Paperback (ISBN-13: 9780898716658)
This text provides an introduction to hidden Markov models (HMMs) for the dynamical systems community. It is a valuable text for third or fourth year undergraduates studying engineering, mathematics, or science that includes work in probability, linear algebra and differential equations. The book presents algorithms for using HMMs, and it explains the derivation of those algorithms. It presents Kalman filtering as the extension to a continuous state space of a basic HMM algorithm. The book concludes with an application to biomedical signals. This text is distinctive for providing essential introductory material as well as presenting enough of the theory behind the basic algorithms so that the reader can use it as a guide to developing their own variants.
* Features illustrations that use the Lorenz system, laser data, and natural
language data * Supporting web site gives a working implementation of each
algorithm from the book * Enables readers to develop their own variants
Preface; 1. Introduction; 2. Basic algorithms; 3. Variants and generalizations; 4. Continuous states and observations and Kalman filtering; 5. Performance bounds and a toy problem; 6. Obstructive sleep apnea; Appendix A. Formulas for matrices and Gaussians; Appendix B. Notes on software; Bibliography; Index.
Hardback (ISBN-13: 9780521874229)
Few branches of mathematics have been more influential in the social sciences than game theory. In recent years, it has become an essential tool for all social scientists studying the strategic behaviour of competing individuals, firms and countries. However, the mathematical complexity of game theory is often very intimidating for students who have only a basic understanding of mathematics. Insights into Game Theory addresses this problem by providing students with an understanding of the key concepts and ideas of game theory without using formal mathematical notation. The authors use four very different topics (college admission, social justice and majority voting, coalitions and co-operative games, and a bankruptcy problem from the Talmud) to investigate four areas of game theory. The result is a fascinating introduction to the world of game theory and its increasingly important role in the social sciences.
* An innovative, non-technical introduction to key topics in game theory
* Suitable for readers with only a basic understanding of mathematics *
End-of-chapter exercises enable students to monitor progress and understanding
of key concepts
Introduction; 1. Mathematical matching; 2. Social justice; 3. The Shapley value in cooperative games; 4. Analysis of a bankruptcy problem from the Talmud; Answers to the exercises; Index.
Series: MAA Problem Book Series
Hardback (ISBN-13: 9780883858295)
Every mathematician (beginner, amateur, and professional alike) thrills to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called eaha! solutions,f a phrase popularized by mathematics and science writer Martin Gardner. Aha! solutions are surprising, stunning, and scintillating: they reveal the beauty of mathematics. This collection includes one hundred problems in the areas of arithmetic, geometry, algebra, calculus, probability, number theory, and combinatorics. The problems start out easy and generally get more difficult as you progress through the book. A few solutions require the use of a computer. An important feature of the book is the discussion of related mathematics that follows the solution of each problem. This material is there to entertain and inform you or point you to new questions.
* Includes a toolkit that lets you look up a definition or concept * Contains
100 problems and their elegant solutions * Progresses through the book
from easy problems to harder ones
Preface; 1. Elementary problems; 2. Intermediate problems; 3. Advanced problems; A. Toolkit; B. List of bonuses; Bibliography; Index.
Hardback (ISBN-13: 9780521899574)
The sheer complexity of computer systems has meant that automated reasoning, i.e. the ability of computers to perform logical inference, has become a vital component of program construction and of programming language design. This book meets the demand for a self-contained and broad-based account of the concepts, the machinery and the use of automated reasoning. The mathematical logic foundations are described in conjunction with practical application, all with the minimum of prerequisites. The approach is constructive, concrete and algorithmic: a key feature is that methods are described with reference to actual implementations (for which code is supplied) that readers can use, modify and experiment with. This book is ideally suited for those seeking a one-stop source for the general area of automated reasoning. It can be used as a reference, or as a place to learn the fundamentals, either in conjunction with advanced courses or for self study.
* One stop reference that is broad-based and self-contained * Constructive
approach that enables topics to be discussed algorithmically; implementation
of these algorithms provided as code * Can be used as a reference, or as
a place to learn the fundamentals, either in conjunction with advanced
courses or for self study
Preface; Ideological orientation; Acknowledgements; How to read this book; 1. Introduction; 2. Propositional logic; 3. First-order logic; 4. Equality; 5. Decidable problems; 6. Interactive theorem proving; 7. Limitations; Appendix 1. Mathematical background; Appendix 2. OCaml made light of; Appendix 3. Parsing and printing of formulas; References; Index.
Series: Cambridge Monographs on Mathematical Physics
Hardback (ISBN-13: 9780521877879)
Quantum field theory in curved spacetime has been remarkably fruitful. It can be used to explain how the large-scale structure of the universe and the anisotropies of the cosmic background radiation that we observe today first arose. Similarly, it provides a deep connection between general relativity, thermodynamics, and quantum field theory. This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime.
* Emphasises physically motivated derivations to gradually introduce the
material to the reader * Takes the reader from introductory to research
level, by including comprehensive discussions of applications to cosmology
and black holes * Describes many other aspects of free and interacting
quantized fields in curved spacetime to provide a deeper understanding
of the material
ContentsPreface; Conventions and notation; 1. Quantum fields in Minkowski
spacetime; 2. Basics of quantum fields in curved spacetimes; 3. Expectation
values quadratic in fields; 4. Particle creation by black holes; 5. The
one-loop effective action; 6. The effective action: non-gauge theories;
7. The effective action: gauge theories; Appendixes; References; Index.