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This book surveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information. Topics include scoring, bidding chess, Wythoff Nim, misere play, partizan bidding, loopy games, and placement games, along with a survey of temperature theory by Elwyn Berlekamp and a list of unsolved problems.

First published in 2000, this book provides a clear and complete picture of research in Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry. The expository nature of the articles makes this an excellent introduction for students as well as a basis for continuing research.

Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.

This 1999 book is a collection of research and expository articles on convex geometry and probability, suitable for researchers and graduate students in several branches of mathematics coming under the broad heading of 'Geometric Functional Analysis'. It arises arises from an MSRI program held in the spring of 1996.

A collection of thirteen articles by many of the leading contributors in the field on the history of the Gross-Zagier formula and its developments. It touches on the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the Gross-Zagier formula.

This comprehensive introduction for beginning graduate students contains articles by the leading experts in the field. It covers basic topics such as algorithmic aspects of number fields, elliptic curves, and lattice basis reduction and advanced topics including cryptography, computational class field theory, zeta functions and L-series, and quantum computing.

This book considers a branch of Riemannian geometry called Comparison Geometry. Comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has recently received great attention. This is an up-to-date reflection of developments in this field.

When the Mathematical Sciences Research Institute was started in the Fall of 1982, one of the programs was "non-linear partial differential equations". A seminar was organized whose audience consisted of graduate students of the University and mature mathematicians who are not experts in the field. This volume contains 18 of these lectures. An effort is made to have an adequate Bibliography for further information. The Editor wishes to take this opportunity to thank all the speakers and the authors of the articles presented in this volume for their cooperation. S. S. Chern, Editor Table of Contents Geometrical and Analytical Questions Stuart S. Antman 1 in Nonlinear Elasticity An Introduction to Euler's Equations Alexandre J. Chorin 31 for an Incompressible Fluid Linearizing Flows and a Cohomology Phillip Griffiths 37 Interpretation of Lax Equations The Ricci Curvature Equation Richard Hamilton 47 A Walk Through Partial Differential Fritz John 73 Equations Remarks on Zero Viscosity Limit for Tosio Kato 85 Nonstationary Navier-Stokes Flows with Boundary Free Boundary Problems in Mechanics Joseph B. Keller 99 The Method of Partial Regularity as Robert V.

Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. In this book, originally published in 2000, leading experts provide the necessary background to understanding the model theory and mathematics behind these applications.

This fascinating 2003 collection of articles runs the gamut from new theoretical approaches, both computational and mathematical, to other games such as Amazons, Chomp, Dot-and-Boxes, Go, Chess, and Hex. Includes an updated bibliography by A. Fraenkel and a list of combinatorial game theory problems by R. K. Guy.

This book develops K-theory, the theory of extensions, and Kasparov's bivariant KK-theory for C*-algebras. Special topics covered include the theory of AF algebras, axiomatic K-theory, the Universal Coefficient Theorem, and E-theory. Although the book is technically complete, motivation and intuition are emphasized. Many examples and applications are discussed.

This book deals with combinatorial games, that is, games not involving chance or hidden information. The first part of the book will be accessible to anyone, regardless of background. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go, plus reports on computer advances and theoretical approaches.

A volume of lectures on four geometrically-influenced fields of mathematics that have experienced great development in recent years, with chapters by well-known researchers on hyperbolic geometry, dynamics in several complex variables, convex geometry, and Banach space geometry.

Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.

This book deals with combinatorial games, that is, games not involving chance or hidden information. The first part of the book will be accessible to anyone, regardless of background. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go, plus reports on computer advances and theoretical approaches.

During the past decade, mathematics education has changed rapidly, creating a polarization of opinions among research mathematicians. This volume, the proceedings of a conference held at the Mathematical Sciences Research Institute in Berkeley in 1996, presents a serious discussion of these educational issues, with a balanced representation of opposing ideas.

This book contains expository contributions by respected researchers on the rich combinatorial problems arising from the study of algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. It will continue to be of use to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.

First published in 2000, this expository volume of surveys and research results covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems.

This book contains eight expository articles by well-known authors on the theory of Galois groups and fundamental groups, focusing on developments in the field. Among the subjects covered are elliptic surfaces, Grothendieck's anabelian conjecture, fundamental groups of curves and differential Galois theory in positive characteristic.

These articles form a broad survey of this exciting field. Topics include pointed Hopf algebras, triangular Hopf algebras, Hopf algebra extensions and cohomology, quantum groups and groupoids, quantum symmetric pairs, monoidal categories, and the Brauer group of a Hopf algebra.

This 1997 book contains six in-depth articles on various aspects of the field of tight and taut submanifolds and concludes with an extensive bibliography of the entire field. The first paper is an unfinished but insightful survey of the field of tight immersions and maps by Nicolaas H. Kuiper.

Presents a complete proof of Connes' Index Theorem generalized to foliated spaces, alongside the necessary background from analysis, geometry, and topology. It thus provides a natural introduction to the basic ideas of noncommutative topology. This edition has improved exposition, an updated bibliography, an index, and covers new developments and applications.

This volume presents the results of discussions among mathematicians, maths education researchers, teachers, test developers, and policymakers who gathered to work through critical issues related to mathematics assessment. It highlights the kinds of information that different assessments can offer, with examples of some of the best mathematics assessments worldwide.

This volume presents the results of discussions among mathematicians, maths education researchers, teachers, test developers, and policymakers who gathered to work through critical issues related to mathematics assessment. It highlights the kinds of information that different assessments can offer, with examples of some of the best mathematics assessments worldwide.

Surveys and research articles based on a 2004 MRSI research workshop, plus a commented problem list by leading experts cover several areas of dynamical systems that have recently experienced substantial progress, including symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory.

This book considers a branch of Riemannian geometry called Comparison Geometry. Comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has recently received great attention. This is an up-to-date reflection of developments in this field.

In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms.

Covering the mathematical basis of signal processing and many areas of application, this book is based on a series of graduate-level lectures held at the Mathematical Sciences Research Institute. Emphasis is on challenges in the subject, particular techniques adapted to particular technologies, and certain advances in algorithms and theory.

This book presents expository accounts of six important topics in Finsler geometry suitable for a special-topics graduate course in differential geometry. They treat issues related to volume, geodesics, curvature and mathematical biology, and provide a good variety of instructive examples.

This 2005 volume, covering a broad range of topics, is an outgrowth of the synergism of Discrete and Computational Geometry. Its surveys and research articles explore geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms, and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension.