Why Should I Care?
Exercises
Multivariate Optimization
Unconstrained Optimization
Constrained Optimization: Equality Constraints
Constrained Optimization: Inequality Constraints
Exercises
Comparative Statics and Implicit Differentiation
Properties of the Maximum and Minimum
Implicit Differentiation
Exercises
Bibliography
Index

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