A Mathematics Course for Political and Social Research
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...
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| Hauptverfasser: | , |
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| Format: | E-Book Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton
Princeton University Press
2013
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| Ausgabe: | STU - Student edition |
| Schlagworte: | |
| ISBN: | 9780691159171, 0691159173, 9780691159959, 0691159955, 9781400848614, 140084861X |
| Online-Zugang: | Volltext |
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Inhaltsangabe:
- Front Matter Table of Contents List of Figures List of Tables Preface Chapter One: Preliminaries Chapter Two: Algebra Review Chapter Three: Functions, Relations, and Utility Chapter Four: Limits and Continuity, Sequences and Series, and More on Sets Chapter Five: Introduction to Calculus and the Derivative Chapter Six: The Rules of Differentiation Chapter Seven: The Integral Chapter Eight: Extrema in One Dimension Chapter Nine: An Introduction to Probability Chapter Ten: An Introduction to (Discrete) Distributions Chapter Eleven: Continuous Distributions Chapter Twelve: Fun with Vectors and Matrices Chapter Thirteen: Vector Spaces and Systems of Equations Chapter Fourteen: Eigenvalues and Markov Chains Chapter Fifteen: Multivariate Calculus Chapter Sixteen: Multivariate Optimization Chapter Seventeen: Comparative Staticsand Implicit Differentiation Bibliography Index
- 10.2 Sample Distributions -- 10.3 Empirical Joint and Marginal Distributions -- 10.4 The Probability Mass Function -- 10.5 The Cumulative Distribution Function -- 10.6 Probability Distributions and Statistical Modeling -- 10.7 Expectations of Random Variables -- 10.8 Summary -- 10.9 Exercises -- 10.10 Appendix -- 11 Continuous Distributions -- 11.1 Continuous Random Variables -- 11.2 Expectations of Continuous Random Variables -- 11.3 Important Continuous Distributions for Statistical Modeling . . -- 11.4 Exercises -- 11.5 Appendix -- IV Linear Algebra -- 12 Fun with Vectors and Matrices -- 12.1 Scalars -- 12.2 Vectors -- 12.3 Matrices -- 12.4 Properties of Vectors and Matrices -- 12.5 Matrix Illustration of OLS Estimation -- 12.6 Exercises -- 13 Vector Spaces and Systems of Equations -- 13.1 Vector Spaces -- 13.2 Solving Systems of Equations -- 13.3 Why Should I Care? -- 13.4 Exercises -- 13.5 Appendix -- 14 Eigenvalues and Markov Chains -- 14.1 Eigenvalues, Eigenvectors, and Matrix Decomposition -- 14.2 Markov Chains and Stochastic Processes -- 14.3 Exercises -- V Multivariate Calculus and Optimization -- 15 Multivariate Calculus -- 15.1 Functions of Several Variables -- 15.2 Calculus in Several Dimensions -- 15.3 Concavity and Convexity Redux -- 15.4 Why Should I Care? -- 15.5 Exercises -- 16 Multivariate Optimization -- 16.1 Unconstrained Optimization -- 16.2 Constrained Optimization: Equality Constraints -- 16.3 Constrained Optimization: Inequality Constraints -- 16.4 Exercises -- 17 Comparative Statics and Implicit Differentiation -- 17.1 Properties of the Maximum and Minimum -- 17.2 Implicit Differentiation -- 17.3 Exercises -- Bibliography -- Index
- Cover -- Title -- Copyright -- Dedication -- Contents -- List of Figures -- List of Tables -- Preface -- I Building Blocks -- 1 Preliminaries -- 1.1 Variables and Constants -- 1.2 Sets -- 1.3 Operators -- 1.4 Relations -- 1.5 Level of Measurement -- 1.6 Notation -- 1.7 Proofs, or How Do We Know This? -- 1.8 Exercises -- 2 Algebra Review -- 2.1 Basic Properties of Arithmetic -- 2.2 Algebra Review -- 2.3 Computational Aids -- 2.4 Exercises -- 3 Functions, Relations, and Utility -- 3.1 Functions -- 3.2 Examples of Functions of One Variable -- 3.3 Preference Relations and Utility Functions -- 3.4 Exercises -- 4 Limits and Continuity, Sequences and Series, and More on Sets -- 4.1 Sequences and Series -- 4.2 Limits -- 4.3 Open, Closed, Compact, and Convex Sets -- 4.4 Continuous Functions -- 4.5 Exercises -- II Calculus in One Dimension -- 5 Introduction to Calculus and the Derivative -- 5.1 A Brief Introduction to Calculus -- 5.2 What Is the Derivative? -- 5.3 The Derivative, Formally -- 5.4 Summary -- 5.5 Exercises -- 6 The Rules of Differentiation -- 6.1 Rules for Differentiation -- 6.2 Derivatives of Functions -- 6.3 What the Rules Are, and When to Use Them -- 6.4 Exercises -- 7 The Integral -- 7.1 The Definite Integral as a Limit of Sums -- 7.2 Indefinite Integrals and the Fundamental Theorem of Calculus -- 7.3 Computing Integrals -- 7.4 Rules of Integration -- 7.5 Summary -- 7.6 Exercises -- 8 Extrema in One Dimension -- 8.1 Extrema -- 8.2 Higher-Order Derivatives, Concavity, and Convexity -- 8.3 Finding Extrema -- 8.4 Two Examples -- 8.5 Exercises -- III Probability -- 9 An Introduction to Probability -- 9.1 Basic Probability Theory -- 9.2 Computing Probabilities -- 9.3 Some Specific Measures of Probabilities -- 9.4 Exercises -- 9.5 Appendix -- 10 An Introduction to (Discrete) Distributions -- 10.1 The Distribution of a Single Concept (Variable)