A mathematics course for political and social research /

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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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Moore, Will H., 1962-2017 (Autor), Siegel, David A. (College teacher) (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, Ã2013.
Temas:
Mathematics > Study and teaching (Higher) > Methodology.
Mathematics > Study and teaching (Higher) > Social aspects.
Mathematics > Study and teaching (Higher) > Political aspects.
MATHEMATICS > Study & Teaching.
MATHEMATICS > General.
Mathematik
Politische Wissenschaft
Methodologie
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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