Essential mathematics for political and social research:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | Repr. |
| Schriftenreihe: | Analytical methods for social research
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXVI, 448 S. graph. Darst. |
| ISBN: | 0521834260 052168403X 9780521684033 9780521834261 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804143160910151680 |
|---|---|
| adam_text | Contents
List of Tables
page
xiii
List of Illustrations
xiv
List of Examples
xvii
Preface
xxi
1
The Basics
1
1.1
Objectives
1
1.2
Essential Arithmetic Principles
2
1.3
Notation, Notation, Notation
4
1.4
Basic Terms
6
1.4.1
Indexing and Referencing
10
1.4.2
Specific Mathematical Use of Terms
13
1.5
Functions and Equations
18
1.5.1
Applying Functions: The Equation of a Line
26
1.5.2
The Factorial Function
29
1.5.3
The Modulo Function
32
1.6
Polynomial Functions
33
1.7
Logarithms and Exponents
34
1.8
New Terminoloev
41
VII
viii Contents
1.9
Chapter Appendix: It s All Greek to Me
49
2
Analytic Geometry
51
2.1
Objectives (the Width of a Circle)
51
2.2
Radian Measurement and Polar Coordinates
51
2.3
What Is Trigonometry?
54
2.3.1
Radian Measures for Trigonometric Functions
59
2.3.2
Conic Sections and Some Analytical Geometry
62
2.4
New Terminology
75
3
Linear Algebra: Vectors, Matrices, and Operations
82
3.1
Objectives
82
3.2
Working with Vectors
83
3.2.1
Vector Norms
93
3.3
So What Is the Matrix?
100
3.3.1
Some Special Matrices
101
3.4
Controlling the Matrix
106
3.5
Matrix Transposition
115
3.6
Advanced Topics
117
3.6.1
Special Matrix Forms
118
3.6.2
Vectorization of Matrices
119
3.7
New Terminology
125
4
Linear Algebra Continued: Matrix Structure
132
4.1
Objectives
132
4.2
Space and Time
133
4.3
The Trace and Determinant of a Matrix
139
4.4
Matrix Rank
146
4.5
Matrix Norms
149
4.6
Matrix Inversion
151
4.7
Linear Systems of Equations
157
4.8
Eigen-Analysis of Matrices
160
Contents
¡x
4.9
Quadratic Forms and
Descriptions
167
4.10
New Terminology
170
Elementary Scalar Calculus
178
5.1
Objectives
178
5.2
Limits and Lines
178
5.3
Understanding Rates, Changes, and Derivatives
182
5.4
Derivative Rules for Common Functions
189
5.4.1
Basic Algebraic Rules for Derivatives
189
5.4.2
Derivatives of Logarithms and Exponents
196
5.4.3
L Hospital s Rule
200
5.4.4
Applications: Rolle s Theorem and the Mean
Value Theorem
202
5.5
Understanding Areas, Slices, and Integrals
204
5.5.1
Riemann Integrals
205
5.6
The Fundamental Theorem of Calculus
209
5.6.1
Integrating Polynomials with
Antiderivatives 211
5.6.2
Indefinite Integrals
217
5.6.3
Integrals Involving Logarithms and Exponents
218
5.6.4
Integration by Parts
219
5.7
Additional Topics: Calculus of Trigonometric Functions
225
5.7.1
Derivatives of Trigonometric Functions
225
5.7.2
Integrals of Trigonometric Functions
226
5.8
New Terminology
228
Additional Topics in Scalar and Vector Calculus
235
6.1
Objectives
235
6.2
Partial Derivatives
235
6.3
Derivatives and Partial Derivatives of Higher Order
239
6.4
Maxima, Minima, and Root Finding
241
6.4.1
Evaluating Zero-Derivative Points
245
6.4.2
Root Finding with Newton-Raphson
247
Contents
6.5
Multidimensional Integrals
250
6.6
Finite and Infinite Series
256
6.6.1
Convergence
259
6.7
The Calculus of Vector and Matrix Forms
266
6.7.1
Vector Function Notation
266
6.7.2
Differentiation and Integration of a Vector
Function
268
6.8
Constrained Optimization
271
6.9
New Terminology
277
Probability Theory
284
7.1
Objectives
284
7.2
Counting Rules and Permutations
285
7.2.1
The Binomial Theorem and Pascal s Triangle
289
7.3
Sets and Operations on Sets
291
7.3.1
General Characteristics of Sets
292
7.3.2
A Special Set: The Empty Set
295
7.3.3
Operations on Sets
295
7.4
The Probability Function
306
7.5
Calculations with Probabilities
308
7.6
Conditional Probability and
Bayes
Law
312
7.6.1
Simpson s Paradox
315
7.7
Independence
317
7.8
Odds
321
7.9
New Terminology
323
Random Variables
330
8.1
Objectives
330
8.2
Levels of Measurement
330
8.3
Distribution Functions
334
8.3.1
Randomness and Variables
337
8.3.2
Probability Mass Functions
338
Contents xi
