Author: Harold Scott Macdonald Coxeter Publisher: American Mathematical Soc. ISBN: 9780821887608 Category : Mathematics Languages : en Pages : 344
Book Description
This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.
Author: Siobhan Roberts Publisher: Bloomsbury Publishing USA ISBN: 0802718329 Category : Mathematics Languages : en Pages : 420
Book Description
"There is perhaps no better way to prepare for the scientific breakthroughs of tomorrow than to learn the language of geometry." -Brian Greene, author of The Elegant Universe The word "geometry" brings to mind an array of mathematical images: circles, triangles, the Pythagorean Theorem. Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives-from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century. Many of the greatest names in intellectual history-Pythagoras, Plato, Archimedes, Euclid- were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions-his famed Coxeter groups and Coxeter diagrams-have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational. Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.
Author: Rafael Stekolshchik Publisher: Springer Science & Business Media ISBN: 3540773991 Category : Mathematics Languages : en Pages : 250
Book Description
Here is a key text on the subject of representation theory in finite groups. The pages of this excellent little book, prepared by Rafael Stekolshchik, contain a number of new proofs relating to Coxeter Transformations and the McKay Correspondence. They include ideas and formulae from a number of luminaries including J. N. Bernstein, I. M. Gelfand and V. A. Ponomarev, as well as material from Coxeter and McKay themselves. Many other authors have material published here too.
Author: Siobhan Roberts Publisher: Princeton University Press ISBN: 0691264759 Category : Mathematics Languages : en Pages : 416
Book Description
An illuminating biography of one of the greatest geometers of the twentieth century Driven by a profound love of shapes and symmetries, Donald Coxeter (1907–2003) preserved the tradition of classical geometry when it was under attack by influential mathematicians who promoted a more algebraic and austere approach. His essential contributions include the famed Coxeter groups and Coxeter diagrams, tools developed through his deep understanding of mathematical symmetry. The Man Who Saved Geometry tells the story of Coxeter’s life and work, placing him alongside history’s greatest geometers, from Pythagoras and Plato to Archimedes and Euclid—and it reveals how Coxeter’s boundless creativity reflects the adventurous, ever-evolving nature of geometry itself. With an incisive, touching foreword by Douglas R. Hofstadter, The Man Who Saved Geometry is an unforgettable portrait of a visionary mathematician.
Author: Robert S. Doran Publisher: American Mathematical Soc. ISBN: 0821811975 Category : Mathematics Languages : en Pages : 568
Book Description
Harish-Chandra was a mathematician of great power, vision, and remarkable ingenuity. His profound contributions to the representation theory of Lie groups, harmonic analysis, and related areas left researchers a rich legacy that continues today. This book presents the proceedings of an AMS Special Session entitled, "Representation Theory and Noncommutative Harmonic Analysis: A Special Session Honoring the Memory of Harish-Chandra", which marked 75 years since his birth and 15 years since his untimely death at age 60. Contributions to the volume were written by an outstanding group of internationally known mathematicians. Included are expository and historical surveys and original research papers. The book also includes talks given at the IAS Memorial Service in 1983 by colleagues who knew Harish-Chandra well. Also reprinted are two articles entitled, "Some Recollections of Harish-Chandra", by A. Borel, and "Harish-Chandra's c-Function: A Mathematical Jewel", by S. Helgason. In addition, an expository paper, "An Elementary Introduction to Harish-Chandra's Work", gives an overview of some of his most basic mathematical ideas with references for further study. This volume offers a comprehensive retrospective of Harish-Chandra's professional life and work. Personal recollections give the book particular significance. Readers should have an advanced-level background in the representation theory of Lie groups and harmonic analysis.
Author: Krzysztof Maurin Publisher: Springer Science & Business Media ISBN: 9401589399 Category : Mathematics Languages : en Pages : 732
Book Description
very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum).
Author: Patricia Hersh Publisher: American Mathematical Soc. ISBN: 1470427249 Category : Biography & Autobiography Languages : en Pages : 369
Book Description
Richard Stanley's work in combinatorics revolutionized and reshaped the subject. His lectures, papers, and books inspired a generation of researchers. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers. This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.
Author: J. L. Bona Publisher: American Mathematical Soc. ISBN: 0821831615 Category : Mathematics Languages : en Pages : 346
Book Description
Swift progress and new applications characterize the area of solitons and the inverse scattering transform. There are rapid developments in current nonlinear optical technology: Larger intensities are more available; pulse widths are smaller; relaxation times and damping rates are less significant. In keeping with these advancements, exactly integrable soliton equations, such as $3$-wave resonant interactions and second harmonic generation, are becoming more and more relevant inexperimental applications. Techniques are now being developed for using these interactions to frequency convert high intensity sources into frequency regimes where there are no lasers. Other experiments involve using these interactions to develop intense variable frequency sources, opening up even morepossibilities. This volume contains new developments and state-of-the-art research arising from the conference on the ``Legacy of the Inverse Scattering Transform'' held at Mount Holyoke College (South Hadley, MA). Unique to this volume is the opening section, ``Reviews''. This part of the book provides reviews of major research results in the inverse scattering transform (IST), on the application of IST to classical problems in differential geometry, on algebraic and analytic aspects ofsoliton-type equations, on a new method for studying boundary value problems for integrable partial differential equations (PDEs) in two dimensions, on chaos in PDEs, on advances in multi-soliton complexes, and on a unified approach to integrable systems via Painleve analysis. This conference provided aforum for general exposition and discussion of recent developments in nonlinear waves and related areas with potential applications to other fields. The book will be of interest to graduate students and researchers interested in mathematics, physics, and engineering.
Author: Michele Emmer Publisher: Springer ISBN: 354028849X Category : Mathematics Languages : en Pages : 489
Book Description
Softcover printing of a popular title (h/c sold over 400 copies in North America) at a price that will make it accessible to a much wider audience Richly illustrated with original art works in addition to well-known and little-known works by Escher A CD-ROM complements the articles, containing color illustrations of work by contemporary artists, movies, animations, and other demonstrations
Author: Doris Schattschneider Publisher: Springer Science & Business Media ISBN: 9783540424581 Category : Art Languages : en Pages : 506
Book Description
"The CD-ROM is an extension of the book. It contains color versions of many of the art works that are shown in the book in black and white, as well as additional work by the artists. It gives vignettes of the conference ... animations, short videos, and interactive puzzles."--Page vii.
Author: Harold Scott Macdonald Coxeter
Author: Siobhan Roberts
Author: Rafael Stekolshchik
Author: Siobhan Roberts
Author: Robert S. Doran
Author: Krzysztof Maurin
Author: Patricia Hersh
Author: J. L. Bona
Author: Michele Emmer
Author: Doris Schattschneider