Springer Texts in Statistics
1st Edition., 2010, XVI, 494 p., Hardcover
ISBN: 978-1-4419-5779-5
Due: March 19, 2010
This is a text encompassing all of the standard topics in introductory probability theory, together with a significant amount of optional material of emerging importance. The emphasis is on a lucid and accessible writing style, mixed with a large number of interesting examples of a diverse nature. The text will prepare students extremely well for courses in more advanced probability and in statistical theory and for the actuary exam.
The book covers combinatorial probability, all the standard univariate discrete and continuous distributions, joint and conditional distributions in the bivariate and the multivariate case, the bivariate normal distribution, moment generating functions, various probability inequalities, the central limit theorem and the laws of large numbers, and the distribution theory of order statistics. In addition, the book gives a complete and accessible treatment of finite Markov chains, and a treatment of modern urn models and statistical genetics. It includes 303 worked out examples and 810 exercises, including a large compendium of supplementary exercises for exam preparation and additional homework. Each chapter has a detailed chapter summary. The appendix includes the important formulas for the distributions in common use and important formulas from calculus, algebra, trigonometry, and geometry.
Anirban DasGupta is Professor of Statistics at Purdue University, USA. He has been the main editor of the Lecture Notes and Monographs series, as well as the Collections series of the Institute of Mathematical Statistics, and is currently the Co-editor of the Selected Works in Statistics and Probability series, published by Springer. He has been an associate editor of the Annals of Statistics, Journal of the American Statistical Association, Journal of Statistical Planning and Inference, International Statistical Review, Sankhya, and Metrika. He is the author of Asymptotic Theory of Statistics and Probability, 2008, and of 70 refereed articles on probability and statistics. He is a Fellow of the Institute of Mathematical Statistics.
Introducing probability.- The birthday and matching problems.- Conditional probability and independence.- Integer-valued and discrete random variables.- Generating functions.- Standard discrete distributions.- Continuous random variables.- Some special continuous distributions.- Normal distribution.- Normal approximations and the Central Limit Theorem.- Multivariate discrete distributions.- Multidimensional densities.- Convolutions and transformations.- Markov chains and applications.- Urn models in physics and genetics.- Appendix I: Supplementary homework and practice problems.- Appendix II: Symbols and formulas.
1st Edition., 2010, 514 p., Hardcover
Series: Trends in Logic, Vol. 30
ISBN: 978-90-481-8784-3
Due: March 2010
Is the first book to show that the scope of application of Natural Deduction systems is far beyond the one usually considered
Is the first comprehensive presentation of hybrid deductive systems mixing Natural Deduction with Resolution
Is the first to label Natural Deduction systems for a wide spectrum of Temporal Logics
Provides a detailed presentation of problems connected with the formalization of Logics of linear time
Gives a detailed exposition of deductive systems for Hybrid Logics
This volume provides an extensive treatment of Natural Deduction and related types of proof systems, with a focus on the practical aspects of proof methods. The book has two main aims: Its first aim is to provide a systematic and historical survey of the variety of Natural Deduction systems in Classical and Modal Logics. The second aim is to present some systems of hybrid character, mixing Natural Deduction with other kinds of proof methods (including Sequent systems, Tableaux, Resolution). Such systems tend to be more universal and effective, because of the possibility of mixing strategies of proof search from different areas. All necessary background material is provided, in particular, a detailed presentation of Modal Logics, including First-Order Modal and Hybrid Modal Logics. The deduction systems presented in the book may be of interest to working logicians, researchers on automated deduction and teachers of logic.
Preface.- Introduction.- 1. Technical preliminaries.- 2. Standard Natural Deduction for Classical and Free Logic.- 3. Other Deductive Systems.- 4. Extended Natural Deduction.- 5. Background on Modal Logics.- 6. Survey of Natural Deduction and related formalizations for Modal Logics.- 7. Nonstandard Formalizations of Modal Logics.- 8. Labelled Natural Deduction.- 9. Case study of Logics with linear accessibility relation.- 10. Hybrid Logics.- Concluding remarks.- Bibliography.- Index.
Applied Mathematical Sciences, Vol. 171
1st Edition., 2010, XVI, 438 p., Hardcover
ISBN: 978-3-642-12054-1
Due: March 2010
Direct application of the theory presented in the book is a branch of the computerized analysis of medical images, called computational anatomy
Provides the background that is required for apprehending shapes in terms that are also suitable for computerized analysis and interpretation
The book explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms
Shapes are complex objects to apprehend, as mathematical entities, in terms that also are suitable for computerized analysis and interpretation. This volume provides the background that is required for this purpose, including different approaches that can be used to model shapes, and algorithms that are available to analyze them. It explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms. The book is, as far as possible, self-contained, with an appendix that describes a series of classical topics in mathematics (Hilbert spaces, differential equations, Riemannian manifolds) and sections that represent the state of the art in the analysis of shapes and their deformations.
