| Description |
1 online resource (xix, 430 pages) : illustrations |
| Contents |
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. Brief Introduction to Calculus -- 5.2. What Is the Derivative? -- 5.3. Derivative, Formally -- 5.4. Summary -- 5.5. Exercises -- 6. 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. Integral -- 7.1. 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. 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. Introduction to (Discrete) Distributions -- 10.1. Distribution of a Single Concept (Variable) -- 10.2. Sample Distributions -- 10.3. Empirical Joint and Marginal Distributions -- 10.4. Probability Mass Function -- 10.5. 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 |
| Summary |
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 m |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Mathematics -- Study and teaching (Higher) -- Methodology
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Mathematics -- Study and teaching (Higher) -- Social aspects
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Mathematics -- Study and teaching (Higher) -- Political aspects
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MATHEMATICS -- Study & Teaching.
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MATHEMATICS -- General.
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Mathematik
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Politische Wissenschaft
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Methodologie
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| Form |
Electronic book
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| Author |
Siegel, David A. (College teacher), author.
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| LC no. |
2013935356 |
| ISBN |
9781400848614 |
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140084861X |
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1299690866 |
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9781299690868 |
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0691159955 |
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9780691159959 |
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0691159173 |
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9780691159171 |
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