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What's Next?

Author : Dylan Thurston
Publisher : Princeton University Press
ISBN 13 : 069116777X
Total Pages : 436 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis What's Next? by : Dylan Thurston

Download or read book What's Next? written by Dylan Thurston and published by Princeton University Press. This book was released on 2020-07-07 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Thurston (1946-2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of mathematical fields, from foliations, contact structures, and Teichm ller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. What's Next? brings together many of today's leading mathematicians to describe recent advances and future directions inspired by Thurston's transformative ideas. Including valuable insights from his colleagues and former students, What's Next? discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. This incisive and wide-ranging book also explores how he introduced new ways of thinking about and doing mathematics, innovations that have had a profound and lasting impact on the mathematical community as a whole.

In the Tradition of Thurston

Author : Ken’ichi Ohshika
Publisher : Springer Nature
ISBN 13 : 3030559289
Total Pages : 724 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis In the Tradition of Thurston by : Ken’ichi Ohshika

Download or read book In the Tradition of Thurston written by Ken’ichi Ohshika and published by Springer Nature. This book was released on 2020-12-07 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.

The Geometry and Topology of Three-Manifolds

Author : William P. Thurston
Publisher : American Mathematical Society
ISBN 13 : 1470474743
Total Pages : 337 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Geometry and Topology of Three-Manifolds by : William P. Thurston

Download or read book The Geometry and Topology of Three-Manifolds written by William P. Thurston and published by American Mathematical Society. This book was released on 2023-06-16 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.

Thurston's Work on Surfaces (MN-48)

Author : Albert Fathi
Publisher : Princeton University Press
ISBN 13 : 0691147353
Total Pages : 272 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Thurston's Work on Surfaces (MN-48) by : Albert Fathi

Download or read book Thurston's Work on Surfaces (MN-48) written by Albert Fathi and published by Princeton University Press. This book was released on 2012-04 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of William Thurston's work on surface homeomorphisms, available here for the first time in English. Based on material of Thurston presented at a seminar in Orsay from 1976 to 1977, it covers topics such as the space of measured foliations on a surface, the Thurston compactification of Teichmüller space, the Nielsen-Thurston classification of surface homeomorphisms, and dynamical properties of pseudo-Anosov diffeomorphisms. Thurston never published the complete proofs, so this text is the only resource for many aspects of the theory. Thurston was awarded the prestigious Fields Medal in 1982 as well as many other prizes and honors, and is widely regarded to be one of the major mathematical figures of our time. Today, his important and influential work on surface homeomorphisms is enjoying continued interest in areas ranging from the Poincaré conjecture to topological dynamics and low-dimensional topology. Conveying the extraordinary richness of Thurston's mathematical insight, this elegant and faithful translation from the original French will be an invaluable resource for the next generation of researchers and students.

Three-dimensional Geometry and Topology

Author : William P. Thurston
Publisher : Princeton University Press
ISBN 13 : 9780691083049
Total Pages : 340 pages
Book Rating : 4.0/5 (83 download)

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Book Synopsis Three-dimensional Geometry and Topology by : William P. Thurston

Download or read book Three-dimensional Geometry and Topology written by William P. Thurston and published by Princeton University Press. This book was released on 1997 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every mathematician should be acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This book contains a great deal of interesting mathematics.

Crocheting Adventures with Hyperbolic Planes

Author : Daina Taimina
Publisher : CRC Press
ISBN 13 : 1351402196
Total Pages : 865 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Crocheting Adventures with Hyperbolic Planes by : Daina Taimina

Download or read book Crocheting Adventures with Hyperbolic Planes written by Daina Taimina and published by CRC Press. This book was released on 2018-02-19 with total page 865 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner, Euler Book Prize, awarded by the Mathematical Association of America. With over 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion & quantum computing.

Mathematical Writing

Author : Donald E. Knuth
Publisher : Cambridge University Press
ISBN 13 : 9780883850633
Total Pages : 132 pages
Book Rating : 4.8/5 (56 download)

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Book Synopsis Mathematical Writing by : Donald E. Knuth

Download or read book Mathematical Writing written by Donald E. Knuth and published by Cambridge University Press. This book was released on 1989 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will help those wishing to teach a course in technical writing, or who wish to write themselves.

Geometrisation of 3-manifolds

Author :
Publisher : European Mathematical Society
ISBN 13 : 9783037190821
Total Pages : 256 pages
Book Rating : 4.1/5 (98 download)

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Book Synopsis Geometrisation of 3-manifolds by :

Download or read book Geometrisation of 3-manifolds written by and published by European Mathematical Society. This book was released on 2010 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition along essential, embedded surfaces into pieces that possess geometric structures. It contains the famous Poincaré Conjecture as a special case. In 2002, Grigory Perelman announced a proof of the Geometrisation Conjecture based on Richard Hamilton’s Ricci flow approach, and presented it in a series of three celebrated arXiv preprints. Since then there has been an ongoing effort to understand Perelman’s work by giving more detailed and accessible presentations of his ideas or alternative arguments for various parts of the proof. This book is a contribution to this endeavour. Its two main innovations are first a simplified version of Perelman’s Ricci flow with surgery, which is called Ricci flow with bubbling-off, and secondly a completely different and original approach to the last step of the proof. In addition, special effort has been made to simplify and streamline the overall structure of the argument, and make the various parts independent of one another. A complete proof of the Geometrisation Conjecture is given, modulo pre-Perelman results on Ricci flow, Perelman’s results on the ℒ-functional and κ-solutions, as well as the Colding–Minicozzi extinction paper. The book can be read by anyone already familiar with these results, or willing to accept them as black boxes. The structure of the proof is presented in a lengthy introduction, which does not require knowledge of geometric analysis. The bulk of the proof is the existence theorem for Ricci flow with bubbling-off, which is treated in parts I and II. Part III deals with the long time behaviour of Ricci flow with bubbling-off. Part IV finishes the proof of the Geometrisation Conjecture.

Really Big Numbers

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
ISBN 13 : 1470414252
Total Pages : 194 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Really Big Numbers by : Richard Evan Schwartz

Download or read book Really Big Numbers written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2014-06-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the vast universe of numbers.

Moduli Spaces and Locally Symmetric Spaces

Author : Lizhen Ji
Publisher :
ISBN 13 : 9781571464095
Total Pages : 370 pages
Book Rating : 4.4/5 (64 download)

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Book Synopsis Moduli Spaces and Locally Symmetric Spaces by : Lizhen Ji

Download or read book Moduli Spaces and Locally Symmetric Spaces written by Lizhen Ji and published by . This book was released on 2021-10-30 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides accessible and systematic introductions to moduli spaces of Riemann surfaces, algebraic curves, moduli spaces of vector bundles on Riemann surfaces, moduli spaces of singularities, and compactification of a natural class of locally symmetric spaces.

Ricci Flow and the Poincare Conjecture

Author : John W. Morgan
Publisher : American Mathematical Soc.
ISBN 13 : 9780821843284
Total Pages : 586 pages
Book Rating : 4.8/5 (432 download)

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Book Synopsis Ricci Flow and the Poincare Conjecture by : John W. Morgan

Download or read book Ricci Flow and the Poincare Conjecture written by John W. Morgan and published by American Mathematical Soc.. This book was released on 2007 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Lectures on Hyperbolic Geometry

Author : Riccardo Benedetti
Publisher : Springer Science & Business Media
ISBN 13 : 3642581587
Total Pages : 343 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Lectures on Hyperbolic Geometry by : Riccardo Benedetti

Download or read book Lectures on Hyperbolic Geometry written by Riccardo Benedetti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as self-contained, complete, detailed and unified as possible. Following some classical material on the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (including a complete proof, following Gromov and Thurston) and Margulis' lemma. These then form the basis for studying Chabauty and geometric topology; a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory; and much space is devoted to the 3D case: a complete and elementary proof of the hyperbolic surgery theorem, based on the representation of three manifolds as glued ideal tetrahedra.

The Geometrization Conjecture

Author : John Morgan
Publisher : American Mathematical Soc.
ISBN 13 : 0821852019
Total Pages : 306 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Geometrization Conjecture by : John Morgan

Download or read book The Geometrization Conjecture written by John Morgan and published by American Mathematical Soc.. This book was released on 2014-05-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a complete proof of the geometrization conjecture, which describes all compact 3-manifolds in terms of geometric pieces, i.e., 3-manifolds with locally homogeneous metrics of finite volume. The method is to understand the limits as time goes to infinity of Ricci flow with surgery. The first half of the book is devoted to showing that these limits divide naturally along incompressible tori into pieces on which the metric is converging smoothly to hyperbolic metrics and pieces that are locally more and more volume collapsed. The second half of the book is devoted to showing that the latter pieces are themselves geometric. This is established by showing that the Gromov-Hausdorff limits of sequences of more and more locally volume collapsed 3-manifolds are Alexandrov spaces of dimension at most 2 and then classifying these Alexandrov spaces. In the course of proving the geometrization conjecture, the authors provide an overview of the main results about Ricci flows with surgery on 3-dimensional manifolds, introducing the reader to this difficult material. The book also includes an elementary introduction to Gromov-Hausdorff limits and to the basics of the theory of Alexandrov spaces. In addition, a complete picture of the local structure of Alexandrov surfaces is developed. All of these important topics are of independent interest. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

How to Be Black

Author : Baratunde Thurston
Publisher : Harper Collins
ISBN 13 : 0062098047
Total Pages : 279 pages
Book Rating : 4.0/5 (62 download)

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Book Synopsis How to Be Black by : Baratunde Thurston

Download or read book How to Be Black written by Baratunde Thurston and published by Harper Collins. This book was released on 2012-01-31 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The comedian chronicles his coming of age while analyzing politics & culture in this New York Times–bestselling memoir and satirical guide. If You Don't Buy This Book, You’re a Racist. Have you ever been called “too black” or “not black enough?” Have you ever befriended or worked with a black person? Have you ever heard of black people? If you answered yes to any of these questions, this book is for you. Raised by a pro-black, Pan-Afrikan single mother during the crack years of 1980s Washington, DC, and educated at Sidwell Friends School and Harvard University, Baratunde Thurston has over thirty years’ experience being black. Now, through stories of his politically inspired Nigerian name, the heroics of his hippie mother, the murder of his drug-abusing father, and other revelatory black details, he shares with readers of all colors his wisdom and expertise in how to be black. Beyond memoir, this guidebook offers practical advice on everything from “How to Be The Black Friend” to “How to Be The (Next) Black President” to “How to Celebrate Black History Month.” To provide additional perspective, Baratunde assembled an award-winning Black Panel—three black women, three black men, and one white man (Christian Lander of Stuff White People Like)—and asked them such revealing questions as “When Did You First Realize You Were Black?” and “How Black Are You?” as well as “Can You Swim?” The result is a humorous, intelligent, and audacious guide that challenges and satirizes the so-called experts, purists, and racists who purport to speak for all black people. With honest storytelling and biting wit, Baratunde plots a path not just to blackness, but one open to anyone interested in simply “how to be.” Praise for How to Be Black “Part autobiography, part stand-up routine, part contemporary political analysis, and astute all over. . . . Reading this book made me both laugh and weep with poignant recognition. . . . A hysterical, irreverent exploration of one of America’s most painful and enduring issues.” —Melissa Harris-Perry “Struggling to figure out how to be black in the 21st century? Baratunde Thurston has the perfect guide for you.” —The Root

Frontiers in Complex Dynamics

Author : Araceli Bonifant
Publisher : Princeton University Press
ISBN 13 : 0691159297
Total Pages : 799 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Frontiers in Complex Dynamics by : Araceli Bonifant

Download or read book Frontiers in Complex Dynamics written by Araceli Bonifant and published by Princeton University Press. This book was released on 2014-03-16 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky.

The Number System

Author : H. A. Thurston
Publisher : Courier Corporation
ISBN 13 : 0486154947
Total Pages : 146 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Number System by : H. A. Thurston

Download or read book The Number System written by H. A. Thurston and published by Courier Corporation. This book was released on 2012-10-23 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.

Analysis

Author : Terence Tao
Publisher :
ISBN 13 :
Total Pages : 284 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Analysis by : Terence Tao

Download or read book Analysis written by Terence Tao and published by . This book was released on 2006 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to real analysis, this text is suitable for honours undergraduates. It starts at the very beginning - the construction of the number systems and set theory, then to the basics of analysis, through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral.