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| List of Figures | |
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| List of Tables | |
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| Preface | |
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| Building Blocks | |
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| Preliminaries | |
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| Variables and Constants | |
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| Sets | |
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| Operators | |
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| Relations | |
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| Level of Measurement | |
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| Notation | |
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| Proofs, or How Do We Know This? | |
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| Exercises | |
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| Algebra Review | |
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| Basic Properties of Arithmetic | |
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| Algebra Review | |
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| Computational Aids | |
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| Exercises | |
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| Functions, Relations, and Utility | |
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| Functions | |
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| Examples of Functions of One Variable | |
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| Preference Relations and Utility Functions | |
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| Exercises | |
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| Limits and Continuity, Sequences and Series, and More on Sets | |
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| Sequences and Series | |
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| Limits | |
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| Open, Closed, Compact, and Convex Sets | |
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| Continuous Functions | |
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| Exercises | |
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| Calculus in One Dimension | |
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| Introduction to Calculus and the Derivative | |
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| A Brief Introduction to Calculus | |
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| What Is the Derivative? | |
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| The Derivative, Formally | |
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| Summary | |
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| Exercises | |
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| The Rules of Differentiation | |
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| Rules for Differentiation | |
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| Derivatives of Functions | |
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| What the Rules Are, and When to Use Them | |
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| Exercises | |
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| The Integral | |
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| The Definite Integral as a Limit of Sums | |
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| Indefinite Integrals and the Fundamental Theorem of Calculus | |
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| Computing Integrals | |
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| Rules of Integration | |
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| Summary | |
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| Exercises | |
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| Extrema in One Dimension | |
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| Extrema | |
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| Higher-Order Derivatives, Concavity, and Convexity | |
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| Finding Extrema | |
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| Two Examples | |
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| Exercises | |
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| Probability | |
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| An Introduction to Probability | |
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| Basic Probability Theory | |
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| Computing Probabilities | |
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| Some Specific Measures of Probabilities | |
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| Exercises | |
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| Appendix | |
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| An Introduction to (Discrete) Distributions | |
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| The Distribution of a Single Concept (Variable) | |
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| Sample Distributions | |
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| Empirical Joint and Marginal Distributions | |
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| The Probability Mass Function | |
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| The Cumulative Distribution Function | |
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| Probability Distributions and Statistical Modeling | |
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| Expectations of Random Variables | |
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| Summary | |
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| Exercises | |
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| Appendix | |
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| Continuous Distributions | |
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| Continuous Random Variables | |
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| Expectations of Continuous Random Variables | |
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| Important Continuous Distributions for Statistical Modeling | |
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| Exercises | |
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| Appendix | |
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| Linear Algebra | |
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| Fun with Vectors and Matrices | |
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| Scalars | |
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| Vectors | |
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| Matrices | |
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| Properties of Vectors and Matrices | |
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| Matrix Illustration of OLS Estimation | |
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| Exercises | |
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| Vector Spaces and Systems of Equations | |
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| Vector Spaces | |
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| Solving Systems of Equations | |
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| Why Should I Care? | |
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| Exercises | |
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| Appendix | |
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| Eigenvalues and Markov Chains | |
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| Eigenvalues, Eigenvectors, and Matrix Decomposition | |
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| Markov Chains and Stochastic Processes | |
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| Exercises | |
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| Multivariate Calculus and Optimization | |
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| Multivariate Calculus | |
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| Functions of Several Variables | |
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| Calculus in Several Dimensions | |
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| Concavity and Convexity Redux | |
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| Why Should I Care? | |
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| Exercises | |
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| Multivariate Optimization | |
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| Unconstrained Optimization | |
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| Constrained Optimization: Equality Constraints | |
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| Constrained Optimization: Inequality Constraints | |
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| Exercises | |
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| Comparative Statics and Implicit Differentiation | |
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| Properties of the Maximum and Minimum | |
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| Implicit Differentiation | |
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| Exercises | |
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| Bibliography | |
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| Index | |