Mathematics Course for Political and Social Research

 
 
Princeton University Press
  • 1. Auflage
  • |
  • erschienen am 24. Juli 2013
  • |
  • 456 Seiten
 
E-Book | PDF mit Adobe DRM | Systemvoraussetzungen
978-1-4008-4861-4 (ISBN)
 

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. Available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts. A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices in the social sciences and a handy reference for seasoned researchers.


The 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; linear algebra, including Markov chains and eigenvectors; and probability. It describes the intermediate steps most other textbooks leave out, features numerous exercises throughout, and grounds all concepts by illustrating their use and importance in political science and sociology.


    • Uniquely designed and ideal for students and researchers in political science and sociology

    • Uses practical examples from political science and sociology

    • Features "Why Do I Care?" sections that explain why concepts are useful

    • Includes numerous exercises

    • Complete online solutions manual (available only to professors, email david.siegel at duke.edu, subject line "Solution Set")

    • Selected solutions available online to students

    Course Book
    • Englisch
    • Princeton
    • |
    • USA
    • Für höhere Schule und Studium
    • Digitale Ausgabe
    • 57 line illus. 18 tables.
    • |
    • 57 line illus. 18 tables.
    • 4,84 MB
    978-1-4008-4861-4 (9781400848614)
    140084861X (140084861X)
    http://www.degruyter.com/isbn/9781400848614
    weitere Ausgaben werden ermittelt
    Will H. Moore & David A. Siegel
    List 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

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