A mathematics course for political and social research:
Gespeichert in:
Beteiligte Personen: | , |
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Format: | Buch |
Sprache: | Englisch |
Veröffentlicht: |
Princeton [u.a.]
Princeton Univ. Press
2013
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Schlagwörter: | |
Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026207013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
Umfang: | XIX, 430 S. graph. Darst. |
ISBN: | 9780691159171 9780691159959 |
Internformat
MARC
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Datensatz im Suchindex
DE-BY-TUM_call_number | 0002 SOZ 720f 2013 A 6895 |
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DE-BY-TUM_katkey | 1957745 |
DE-BY-TUM_location | 00 |
DE-BY-TUM_media_number | 040008345351 |
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adam_text | Titel: A mathematics course for political and social research
Autor: Moore, Will H
Jahr: 2013
Contents List of Figures xi List of Tables xiii 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
CONTENTS viii 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 Definite Integral as a Limit of Sums.............134 7.2 Indefinite 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 Specific 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
CONTENTS IX 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
x CONTENTS 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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any_adam_object | 1 |
author | Moore, Will H. 1962- Siegel, David A. |
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classification_rvk | MB 2520 SK 990 |
classification_tum | SOZ 720f |
ctrlnum | (OCoLC)864554762 (DE-599)BSZ391330640 |
discipline | Politologie Soziologie Mathematik |
format | Book |
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genre_facet | Lehrbuch |
id | DE-604.BV041232672 |
illustrated | Illustrated |
indexdate | 2024-12-20T16:33:48Z |
institution | BVB |
isbn | 9780691159171 9780691159959 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026207013 |
oclc_num | 864554762 |
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physical | XIX, 430 S. graph. Darst. |
publishDate | 2013 |
publishDateSearch | 2013 |
publishDateSort | 2013 |
publisher | Princeton Univ. Press |
record_format | marc |
spellingShingle | Moore, Will H. 1962- Siegel, David A. A mathematics course for political and social research Mathematik (DE-588)4037944-9 gnd Methodologie (DE-588)4139716-2 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Politische Wissenschaft (DE-588)4076229-4 gnd |
subject_GND | (DE-588)4037944-9 (DE-588)4139716-2 (DE-588)4055916-6 (DE-588)4076229-4 (DE-588)4123623-3 |
title | A mathematics course for political and social research |
title_auth | A mathematics course for political and social research |
title_exact_search | A mathematics course for political and social research |
title_full | A mathematics course for political and social research Will Moore & David A. Siegel |
title_fullStr | A mathematics course for political and social research Will Moore & David A. Siegel |
title_full_unstemmed | A mathematics course for political and social research Will Moore & David A. Siegel |
title_short | A mathematics course for political and social research |
title_sort | a mathematics course for political and social research |
topic | Mathematik (DE-588)4037944-9 gnd Methodologie (DE-588)4139716-2 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Politische Wissenschaft (DE-588)4076229-4 gnd |
topic_facet | Mathematik Methodologie Sozialwissenschaften Politische Wissenschaft Lehrbuch |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026207013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT moorewillh amathematicscourseforpoliticalandsocialresearch AT siegeldavida amathematicscourseforpoliticalandsocialresearch |
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Teilbibliothek Stammgelände
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0002 SOZ 720f 2013 A 6895 Lageplan |
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Exemplar 1 | Ausleihbar Am Standort |