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).

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.