Introduction.- 1. Parametrized Plane Curves.- 2. Medial Axis.- 3. Moment-Based Representation.- 4. Local Properties of Surfaces.- 5. Isocontours and Isosurfaces.- 6. Evolving Curves and Surfaces.- 7. Deformable templates.- 8. Ordinary Differential Equations and Groups of Diffeomorphisms.- 9. Building Admissible Spaces.- 10. Deformable Objects and Matching Functionals.- 11. Diffeomorphic Matching.- 12. Distances and Group Actions.- 13. Metamorphosis.- A. Elements from Hilbert Space Theory.- B. Elements from Differential Geometry.- C. Ordinary Differential Equations.- D. Optimization Algorithms.- E. Principal Component Analysis.- F. Dynamic Programming.- References.- Index.
Series: Universitext
Originally published by Prentice Hall, 2004
2010, XII, 424 p. 68 illus., Softcover
ISBN: 978-1-4419-5782-5
Due: May 29, 2010
- Provides 81 new problems in the exercises in addition to the problems from the first edition - Elegant and carefully written, with many examples and exercises throughout the book - Any needed concepts from linear algebra are introduced with examples as needed throughout the text - Contains up-to-date material as well as classical topics - Includes topics not normally discussed in most books in the subject area, such as perturbation methods and differential equations in Mathematica
For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as a chapter on perturbation methods and a section in Chapter 3 that shows how to solve differential equations using Mathematica codes. In addition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible with Mathematica, version 7.0, and all Mathematica codes are in the book itself. This new edition also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2 concerning fundamental matrices, and many further enhancements to the first edition. This book can be used either for a second course in ordinary differential equations or as an introductory course for well-prepared students. The prerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from linear algebra are introduced along with examples in the book. An undergraduate course in analysis is needed for the more theoretical subjects covered in the final two chapters.
Preface.- Chapter 1 First-Order Differential Equations.- 1.1 Basic Results.- 1.2 First-Order Linear Equations.- 1.3 Autonomous Equations.- 1.4 Generalized Logistic Equation.- 1.5 Bifurcation.- 1.6 Exercises.- Chapter 2 Linear Systems.- 2.1 Introduction.- 2.2 The Vector Equation x' = A(t)x.- 2.3 The Matrix Exponential Function.- 2.4 Induced Matrix Norm.- 2.5 Floquet Theory.- 2.6 Exercises.- Chapter 3 Autonomous Systems.- 3.1 Introduction.- 3.2 Phase Plane Diagrams.- 3.3 Phase Plane Diagrams for Linear Systems.- 3.4 Stability of Nonlinear Systems.- 3.5 Linearization of Nonlinear Systems.- 3.6 Existence and Nonexistence of Periodic Solutions.- 3.7 Three-Dimensional Systems.- 3.8 Differential Equations and Mathematica.- 3.9 Exercises.- Chapter 4 Perturbation Methods.- 4.1 Introduction.- 4.2 Periodic Solutions.- 4.3 Singular Perturbations.- 4.4 Exercises.- Chapter 5 The Self-Adjoint Second-Order Differential Equation.- 5.1 Basic Definitions.- 5.2 An Interesting Example.- 5.3 Cauchy Function and Variation of Constants Formula.- 5.4 Sturm-Liouville Problems.- 5.5 Zeros of Solutions and Disconjugacy.- 5.6 Factorizations and Recessive and Dominant Solutions.- 5.7 The Riccati Equation.- 5.8 Calculus of Variations.- 5.9 Greenfs Functions.- 5.10 Exercises.- Chapter 6 Linear Differential Equations of Order n.- 6.1 Basic Results.- 6.2 Variation of Constants Formula.- 6.3 Greenfs Functions.- 6.4 Factorizations and Principal Solutions.- 6.5 Adjoint Equation.- 6.6 Exercises.- Chapter 7 BVPs for Nonlinear Second-Order DEs.- 7.1 Contraction Mapping Theorem (CMT).- 7.2 Application of the CMT to a Forced Equation.- 7.3 Applications of the CMT to BVPs.- 7.4 Lower and Upper Solutions.- 7.5 Nagumo Condition.- 7.6 Exercises.- Chapter 8 Existence and Uniqueness Theorems.- 8.1 Basic Results.- 8.2 Lipschitz Condition and Picard-Lindelof Theorem.- 8.3 Equicontinuity and the Ascoli-Arzela Theorem.- 8.4 Cauchy-Peano Theorem.- 8.5 Extendability of Solutions.- 8.6 Basic Convergence Theorem.- 8.7 Continuity of Solutions with Respect to ICs.- 8.8 Kneserfs Theorem.- 8.9 Differentiating Solutions with Respect to ICs.- 8.10 Maximum and Minimum Solutions.- 8.11 Exercises.- Solutions to Selected Problems.- Bibliography.- Index