8.3.3
Bernoulli Trials
339
8.3.4
Binomial Experiments
340
8.3.5
Poisson
Counts
344
8.3.6
The Cumulative Distribution Function: Discrete
Version
347
8.3.7
Probability Density Functions
350
8.3.8
Exponential and Gamma PDFs
351
8.3.9
Normal PDF
354
8.3.10
The Cumulative Distribution Function:
Continuous Version
356
8.3.11
The Uniform Distributions
358
8.4
Measures of Central Tendency: Mean, Median, and Mode
361
8.5
Measures of Dispersion: Variance, Standard Deviation,
and MAD
365
8.6
Correlation and Covariance
367
8.7
Expected Value
370
8.8
Some Handy Properties and Rules
372
8.9
Inequalities Based on Expected Values
378
8.10
Moments of a Distribution
380
8.11
New Terminology
383
Markov Chains
392
9.1
Objectives
392
9.2
Defining Stochastic Processes and Markov Chains
393
9.2.1
The Markov Chain Kernel
397
9.2.2
The Stationary Distribution of a Markov Chain
401
9.3
Properties of Markov Chains
405
9.3.1
Homogeneity and Periodicity
405
9.3.2
Irreducibility
407
9.3.3
Recurrence
409
9.3.4
Stationarity and Ergodicity
413
xii Contents
9.3.5
Reversibility
417
9.4 New
Terminology
419
References
428
Author Index
438
Subject Index
441
|
| any_adam_object | 1 |
| author | Gill, Jeff |
| author_facet | Gill, Jeff |
| author_role | aut |
| author_sort | Gill, Jeff |
| author_variant | j g jg |
| building | Verbundindex |
| bvnumber | BV036576181 |
| classification_rvk | MB 2520 MR 2200 QH 110 |
| ctrlnum | (OCoLC)657656536 (DE-599)GBV600056775 |
| discipline | Politologie Soziologie Wirtschaftswissenschaften |
| edition | Repr. |
| format | Book |
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| isbn | 0521834260 052168403X 9780521684033 9780521834261 |
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| spelling | Gill, Jeff Verfasser aut Essential mathematics for political and social research Jeff Gill Repr. Cambridge [u.a.] Cambridge Univ. Press 2008 XXVI, 448 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analytical methods for social research Hier auch später erschienene, unveränderte Nachdrucke Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Politische Wissenschaft (DE-588)4076229-4 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Sozialwissenschaften (DE-588)4055916-6 s Grundlage (DE-588)4158388-7 s Mathematik (DE-588)4037944-9 s DE-604 Politische Wissenschaft (DE-588)4076229-4 s Mathematische Methode (DE-588)4155620-3 s 2\p DE-604 3\p DE-604 DE-601 pdf/application http://www.gbv.de/dms/bowker/toc/9780521684033.pdf Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020497185&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gill, Jeff Essential mathematics for political and social research Mathematische Methode (DE-588)4155620-3 gnd Politische Wissenschaft (DE-588)4076229-4 gnd Grundlage (DE-588)4158388-7 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4076229-4 (DE-588)4158388-7 (DE-588)4055916-6 (DE-588)4037944-9 (DE-588)4123623-3 |
| title | Essential mathematics for political and social research |
| title_auth | Essential mathematics for political and social research |
| title_exact_search | Essential mathematics for political and social research |
| title_full | Essential mathematics for political and social research Jeff Gill |
| title_fullStr | Essential mathematics for political and social research Jeff Gill |
| title_full_unstemmed | Essential mathematics for political and social research Jeff Gill |
| title_short | Essential mathematics for political and social research |
| title_sort | essential mathematics for political and social research |
| topic | Mathematische Methode (DE-588)4155620-3 gnd Politische Wissenschaft (DE-588)4076229-4 gnd Grundlage (DE-588)4158388-7 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematische Methode Politische Wissenschaft Grundlage Sozialwissenschaften Mathematik Lehrbuch |
| url | http://www.gbv.de/dms/bowker/toc/9780521684033.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020497185&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gilljeff essentialmathematicsforpoliticalandsocialresearch |
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