This second edition of the classic text incldues data and methods in a way that is approachable to practitioners and those new to the field. This update edition removes information and data that have lost relevance with time, while maintaining timeless, core methods and integrating them with new developments to the field.
Inhoudsopgave:
Preface to the Second Edition ix
Preface to the First Edition xiii
Abbreviations xv
Introduction 1
Types of Problems Considered, 2
Description or Interpretation?, 8
1. Preliminaries 11
1.1 Random Functions, 11
1.2 On the Objectivity of Probabilistic Statements, 22
1.3 Transitive Theory, 24
2. Structural Analysis 28
2.1 General Principles, 28
2.2 Variogram Cloud and Sample Variogram, 33
2.3 Mathematical Properties of the Variogram, 59
2.4 Regularization and Nugget Effect, 78
2.5 Variogram Models, 84
2.6 Fitting a Variogram Model, 109
2.7 Variography in the Presence of a Drift, 122
2.8 Simple Applications of the Variogram, 130
2.9 Complements: Theory of Variogram Estimation and Fluctuation, 138
3. Kriging 147
3.1 Introduction, 147
3.2 Notations and Assumptions, 149
3.3 Kriging with a Known Mean, 150
3.4 Kriging with an Unknown Mean, 161
3.5 Estimation of a Spatial Average, 196
3.6 Selection of a Kriging Neighborhood, 204
3.7 Measurement Errors and Outliers, 216
3.8 Case Study: The Channel Tunnel, 225
3.9 Kriging Under Inequality Constraints, 232
4. Intrinsic Model of Order k 238
4.1 Introduction, 238
4.2 A Second Look at the Model of Universal Kriging, 240
4.3 Allowable Linear Combinations of Order k, 245
4.4 Intrinsic Random Functions of Order k, 252
4.5 Generalized Covariance Functions, 257
4.6 Estimation in the IRF Model, 269
4.7 Generalized Variogram, 281
4.8 Automatic Structure Identification, 286
4.9 Stochastic Differential Equations, 294
5. Multivariate Methods 299
5.1 Introduction, 299
5.2 Notations and Assumptions, 300
5.3 Simple Cokriging, 302
5.4 Universal Cokriging, 305
5.5 Derivative Information, 320
5.6 Multivariate Random Functions, 330
5.7 Shortcuts, 360
5.8 SpaceTime Models, 370
6. Nonlinear Methods 386
6.1 Introduction, 386
6.2 Global Point Distribution, 387
6.3 Local Point Distribution: Simple Methods, 392
6.4 Local Estimation by Disjunctive Kriging, 401
6.5 Selectivity and Support Effect, 433
6.6 Multi-Gaussian Change-of-Support Model, 445
6.7 Affine Correction, 448
6.8 Discrete Gaussian Model, 449
6.9 Non-Gaussian Isofactorial Change-of-Support Models, 466
6.10 Applications and Discussion, 469
6.11 Change of Support by the Maximum (C. Lantue´ joul), 470
7. Conditional Simulations 478
7.1 Introduction and Definitions, 478
7.2 Direct Conditional Simulation of a Continuous Variable, 489
7.3 Conditioning by Kriging, 495
7.4 Turning Bands, 502
7.5 Nonconditional Simulation of a Continuous Variable, 508
7.6 Simulation of a Categorical Variable, 546
7.7 Object-Based Simulations: Boolean Models, 574
7.8 Beyond Standard Conditioning, 590
7.9 Additional Topics, 606
7.10 Case Studies, 615
Appendix 629
References 642
Index 689
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Chilès, Jean-Paul, Geostatistics
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Galois Theory
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This book brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike. The Second Edition features new exercises and an updated bibliography. A new discussion provides a different method for computing the Galois group of a quartic polynomial.
Inhoudsopgave:
Preface to the First Edition xvii
Preface to the Second Edition xxi
Notation xxiii
1 Basic Notation xxiii
2 Chapter-by-Chapter Notation xxv
PART I POLYNOMIALS
1 Cubic Equations 3
1.1 Cardan`s Formulas 4
1.2 Permutations of the Roots 10
1.3 Cubic Equations over the Real Numbers 15
2 Symmetric Polynomials 25
2.1 Polynomials of Several Variables 25
2.2 Symmetric Polynomials 30
2.3 Computing with Symmetric Polynomials (Optional) 42
2.4 The Discriminant 46
3 Roots of Polynomials 55
3.1 The Existence of Roots 55
3.2 The Fundamental Theorem of Algebra 62
PART II FIELDS
4 Extension Fields 73
4.1 Elements of Extension Fields 73
4.2 Irreducible Polynomials 81
4.3 The Degree of an Extension 89
4.4 Algebraic Extensions 95
5 Normal and Separable Extensions 101
5.1 Splitting Fields 101
5.2 Normal Extensions 107
5.3 Separable Extensions 109
5.4 Theorem of the Primitive Element 119
6 The Galois Group 125
6.1 Definition of the Galois Group 125
6.2 Galois Groups of Splitting Fields 130
6.3 Permutations of the Roots 132
6.4 Examples of Galois Groups 136
6.5 Abelian Equations (Optional) 143
7 The Galois Correspondence 147
7.1 Galois Extensions 147
7.2 Normal Subgroups and Normal Extensions 154
7.3 The Fundamental Theorem of Galois Theory 161
7.4 First Applications 167
7.5 Automorphisms and Geometry (Optional) 173
PART III APPLICATIONS
8 Solvability by Radicals 191
8.1 Solvable Groups 191
8.2 Radical and Solvable Extensions 196
8.3 Solvable Extensions and Solvable Groups 201
8.4 Simple Groups 210
8.5 Solving Polynomials by Radicals 215
8.6 The Casus Irreducbilis (Optional) 220
9 Cyclotomic Extensions 229
9.1 Cyclotomic Polynomials 229
9.2 Gauss and Roots of Unity (Optional) 238
10 Geometric Constructions 255
10.1 Constructible Numbers 255
10.2 Regular Polygons and Roots of Unity 270
10.3 Origami (Optional) 274
11 Finite Fields 291
11.1 The Structure of Finite Fields 291
11.2 Irreducible Polynomials over Finite Fields (Optional) 301
PART IV FURTHER TOPICS
12 Lagrange, Galois, and Kronecker 315
12.1 Lagrange 315
12.2 Galois 334
12.3 Kronecker 347
13 Computing Galois Groups 357
13.1 Quartic Polynomials 357
13.2 Quintic Polynomials 368
13.3 Resolvents 386
13.4 Other Methods 400
14 Solvable Permutation Groups 413
14.1 Polynomials of Prime Degree 413
14.2 Imprimitive Polynomials of Prime-Squared Degree 419
14.3 Primitive Permutation Groups 429
14.4 Primitive Polynomials of Prime-Squared Degree 444
15 The Lemniscate 463
15.1 Division Points and Arc Length 464
15.2 The Lemniscatic Function 470
15.3 The Complex Lemniscatic Function 482
15.4 Complex Multiplication 489
15.5 Abel`s Theorem 504
A Abstract Algebra 515
A.1 Basic Algebra 515
A.2 Complex Numbers 524
A.3 Polynomials with Rational Coefficients 528
A.4 Group Actions 530
A.5 More Algebra 532
Index 557
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Cox, David A., Galois Theory
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The Universe in Zero Words
The Story of Mathematics As Told Through Equations
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A history of 24 great and beautiful equations that have shaped mathematics, science and society. Illustrated in colour throughout, the book tells the human and often surprising stories behind each one, and shows why they have something timeless to say about the universe, and how they do it with an economy (zero words) that no other form of human ex
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Mackenzie, Universe in Zero Words
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Space Chronicles - Facing the Ultimate Frontier
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Rosenhouse, Jason, Taalman, Laura
Taking Sudoku Seriously
The Math Behind the World`s Most Popular Pencil Puzzle
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Games Primates Play
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Maestripieri, Dario, Games Primates Play
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A Guide to the Elements
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Stwertka, Albert, Guide to the Elements
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