Book Description

Is Nine-Men's Morris, in the hands of perfect players, a win for white or for black--or a draw? Can king, rook, and knight always defeat king and two knights in chess? What can Go players learn from economists? What are nimbers, tinies, switches, minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full analysis of a nontrivial combinatorial game (Nim) only appeared in 1902. This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full anlaysis of a nontrivial combinatorial game (Nim) only appeared in 1902. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go; reports on computer advances such as the solution of Nine-Men's Morris and Pentominoes; and new theoretical approaches to such problems as games with many players.If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you. ... Read more

Reviews (3)

Fascinating
I don't have read all the book, but I read most of the scientific papers it is composed by. I think they are very interesting and puzzling, on the border line between serious mathematics (game theory and all this stuff) and "recreational math" (like the angel problem). It would be a good read also for people interested in computer games.

great book
This book is full of beatiful work. Every section is an investigation into some combinatorial game, or some idea in combinatorial game theory. Most of the material is clearly presented and all should be accessible to undergrads, but be warned: this is not simple stuff. But, as we all know, beautiful mathematics isn't always simple. The book also includes a section with 52 unsolved problems, which should be of considerable interest to the curious.

MAA Online review
See Ed Sandifer's MAA Online review at: http://www.maa.org/reviews/nochance.htm ... Read more

Book Description

Stochastic approximation is a relatively new technique for studying the properties of an experimental situation; it has important applications in fields such as medicine and engineering. The subject can be treated either largely as a branch of pure mathematics, or else from an empirical and practical angle. In this book, Dr Wasan gives a rigorous mathematical treatment of the subject, drawing together the scattered results of a number of authors. He discusses the conditions under which the method gives a valid approximation to the required solution; methods for optimal choice of parameters to hasten convergence; the comparison of the method with other techniques. The discussion and proofs of theorems are given in enough detail to make them easy to follow, while a number of interesting examples show how the techniques may be applied in many fields. ... Read more

Book Description

The appearance of Gruenbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way. --Gil Kalai, The Hebrew University of Jerusalem The original book of Gruenbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day. --Louis J. Billera, Cornell University The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again. --Peter McMullen, University College London

The combinatorial study of convex polytopes is today an extremely active and healthy area of mathematical research, and the number and depth of its relationships to other parts of mathematics have grown astonishingly since Convex Polytopes was first published in 1966. The new edition contains the full text of the original and the addition of notes at the end of each chapter. The notes are intended to bridge the thirty five years of intensive research on polytopes that were to a large extent initiated, guided, motivated and fuelled by the first edition of Convex Polytopes. The new material provides a direct guide to more than 400 papers and books that have appeared since 1967. Branko Grünbaum is Professor of Mathematics at the University of Washington. ... Read more

Book Description

This volume contains selected papers that were presented at theAMS-IMS-SIAM Joint Summer Research Conference on "DifferentialGeometric Methods in the Control of Partial DifferentialEquations", which was held at the University of Colorado inBoulder in June 1999.

The aim of the conference was to explore the infusion ofdifferential-geometric methods into the analysis of controltheory of partial differential equations, particularly in thechallenging case of variable coefficients, where the physicalcharacteristics of the medium vary from point to point. While amutually profitable link has been long established, for at least30 years, between differential geometry and control of ordinarydifferential equations, a comparable relationship betweendifferential geometry and control of partial differentialequations (PDEs) is a new and promising topic. Very recentresearch, just prior to the Colorado conference, supported theexpectation that differential geometric methods, when brought tobear on classes of PDE modelling and control problems withvariable coefficients, will yield significant mathematicaladvances.

The papers included in this volume---written by specialists inPDEs and control of PDEs as well as by geometers---collectivelysupport the claim that the aims of the conference are beingfulfilled. In particular, they endorse the belief that bothsubjects---differential geometry and control of PDEs---have muchto gain by closer interaction with one another. Consequently,further research activities in this area are bound to grow. ... Read more

Book Description

Numbers, Information and Complexity is a collection of about 50 articles in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, `Numbers and Combinations', `Information Theory (Channels and Networks, Combinatorial and Algebraic Coding, Cryptology, with the related fields Data Compression, Entropy Theory, Symbolic Dynamics, Probability and Statistics)', and `Complexity'.Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results.The book features surveys on Combinatorics about topics such as intersection theorems, which are not yet covered in textbooks, several contributions by leading experts in data compression, and relations to Natural Sciences are discussed. ... Read more

Book Description

The description of the structure of group C*-algebras is a difficult problem, but relevant to important new developments in mathematics, such as non-commutative geometry and quantum groups. Although a significant number of new methods and results have been obtained, until now they have not been available in book form.This volume provides an introduction to and presents research on the study of group C*-algebras, suitable for all levels of readers - from graduate students to professional researchers. The introduction provides the essential features of the methods used. In Part I, the author offers an elementary overview - using concrete examples-of using K-homology, BFD functors, and KK-functors to describe group C*-algebras. In Part II, he uses advanced ideas and methods from representation theory, differential geometry, and KK-theory, to explain two primary tools used to study group C*-algebras: multidimensional quantization and construction of the index of group C*-algebras through orbit methods.The structure of group C*-algebras is an important issue both from a theoretical viewpoint and in its applications in physics and mathematics. Armed with the background, tools, and research provided in Methods of Noncommutative Geometry for Group C*-Algebras, readers can continue this work and make significant contributions to perfecting the theory and solving this problem. ... Read more

Reviews (2)

A Compliment to Anyone's Library
This is a wonderful book that challenges the reader to examine that relationships between philosophy and mathematics.While I may not agree with all of it, it is definately worthy of the read.

Oh no
this is the most pretentious and hollow book I have ever read, and to think it came so highly recommended. If there is such a thing as prog-litterature then this almost certainly is a prime example. ... Read more

Book Description

This book will interest and assist people who are dealing with the problems of predicitons of time series in higher education and research. It will greatly assist people who apply time series theory to practical problems in their work and also serve as a textbook for postgraduate students in statistics economics and related subjects. ... Read more

Book Description

This book focuses on the analysis of eigenvalues andeigenfunctions that describe singularities of solutions toelliptic boundary value problems in domains with corners andedges. The authors treat both classical problems of mathematicalphysics and general elliptic boundary value problems.

The volume is divided into two parts: The first is devoted to thepower-logarithmic singularities of solutions to classicalboundary value problems of mathematical physics. The seconddeals with similar singularities for higher order ellipticequations and systems.

Chapter 1 collects basic facts concerning operator pencils actingin a pair of Hilbert spaces. Related properties of ordinarydifferential equations with constant operator coefficients arediscussed and connections with the theory of general ellipticboundary value problems in domains with conic vertices areoutlined. New results are presented. Chapter 2 treats theLaplace operator as a starting point and a model for thesubsequent study of angular and conic singularities ofsolutions. Chapter 3 considers the Dirichlet boundary conditionbeginning with the plane case and turning to the space problems.Chapter 4 investigates some mixed boundary conditions. TheStokes system is discussed in Chapters 5 and 6, and Chapter 7concludes with the Dirichlet problem for the polyharmonicoperator.

Chapter 8 studies the Dirichlet problem for general ellipticdifferential equations of order $2m$ in an angle. In Chapter 9,an asymptotic formula for the distribution of eigenvalues ofoperator pencils corresponding to general elliptic boundaryvalue problems in an angle is obtained. Chapters 10 and 11discuss the Dirichlet problem for elliptic systems ofdifferential equations of order $2$ in an $n$-dimensional cone.Chapter 12 studies the Neumann problem for general ellipticsystems, in particular with eigenvalues of the correspondingoperator pencil in the strip $\mid {\Re} \lambda - m +/2n \mid \leq 1/2$. It is shown that only integer numberscontained in this strip are eigenvalues.

Applications are placed within chapter introductions and asspecial sections at the end of chapters. Prerequisites includestandard PDE and functional analysis courses. ... Read more

Book Description

This volume contains a selection of eighteen peer-reviewed articles that were presented at the 5th International Conference on Multivariate Approximation, held in Witten-Bommerholz in September 2002. The contributions cover recent developments of constructive approximation on manifolds, approximation by splines and kernels, subdivision techniques and wavelet methods.The main topics are: - applications of multivariate approximation in finance - approximation and stable reconstruction of images, data reduction - multivariate splines for Lagrange interpolation and quasi-interpolation - radial basis functions - spherical point sets - refinable function vectors and non-stationary subdivision - applications of adaptive wavelet methods - blending functions and cubature formulae - singularities of harmonic functions The book provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics, with many links to computer science and geophysics. ... Read more

Book Description

Volume III of Research in Collegiate Mathematics Education (RCME)presents state-of-the-art research on understanding, teaching,and learning mathematics at the post-secondary level. Thisvolume contains information on methodology and researchconcentrating on these areas of student learning:

Problem solving. Included here are three different articlesanalyzing aspects of Schoenfeld's undergraduate problem-solvinginstruction. The articles provide new detail and insight on awell-known and widely discussed course taught by Schoenfeld formany years.

Understanding concepts. These articles feature a variety ofmethods used to examine students' understanding of the conceptof a function and selected concepts from calculus. Theconclusions presented offer unique and interesting perspectiveson how students learn concepts.

Understanding proofs. This section provides insight from adistinctly psychological framework. Researchers examine howexisting practices can foster certain weaknesses. They offerways to recognize and interpret students' proof behaviors andsuggest alternative practices and curricula to build morepowerful schemes. The section concludes with a focused look atusing diagrams in the course of proving a statement. ... Read more