Poincare S Prize

Author : George G. Szpiro
Publisher : Penguin
Page : 321 pages
File Size : 53,7 Mb
Release : 2008-07-29
Category : Mathematics
ISBN : 9780452289642

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Poincare's Prize by George G. Szpiro Pdf

The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.

Author : George G. Szpiro
Publisher : Unknown
Page : 128 pages
File Size : 45,7 Mb
Release : 2008
Category : Electronic
ISBN : 1322835683

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Poincare's Prize by George G. Szpiro Pdf

Author : John W. Morgan,Gang Tian
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 42,7 Mb
Release : 2007
Category : Mathematics
ISBN : 0821843281

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Ricci Flow and the Poincare Conjecture by John W. Morgan,Gang Tian Pdf

For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Author : George G. Szpiro
Publisher : Penguin
Page : 324 pages
File Size : 55,6 Mb
Release : 2008-07-29
Category : Mathematics
ISBN : 9781440634284

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Poincare's Prize by George G. Szpiro Pdf

The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.

Author : Donal O'Shea
Publisher : Penguin UK
Page : 284 pages
File Size : 55,6 Mb
Release : 2008-10-30
Category : Science
ISBN : 9780141900346

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The Poincaré Conjecture by Donal O'Shea Pdf

The Poincaré Conjecture tells the story behind one of the world’s most confounding mathematical theories. Formulated in 1904 by Henri Poincaré, his Conjecture promised to describe the very shape of the universe, but remained unproved until a huge prize was offered for its solution in 2000. Six years later, an eccentric Russian mathematician had the answer. Here, Donal O’Shea explains the maths behind the Conjecture and its proof, and illuminates the curious personalities surrounding this perplexing conundrum, along the way taking in a grand sweep of scientific history from the ancient Greeks to Christopher Columbus. This is an enthralling tale of human endeavour, intellectual brilliance and the thrill of discovery.

Author : June Barrow-Green
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 47,7 Mb
Release : 1997
Category : Biography & Autobiography
ISBN : 0821803670

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Poincare and the Three Body Problem by June Barrow-Green Pdf

Poincare's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincare discovered mathematical chaos, as is now clear from June Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincare himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincare and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincare's related earlier work. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincare's subsequent highly influential work in celestial mechanics.

Author : Ahsan Habib Khandoker,Chandan Karmakar,Michael Brennan,Marimuthu Palaniswami,Andreas Voss
Publisher : Springer Science & Business Media
Page : 146 pages
File Size : 52,7 Mb
Release : 2013-08-15
Category : Medical
ISBN : 9781461473756

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Poincaré Plot Methods for Heart Rate Variability Analysis by Ahsan Habib Khandoker,Chandan Karmakar,Michael Brennan,Marimuthu Palaniswami,Andreas Voss Pdf

The Poincaré plot (named after Henri Poincaré) is a popular two-dimensional visualization tool for dynamic systems due to its intuitive display of the dynamic properties of a system from a time series. This book presents the basis of Poincaré plot and focus especially on traditional and new methods for analysing the geometry, temporal and spatial dynamics disclosed by the Poincaré plot to evaluate heart rate variability (HRV). Mathematical descriptors of Poincaré plot have been developed to quantify the autonomic nervous system activity (sympathetic and parasympathetic modulation of heart rate). Poincaré plot analysis has also been used in various clinical diagnostic settings like diabetes, chronic heart failure, chronic renal failure and sleep apnea syndrome. The primary aims of quantification of the Poincaré plots are to discriminate healthy physiological systems from pathological conditions and to classify the stage of a disease. The HRV analysis by Poincaré plot has opened up ample opportunities for important clinical and research applications. Therefore, the present book can be used either for self-study, as a supplement to courses in linear and nonlinear systems, or as a modern monograph by researchers in this field of HRV analysis.

Author : Vincent Rivasseau
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 54,6 Mb
Release : 2003-04-24
Category : Science
ISBN : 3764305274

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Poincaré Seminar 2002 by Vincent Rivasseau Pdf

The Poincaré Seminar is held twice a year at the Institut Henri Poincaré in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics. Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts.

Author : Jean-Marc Ginoux
Publisher : Springer Nature
Page : 150 pages
File Size : 53,8 Mb
Release : 2024-06-03
Category : Electronic
ISBN : 9783031513879

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Poincaré, Einstein and the Discovery of Special Relativity by Jean-Marc Ginoux Pdf

Author : Dagmar M. Meyer,Larry Smith
Publisher : Cambridge University Press
Page : 210 pages
File Size : 53,6 Mb
Release : 2005-08-18
Category : Mathematics
ISBN : 0521850649

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Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations by Dagmar M. Meyer,Larry Smith Pdf

A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.

