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Developed from the authors' introductory combinatorics course, this book focuses on a branch of mathematics which plays a crucial role in computer science. Combinatorial methods provide many analytical tools used for determining the expected performance of computer algorithms. Elementary subjects such as combinations and permutations, and mathematical tools such as generating functions and Pólya's Theory of Counting, are covered, as are analyses of specific problems such as Ramsey Theory, matchings, and Hamiltonian and Eulerian paths. This introduction will provide students with a solid foundation in the subject. ---- "This is a delightful little paperback which presents a day-by-day transcription of a course taught jointly by Pólya and Tarjan at Stanford University. Woods, the teaching assistant for the class, did a very good job of merging class notes into an interesting mini-textbook; he also included the exercises, homework, and tests assigned in the class (a very helpful addition for other instructors in the field). The notes are very well illustrated throughout and Woods and the Birkhäuser publishers produced a very pleasant text. One can count on [Pólya and Tarjan] for new insights and a fresh outlook. Both instructors taught by presenting a succession of examples rather than by presenting a body of theory ¦[The book] is very well suited as supplementary material for any introductory class on combinatorics; as such, it is very highly recommended. Finally, for all of us who like the topic and delight in observing skilled professionals at work, this book is entertaining and, yes, instructive, reading." Mathematical Reviews (Review of the original hardcover edition) "The mathematical community welcomes this book as a final contribution to honour the teacher G. Pólya." Zentralblatt MATH (Review of the original hardcover edition)

Discrete mathematics --- MATHEMATICS --- Cominations --- Monograph --- Mathematics. --- Math --- Science --- Combinatorial analysis --- Combinatorial analysis.

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Spatial statistics are useful in subjects as diverse as climatology, ecology, economics, environmental and earth sciences, epidemiology, image analysis and more. This book covers the best-known spatial models for three types of spatial data: geostatistical data (stationarity, intrinsic models, variograms, spatial regression and space-time models), areal data (Gibbs-Markov fields and spatial auto-regression) and point pattern data (Poisson, Cox, Gibbs and Markov point processes). The level is relatively advanced, and the presentation concise but complete. The most important statistical methods and their asymptotic properties are described, including estimation in geostatistics, autocorrelation and second-order statistics, maximum likelihood methods, approximate inference using the pseudo-likelihood or Monte-Carlo simulations, statistics for point processes and Bayesian hierarchical models. A chapter is devoted to Markov Chain Monte Carlo simulation (Gibbs sampler, Metropolis-Hastings algorithms and exact simulation). A large number of real examples are studied with R, and each chapter ends with a set of theoretical and applied exercises. While a foundation in probability and mathematical statistics is assumed, three appendices introduce some necessary background. The book is accessible to senior undergraduate students with a solid math background and Ph.D. students in statistics. Furthermore, experienced statisticians and researchers in the above-mentioned fields will find the book valuable as a mathematically sound reference. This book is the English translation of Modélisation et Statistique Spatiales published by Springer in the series Mathématiques & Applications, a series established by Société de Mathématiques Appliquées et Industrielles (SMAI). Carlo Gaetan is Associate Professor of Statistics in the Department of Statistics at the Ca' Foscari University of Venice. Xavier Guyon is Professor Emeritus at the University of Paris 1 Panthéon-Sorbonne. He is author of a Springer monograph on random fields.

Statistics. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Mathematical Applications in Earth Sciences. --- Econometrics. --- Math. Appl. in Environmental Science. --- Mathematical geography. --- Distribution (Probability theory). --- Mathematical statistics. --- Environmental sciences. --- Statistique --- Géographique mathématique --- Distribution (Théorie des probabilités) --- Statistique mathématique --- Sciences de l'environnement --- Econométrie --- Spatial analysis (Statistics) --- Statistik --- Raum --- Räumliche Statistik. --- Statistisches Modell. --- Mathematical models. --- Raum (Math.) --- (Math.) --- Statistik.

