A Mathematics Course for Political and Social Research ：A Mathematics Course for Political and Social Research

Publication subTitle ：A Mathematics Course for Political and Social Research

Author： Moore Will H.;Siegel David A.;;  

Publisher： Princeton University Press‎

Publication year： 2013

E-ISBN: 9781400848614

P-ISBN(Paperback): 9780691159171

Subject： C91 Sociology;D0 Political Theory;D09 in the history of politics, political history;O1 Mathematics

Keyword： 政治理论,社会学,数学

Language： ENG

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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 necessary skills. 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 in the social sciences 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 and ideal for students and researchers in political science and sociology
  • Uses practical examples from political science and sociology
  • Features "Why Do I Care?" sections that explain why concepts are useful
  • Includes numerous exercises
  • Complete online solutions manual (available only to professors, email david.siegel at duke.edu, subject line "Solution Set")
  • Selected solutions available online to students

Chapter

Cover

Cover

Title

Title

Copyright

Copyright

Dedication

Dedication

Contents

Contents

List of Figures

List of Figures

List of Tables

List of Tables

Preface

Preface

I Building Blocks

I Building Blocks

1 Preliminaries

1 Preliminaries

1.1 Variables and Constants

1.1 Variables and Constants

1.2 Sets

1.2 Sets

1.3 Operators

1.3 Operators

1.4 Relations

1.4 Relations

1.5 Level of Measurement

1.5 Level of Measurement

1.6 Notation

1.6 Notation

1.7 Proofs, or How Do We Know This?

1.7 Proofs, or How Do We Know This?

1.8 Exercises

1.8 Exercises

2 Algebra Review

2 Algebra Review

2.1 Basic Properties of Arithmetic

2.1 Basic Properties of Arithmetic

2.2 Algebra Review

2.2 Algebra Review

2.3 Computational Aids

2.3 Computational Aids

2.4 Exercises

2.4 Exercises

3 Functions, Relations, and Utility

3 Functions, Relations, and Utility

3.1 Functions

3.1 Functions

3.2 Examples of Functions of One Variable

3.2 Examples of Functions of One Variable

3.3 Preference Relations and Utility Functions

3.3 Preference Relations and Utility Functions

3.4 Exercises

3.4 Exercises

4 Limits and Continuity, Sequences and Series, and More on Sets

4 Limits and Continuity, Sequences and Series, and More on Sets

4.1 Sequences and Series

4.1 Sequences and Series

4.2 Limits

4.2 Limits

4.3 Open, Closed, Compact, and Convex Sets

4.3 Open, Closed, Compact, and Convex Sets

4.4 Continuous Functions

4.4 Continuous Functions

4.5 Exercises

4.5 Exercises

II Calculus in One Dimension

II Calculus in One Dimension

5 Introduction to Calculus and the Derivative

5 Introduction to Calculus and the Derivative

5.1 A Brief Introduction to Calculus

5.1 A Brief Introduction to Calculus

5.2 What Is the Derivative?

5.2 What Is the Derivative?

5.3 The Derivative, Formally

5.3 The Derivative, Formally

5.4 Summary

5.4 Summary

5.5 Exercises

5.5 Exercises

6 The Rules of Differentiation

6 The Rules of Differentiation

6.1 Rules for Differentiation

6.1 Rules for Differentiation

6.2 Derivatives of Functions

6.2 Derivatives of Functions

6.3 What the Rules Are, and When to Use Them

6.3 What the Rules Are, and When to Use Them

6.4 Exercises

6.4 Exercises

7 The Integral

7 The Integral

7.1 The Definite Integral as a Limit of Sums

7.1 The Definite Integral as a Limit of Sums

7.2 Indefinite Integrals and the Fundamental Theorem of Calculus

7.2 Indefinite Integrals and the Fundamental Theorem of Calculus

7.3 Computing Integrals

7.3 Computing Integrals

7.4 Rules of Integration

7.4 Rules of Integration

7.5 Summary

7.5 Summary

7.6 Exercises

7.6 Exercises

8 Extrema in One Dimension

8 Extrema in One Dimension

8.1 Extrema

8.1 Extrema

8.2 Higher-Order Derivatives, Concavity, and Convexity

8.2 Higher-Order Derivatives, Concavity, and Convexity

8.3 Finding Extrema

8.3 Finding Extrema

8.4 Two Examples

8.4 Two Examples

8.5 Exercises

8.5 Exercises

III Probability

III Probability

9 An Introduction to Probability

9 An Introduction to Probability

9.1 Basic Probability Theory

9.1 Basic Probability Theory

9.2 Computing Probabilities

9.2 Computing Probabilities

9.3 Some Specific Measures of Probabilities

9.3 Some Specific Measures of Probabilities

9.4 Exercises

9.4 Exercises

9.5 Appendix

9.5 Appendix

10 An Introduction to (Discrete) Distributions

10 An Introduction to (Discrete) Distributions

10.1 The Distribution of a Single Concept (Variable)

10.1 The Distribution of a Single Concept (Variable)

10.2 Sample Distributions

10.2 Sample Distributions

10.3 Empirical Joint and Marginal Distributions

10.3 Empirical Joint and Marginal Distributions

10.4 The Probability Mass Function

10.4 The Probability Mass Function

10.5 The Cumulative Distribution Function

10.5 The Cumulative Distribution Function

10.6 Probability Distributions and Statistical Modeling

10.6 Probability Distributions and Statistical Modeling

10.7 Expectations of Random Variables

10.7 Expectations of Random Variables

10.8 Summary

10.8 Summary

10.9 Exercises

10.9 Exercises

10.10 Appendix

10.10 Appendix

11 Continuous Distributions

11 Continuous Distributions

11.1 Continuous Random Variables

11.1 Continuous Random Variables

11.2 Expectations of Continuous Random Variables

11.2 Expectations of Continuous Random Variables

11.3 Important Continuous Distributions for Statistical Modeling . .

11.3 Important Continuous Distributions for Statistical Modeling . .

11.4 Exercises

11.4 Exercises

11.5 Appendix

11.5 Appendix

IV Linear Algebra

IV Linear Algebra

12 Fun with Vectors and Matrices

12 Fun with Vectors and Matrices

12.1 Scalars

12.1 Scalars

12.2 Vectors

12.2 Vectors

12.3 Matrices

12.3 Matrices

12.4 Properties of Vectors and Matrices

12.4 Properties of Vectors and Matrices

12.5 Matrix Illustration of OLS Estimation

12.5 Matrix Illustration of OLS Estimation

12.6 Exercises

12.6 Exercises

13 Vector Spaces and Systems of Equations

13 Vector Spaces and Systems of Equations

13.1 Vector Spaces

13.1 Vector Spaces

13.2 Solving Systems of Equations

13.2 Solving Systems of Equations

13.3 Why Should I Care?

13.3 Why Should I Care?

13.4 Exercises

13.4 Exercises

13.5 Appendix

13.5 Appendix

14 Eigenvalues and Markov Chains

14 Eigenvalues and Markov Chains

14.1 Eigenvalues, Eigenvectors, and Matrix Decomposition

14.1 Eigenvalues, Eigenvectors, and Matrix Decomposition

14.2 Markov Chains and Stochastic Processes

14.2 Markov Chains and Stochastic Processes

14.3 Exercises

14.3 Exercises

V Multivariate Calculus and Optimization

V Multivariate Calculus and Optimization

15 Multivariate Calculus

15 Multivariate Calculus

15.1 Functions of Several Variables

15.1 Functions of Several Variables

15.2 Calculus in Several Dimensions

15.2 Calculus in Several Dimensions

15.3 Concavity and Convexity Redux

15.3 Concavity and Convexity Redux

15.4 Why Should I Care?

15.4 Why Should I Care?

15.5 Exercises

15.5 Exercises

16 Multivariate Optimization

16 Multivariate Optimization

16.1 Unconstrained Optimization

16.1 Unconstrained Optimization

16.2 Constrained Optimization: Equality Constraints

16.2 Constrained Optimization: Equality Constraints

16.3 Constrained Optimization: Inequality Constraints

16.3 Constrained Optimization: Inequality Constraints

16.4 Exercises

16.4 Exercises

17 Comparative Statics and Implicit Differentiation

17 Comparative Statics and Implicit Differentiation

17.1 Properties of the Maximum and Minimum

17.1 Properties of the Maximum and Minimum

17.2 Implicit Differentiation

17.2 Implicit Differentiation

17.3 Exercises

17.3 Exercises

Bibliography

Bibliography

Index

Index

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