{"product_id":"a-mathematics-course-for-political-and-social-research-9780691159171","title":"A Mathematics Course for Political and Social","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSuitable for students and researchers in political science and sociology, this book begins with the fundamental building blocks of mathematics and basic algebra, then goes on to cover essential subjects such as calculus in one and more than one variable, including optimization, constrained optimization, and implicit functions.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book by Moore and Siegel, intended for the advanced political and social science student, appropriately avoids mathematical proofs and unnecessarily formal definitions while maintaining rigor and proper terminology... When needed, the clear illustrations accompany the material, providing strong visualization of the related concept.\"--Choice \"Written in an intuitive and accessible way, this book can be used as a primer for math novices in the social sciences as well as a handy reference for the researchers in this area.\"--Nicolae Popovici, Studia Mathematica\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList of Figures xi  List of Tables xii  Preface xv   I Building Blocks 1  1 Preliminaries 3  1.1 Variables and Constants 3  1.2 Sets 5  1.3 Operators 9  1.4 Relations 13  1.5 Level of Measurement 14  1.6 Notation 18  1.7 Proofs, or How Do We Know This? 22  1.8 Exercises 26  2 Algebra Review 28  2.1 Basic Properties of Arithmetic 28  2.2 Algebra Review 30  2.3 Computational Aids 40  2.4 Exercises 41  3 Functions, Relations, and Utility 44  3.1 Functions 45  3.2 Examples of Functions of One Variable 53  3.3 Preference Relations and Utility Functions 74  3.4 Exercises 78  4 Limits and Continuity, Sequences and Series, and More on Sets 81  4.1 Sequences and Series 81  4.2 Limits 84  4.3 Open, Closed, Compact, and Convex Sets 92  4.4 Continuous Functions 96  4.5 Exercises 99  II Calculus in One Dimension 101  5 Introduction to Calculus and the Derivative 103  5.1 A Brief Introduction to Calculus 103  5.2 What Is the Derivative? 105  5.3 The Derivative, Formally 109  5.4 Summary 114  5.5 Exercises 115  6 The Rules of Differentiation 117  6.1 Rules for Differentiation 118  6.2 Derivatives of Functions 125  6.3 What the Rules Are, and When to Use Them 130  6.4 Exercises 131  7 The Integral 133  7.1 The Defnite Integral as a Limit of Sums 134  7.2 Indefnite Integrals and the Fundamental Theorem of Calculus 136  7.3 Computing Integrals 140  7.4 Rules of Integration 148  7.5 Summary 149  7.6 Exercises 150  8 Extrema in One Dimension 152  8.1 Extrema 153  8.2 Higher-Order Derivatives, Concavity, and Convexity 157  8.3 Finding Extrema 162  8.4 Two Examples 169  8.5 Exercises 170  III Probability 173  9 An Introduction to Probability 175  9.1 Basic Probability Theory 175  9.2 Computing Probabilities 182  9.3 Some Specifc Measures of Probabilities 192  9.4 Exercises 194  9.5 Appendix 197  10 An Introduction to (Discrete) Distributions 198  10.1 The Distribution of a Single Concept (Variable) 199  10.2 Sample Distributions 202  10.3 Empirical Joint and Marginal Distributions 206  10.4 The Probability Mass Function 209  10.5 The Cumulative Distribution Function 216  10.6 Probability Distributions and Statistical Modeling 218  10.7 Expectations of Random Variables 229  10.8 Summary 239  10.9 Exercises 239  10.10 Appendix 241  11 Continuous Distributions 242  11.1 Continuous Random Variables 242  11.2 Expectations of Continuous Random Variables 249  11.3 Important Continuous Distributions for Statistical Modeling 258  11.4 Exercises 271  11.5 Appendix 272  IV Linear Algebra 273  12 Fun with Vectors and Matrices 275  12.1 Scalars 276  12.2 Vectors 277  12.3 Matrices 282  12.4 Properties of Vectors and Matrices 297  12.5 Matrix Illustration of OLS Estimation 298  12.6 Exercises 300  13 Vector Spaces and Systems of Equations 304  13.1 Vector Spaces 305  13.2 Solving Systems of Equations 310  13.3 Why Should I Care? 320  13.4 Exercises 324  13.5 Appendix 326  14 Eigenvalues and Markov Chains 327  14.1 Eigenvalues, Eigenvectors, and Matrix Decomposition 328  14.2 Markov Chains and Stochastic Processes 340  14.3 Exercises 351  V Multivariate Calculus and Optimization 353  15 Multivariate Calculus 355  15.1 Functions of Several Variables 356  15.2 Calculus in Several Dimensions 359  15.3 Concavity and Convexity Redux 371  15.4 Why Should I Care? 372  15.5 Exercises 374  16 Multivariate Optimization 376  16.1 Unconstrained Optimization 377  16.2 Constrained Optimization: Equality Constraints 383  16.3 Constrained Optimization: Inequality Constraints 391  16.4 Exercises 398  17 Comparative Statics and Implicit Differentiation 400  17.1 Properties of the Maximum and Minimum 401  17.2 Implicit Differentiation 405  17.3 Exercises 411  Bibliography 413  Index 423","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403800650071,"sku":"9780691159171","price":38.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691159171.jpg?v=1730484583","url":"https:\/\/bookcurl.com\/products\/a-mathematics-course-for-political-and-social-research-9780691159171","provider":"Book Curl","version":"1.0","type":"link"}