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This book attempts to fill two gaps which exist in the standard textbooks on the History of Mathematics. One is to provide students with material that could encourage more critical thinking. General textbooks, attempting to cover three thousand years of mathematical history, must necessarily oversimplify almost everything, the practice of which can scarcely promote a critical approach to the subject. For this reason, Craig Smorynski chooses a more narrow but deeper coverage of a few select topics. The second aim of this book is to include the proofs of important results which are typically neglected in the modern history of mathematics curriculum. The most obvious of these is the oft-cited necessity of introducing complex numbers in applying the algebraic solution of cubic equations. This solution, though it is now relegated to courses in the History of Mathematics, was a major occurrence in the history of mathematics. It was the first substantial piece of mathematics in Europe that was not a mere extension of what the Greeks had done and thus signified the coming of age of European mathematics. The fact that the solution, in the case of three distinct real roots to a cubic, necessarily involved complex numbers both made inevitable the acceptance and study of these numbers and provided a stimulus for the development of numerical approximation methods. Other unique features include: * a prefatory essay on the ways in which sources may be unreliable, followed by an annotated bibliography; * a modern recounting of a Chinese word problem from the 13th century, illustrating the need for consulting multiple sources when the primary source is unavailable; * the solution of the cubic equation, including multiple proofs that the algebraic solution uses complex numbers whenever the cubic equation has three distinct real solutions; * a critical reappraisal of Horner's Method; The final chapter contains lighter material, including a critical look at North Korea's stamps commemorating the 350th birthday of Newton, historically interesting (and hard to find) poems, and drinking songs or limericks with mathematical themes. The appendix outlines a few, small projects which could serve as replacements for the usual term papers. Craig Smorynski is also the author of "Self-Reference and Modal Logic" and "Logical Number Theory I".

Geometry --- Mathematics --- History. --- Math --- Science --- Geometry. --- Algebra. --- History of Mathematical Sciences. --- Mathematical analysis --- Euclid's Elements --- Mathematics. --- Annals --- Auxiliary sciences of history --- Histoire des mathematiques

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Retelling the best solutions and sharing the secrets of discovery are part of the process of teaching problem solving. Ideally, this process is characterized by mathematical skill, good taste, and wit. It is a characteristically personal process and the best such teachers have surely left their personal marks on students and readers. Alexander Soifer is a teacher of problem solving and his book, Mathematics as Problem Solving, is designed to introduce problem solving to the next generation. --Cecil Rousseau The American Mathematical Monthly The problems faithfully reflect the world famous Russian school of mathematics, whose folklore is carefully interwoven with more traditional topics. Many of the problems are drawn from the author's rich repertoire of personal experiences, dating back to his younger days as an outstanding competitor in his native Russia, and spanning decades and continents as an organizer of competitions at the highest level. --George Bersenyi The book contains a very nice collection of problems of various difficulty. I particularly liked the problems on combinatorics and geometry. --Paul Erdos Professor Soifer has put together a splendid collection of elementary problems designed to lead students into significant mathematical concepts and techniques. Highly recommended. --Martin Gardner To assemble so much material of the type used in Mathematical Olympiads, which has been tried and tested there, is unusual. To then present it in a form which develops themes, supported by relevant examples and problems for the reader, does the author great credit. --R. W. Whitworth The Mathematical Gazette.

Geometry --- geometrie --- algebra --- wiskunde --- Mathematics --- Discrete mathematics --- discrete wiskunde --- Algebra --- Problem solving. --- Algebra. --- Combinatorics. --- Geometry. --- Mathematics. --- Mathematics, general. --- Math --- Science --- Euclid's Elements --- Combinatorics --- Mathematical analysis

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The method of wavelet transforms is one key tool in signal processing and control. Modern wavelet theory defines outlines for construction of wavelets and transformations using them. It gives rules that one has to obey to get a wavelet basis with desired properties, meaning that everyone can create a wavelet adequate for the given task. An oscillatory property and multiresolution nature of wavelets recommends them for use both in signal processing and in solving complex mathematical models of real world phenomena. This book brings to engineers and other practitioners help in understanding how wavelets work in order to be able to create new or modify the existing wavelets according to their needs and tries to satisfy different user groups. It is self contained and no previous knowledge is assumed. In seven chapters, the book gives a concise understanding of the theory of wavelets, explains how to compute them in practise and finally presents typical applications of wavelets and how they work. The book is written for graduate students and practising Engineers of electrical communications, signal processing and control.

Engineering. --- Signal, Image and Speech Processing. --- Computational Science and Engineering. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Math Applications in Computer Science. --- Appl.Mathematics/Computational Methods of Engineering. --- Computer science. --- Engineering mathematics. --- Ingénierie --- Informatique --- Mathématiques de l'ingénieur --- Wavelets (Mathematics) --- Wavelets (Mathematics). --- Mathematics. --- Math --- Wavelet analysis --- Science --- Harmonic analysis