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 i...
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Full text (MCPHS users only) |
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| Main Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, NJ :
Princeton University Press,
2013
|
| Subjects: | |
| Local Note: | ProQuest Ebook Central |
Table of 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.