Author : Bruce D Popp
Publisher : Springer Nature
Page : 285 pages
File Size : 47,5 Mb
Release : 2020-08-04
Category : Science
ISBN : 9783030480394

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Henri Poincaré: Electrons to Special Relativity by Bruce D Popp Pdf

Produced by an award-winning translator of Henri Poincaré, this book contains translations of several seminal articles by Poincaré and discusses the experimental and theoretical investigations of electrons that form their context. In the 1950s, a dispute ignited about the origin of the theory of special relativity and thrust considerable notoriety on a paper written by Henri Poincaré in 1905. Accordingly, Part I presents the relevant translations of Poincaré’s work showing that radiation carries momentum and the covariance of the equations of electrodynamics, the continuity equation for charge, and the spacetime interval. Part II then discusses investigations by Thomson, Becquerel, and Kaufmann of electrons in diverse contexts; contributions of Abraham, Lorentz and Poincaré to a theory of electrons that includes Lorentz transformations and explains the dependence of mass on velocity; and finally, Poincaré’s exploration of the relativity principle, electron stability, and gravitation while rejecting absolute motion (ether) and an electromagnetic origin of mass. Part III contains the 1904 article by H. A. Lorentz presenting his transformations.This book will be a fascinating read to graduate-level students, physicists, and science historians who are interested in the development of electrodynamics and the classical, relativistic theory of electrons at the beginning of the 20th century.

Author : Henri Poincar\'e
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 44,9 Mb
Release : 2010
Category : Algebraic topology
ISBN : 9780821852347

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Papers on Topology by Henri Poincar\'e Pdf

I am a proud owner of the original complete works in green leather in French bought for a princely sum in Paris around 1975. I have read in them exten-sively, and often during topology lectures I refer to parts of these works. I am happy that there is now the option for my students to read them in English---Dennis Sullivan --Book Jacket.

Author : Peter Galison
Publisher : W. W. Norton & Company
Page : 400 pages
File Size : 45,8 Mb
Release : 2004-09-17
Category : Science
ISBN : 9780393243864

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Einstein's Clocks, Poincare's Maps: Empires of Time by Peter Galison Pdf

"More than a history of science; it is a tour de force in the genre."—New York Times Book Review A dramatic new account of the parallel quests to harness time that culminated in the revolutionary science of relativity, Einstein's Clocks, Poincaré's Maps is "part history, part science, part adventure, part biography, part meditation on the meaning of modernity....In Galison's telling of science, the meters and wires and epoxy and solder come alive as characters, along with physicists, engineers, technicians and others....Galison has unearthed fascinating material" (New York Times). Clocks and trains, telegraphs and colonial conquest: the challenges of the late nineteenth century were an indispensable real-world background to the enormous theoretical breakthrough of relativity. And two giants at the foundations of modern science were converging, step-by-step, on the answer: Albert Einstein, an young, obscure German physicist experimenting with measuring time using telegraph networks and with the coordination of clocks at train stations; and the renowned mathematician Henri Poincaré, president of the French Bureau of Longitude, mapping time coordinates across continents. Each found that to understand the newly global world, he had to determine whether there existed a pure time in which simultaneity was absolute or whether time was relative. Esteemed historian of science Peter Galison has culled new information from rarely seen photographs, forgotten patents, and unexplored archives to tell the fascinating story of two scientists whose concrete, professional preoccupations engaged them in a silent race toward a theory that would conquer the empire of time.

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 305 pages
File Size : 52,7 Mb
Release : 2009
Category : Differential equations, Partial
ISBN : 9780821848852

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Poincare's Legacies, Part II by Terence Tao Pdf

Focuses on geometry, topology, and partial differential equations. This book discusses a variety of topics, including expository articles on topics such as gauge theory, the Kakeya needle problem, and the Black-Scholes equation. It is suitable for graduate students and research mathematicians interested in broad exposure to mathematical topics.

Author : James Carlson,Arthur Jaffe,Andrew Wiles
Publisher : American Mathematical Society, Clay Mathematics Institute
Page : 185 pages
File Size : 55,9 Mb
Release : 2023-09-14
Category : Mathematics
ISBN : 9781470474607

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The Millennium Prize Problems by James Carlson,Arthur Jaffe,Andrew Wiles Pdf

On August 8, 1900, at the second International Congress of Mathematicians in Paris, David Hilbert delivered his famous lecture in which he described twenty-three problems that were to play an influential role in mathematical research. A century later, on May 24, 2000, at a meeting at the Collège de France, the Clay Mathematics Institute (CMI) announced the creation of a US$7 million prize fund for the solution of seven important classic problems which have resisted solution. The prize fund is divided equally among the seven problems. There is no time limit for their solution. The Millennium Prize Problems were selected by the founding Scientific Advisory Board of CMI—Alain Connes, Arthur Jaffe, Andrew Wiles, and Edward Witten—after consulting with other leading mathematicians. Their aim was somewhat different than that of Hilbert: not to define new challenges, but to record some of the most difficult issues with which mathematicians were struggling at the turn of the second millennium; to recognize achievement in mathematics of historical dimension; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; and to emphasize the importance of working towards a solution of the deepest, most difficult problems. The present volume sets forth the official description of each of the seven problems and the rules governing the prizes. It also contains an essay by Jeremy Gray on the history of prize problems in mathematics.