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Mathematics Course for Political and Social Research [Pehme köide]

4.06/5 (66 hinnangut Goodreads-ist)
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  • Formaat: Paperback / softback, 450 pages, kõrgus x laius: 235x152 mm, kaal: 765 g, 57 line illus. 18 tables.
  • Ilmumisaeg: 11-Aug-2013
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691159173
  • ISBN-13: 9780691159171
Teised raamatud teemal:
Mathematics Course for Political and Social ResearchSuurem pilt
  • Formaat: Paperback / softback, 450 pages, kõrgus x laius: 235x152 mm, kaal: 765 g, 57 line illus. 18 tables.
  • Ilmumisaeg: 11-Aug-2013
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691159173
  • ISBN-13: 9780691159171
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780691159171.html
Märksõnad:

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

Arvustused

"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

List of Figures
xi
List of Tables
xiii
Preface xv
I Building Blocks
1(100)
1 Preliminaries
3(25)
1.1 Variables and Constants
3(2)
1.2 Sets
5(4)
1.3 Operators
9(4)
1.4 Relations
13(1)
1.5 Level of Measurement
14(4)
1.6 Notation
18(4)
1.7 Proofs, or How Do We Know This?
22(4)
1.8 Exercises
26(2)
2 Algebra Review
28(16)
2.1 Basic Properties of Arithmetic
28(2)
2.2 Algebra Review
30(10)
2.3 Computational Aids
40(1)
2.4 Exercises
41(3)
3 Functions, Relations, and Utility
44(37)
3.1 Functions
45(8)
3.2 Examples of Functions of One Variable
53(21)
3.3 Preference Relations and Utility Functions
74(4)
3.4 Exercises
78(3)
4 Limits and Continuity, Sequences and Series, and More on Sets
81(20)
4.1 Sequences and Series
81(3)
4.2 Limits
84(8)
4.3 Open, Closed, Compact, and Convex Sets
92(4)
4.4 Continuous Functions
96(3)
4.5 Exercises
99(2)
II Calculus in One Dimension
101(72)
5 Introduction to Calculus and the Derivative
103(14)
5.1 A Brief Introduction to Calculus
103(2)
5.2 What Is the Derivative?
105(4)
5.3 The Derivative, Formally
109(5)
5.4 Summary
114(1)
5.5 Exercises
115(2)
6 The Rules of Differentiation
117(16)
6.1 Rules for Differentiation
118(7)
6.2 Derivatives of Functions
125(5)
6.3 What the Rules Are, and When to Use Them
130(1)
6.4 Exercises
131(2)
7 The Integral
133(19)
7.1 The Definite Integral as a Limit of Sums
134(2)
7.2 Indefinite Integrals and the Fundamental Theorem of Calculus
136(4)
7.3 Computing Integrals
140(8)
7.4 Rules of Integration
148(1)
7.5 Summary
149(1)
7.6 Exercises
150(2)
8 Extrema in One Dimension
152(21)
8.1 Extrema
153(4)
8.2 Higher-Order Derivatives, Concavity, and Convexity
157(5)
8.3 Finding Extrema
162(7)
8.4 Two Examples
169(1)
8.5 Exercises
170(3)
III Probability
173(100)
9 An Introduction to Probability
175(23)
9.1 Basic Probability Theory
175(7)
9.2 Computing Probabilities
182(10)
9.3 Some Specific Measures of Probabilities
192(2)
9.4 Exercises
194(3)
9.5 Appendix
197(1)
10 An Introduction to (Discrete) Distributions
198(44)
10.1 The Distribution of a Single Concept (Variable)
199(3)
10.2 Sample Distributions
202(4)
10.3 Empirical Joint and Marginal Distributions
206(3)
10.4 The Probability Mass Function
209(7)
10.5 The Cumulative Distribution Function
216(2)
10.6 Probability Distributions and Statistical Modeling
218(11)
10.7 Expectations of Random Variables
229(10)
10.8 Summary
239(1)
10.9 Exercises
239(2)
10.10 Appendix
241(1)
11 Continuous Distributions
242(31)
11.1 Continuous Random Variables
242(7)
11.2 Expectations of Continuous Random Variables
249(9)
11.3 Important Continuous Distributions for Statistical Modeling
258(13)
11.4 Exercises
271(1)
11.5 Appendix
272(1)
IV Linear Algebra
273(80)
12 Fun with Vectors and Matrices
275(29)
12.1 Scalars
276(1)
12.2 Vectors
277(5)
12.3 Matrices
282(15)
12.4 Properties of Vectors and Matrices
297(1)
12.5 Matrix Illustration of OLS Estimation
298(2)
12.6 Exercises
300(4)
13 Vector Spaces and Systems of Equations
304(23)
13.1 Vector Spaces
305(5)
13.2 Solving Systems of Equations
310(10)
13.3 Why Should I Care?
320(4)
13.4 Exercises
324(2)
13.5 Appendix
326(1)
14 Eigenvalues and Markov Chains
327(26)
14.1 Eigenvalues, Eigenvectors, and Matrix Decomposition
328(12)
14.2 Markov Chains and Stochastic Processes
340(11)
14.3 Exercises
351(2)
V Multivariate Calculus and Optimization
353(60)
15 Multivariate Calculus
355(21)
15.1 Functions of Several Variables
356(3)
15.2 Calculus in Several Dimensions
359(12)
15.3 Concavity and Convexity Redux
371(1)
15.4 Why Should I Care?
372(2)
15.5 Exercises
374(2)
16 Multivariate Optimization
376(24)
16.1 Unconstrained Optimization
377(6)
16.2 Constrained Optimization: Equality Constraints
383(8)
16.3 Constrained Optimization: Inequality Constraints
391(7)
16.4 Exercises
398(2)
17 Comparative Statics and Implicit Differentiation
400(13)
17.1 Properties of the Maximum and Minimum
401(4)
17.2 Implicit Differentiation
405(6)
17.3 Exercises
411(2)
Bibliography 413(10)
Index 423
Will H. Moore is professor of political science at Florida State University. David A. Siegel is associate professor of political science at Duke University. He is the coauthor of A Behavioral Theory of Elections (Princeton).