Birth Of A Theorem

Author : Cédric Villani
Publisher : Farrar, Straus and Giroux
Page : 272 pages
File Size : 46,9 Mb
Release : 2015-04-14
Category : Biography & Autobiography
ISBN : 9780374710231

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Birth of a Theorem by Cédric Villani Pdf

In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of a Theorem is Villani's own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career. But you don't have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn't simplify or overexplain; rather, it invites readers into collaboration. Villani's diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You're privy to the dining-hall conversations at the world's greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker's whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

Author : David S. Richeson
Publisher : Princeton University Press
Page : 336 pages
File Size : 41,8 Mb
Release : 2019-07-23
Category : Mathematics
ISBN : 9780691191997

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Euler's Gem by David S. Richeson Pdf

How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.

Author : Judith R. Goodstein
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 42,6 Mb
Release : 2018-07-20
Category : Calculus of tensors
ISBN : 9781470428464

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Einstein’s Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity by Judith R. Goodstein Pdf

In the first decade of the twentieth century as Albert Einstein began formulating a revolutionary theory of gravity, the Italian mathematician Gregorio Ricci was entering the later stages of what appeared to be a productive if not particularly memorable career, devoted largely to what his colleagues regarded as the dogged development of a mathematical language he called the absolute differential calculus. In 1912, the work of these two dedicated scientists would intersect—and physics and mathematics would never be the same. Einstein's Italian Mathematicians chronicles the lives and intellectual contributions of Ricci and his brilliant student Tullio Levi-Civita, including letters, interviews, memoranda, and other personal and professional papers, to tell the remarkable, little-known story of how two Italian academicians, of widely divergent backgrounds and temperaments, came to provide the indispensable mathematical foundation—today known as the tensor calculus—for general relativity.

Author : Robin Wilson
Publisher : Unknown
Page : 170 pages
File Size : 53,7 Mb
Release : 2019-07-17
Category : Equations
ISBN : 9780198794936

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Euler's Pioneering Equation by Robin Wilson Pdf

In just seven symbols, with profound and beautiful simplicity, Euler's Equation connects five of the most important numbers in mathematics. Robin Wilson explores each number in turn, then brings them together to consider the power of the equation as a whole.

Author : Cedric Villani
Publisher : Oxford University Press, USA
Page : 84 pages
File Size : 55,6 Mb
Release : 2020-03-04
Category : Mathematics
ISBN : 9780198846437

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Mathematics Is the Poetry of Science by Cedric Villani Pdf

In the words of the great poet Senghor, Cedric Villani makes the bold claim that Mathematics is the Poetry of Science. Perhaps paradoxical to some, both disciplines are concerned with describing the world around us, understanding its parts, and using this knowledge to create something profound. World-renowned mathematician and Fields Medallist Cedric Villani explores this analogy in this engaging and intelligent text, and shows how mathematics, one of the world's few universal languages, holds deep similarities to the literary genre. A great lover of poetry, he insists that the two are intrinsically linked in their aim of both tackling the complexities of our reality as well as distancing us from it so that we may better appreciate its beauty. In a more light-hearted and concise approach than his more theoretical academic works, this book represents one of Villani's attempts to communicate his love of mathematics to a wider audience, drawing daring parallels between two universes that meet in their aspiration of the sublime.

Author : Richard H. Hammack
Publisher : Unknown
Page : 314 pages
File Size : 54,5 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 0989472116

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Book of Proof by Richard H. Hammack Pdf

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Author : Michael J. Bradley
Publisher : Infobase Publishing
Page : 161 pages
File Size : 42,6 Mb
Release : 2006
Category : Mathematicians
ISBN : 9780791097236

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The Birth of Mathematics by Michael J. Bradley Pdf

Author : John Derbyshire
Publisher : National Academies Press
Page : 391 pages
File Size : 41,8 Mb
Release : 2006-06-02
Category : Science
ISBN : 9780309096577

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Unknown Quantity by John Derbyshire Pdf

Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages-and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics-it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.

Author : Loren Graham,Jean-Michel Kantor
Publisher : Harvard University Press
Page : 252 pages
File Size : 46,5 Mb
Release : 2009-03-31
Category : History
ISBN : 9780674032934

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Naming Infinity by Loren Graham,Jean-Michel Kantor Pdf

In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.

Author : Johann M. Schumann
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 41,9 Mb
Release : 2013-06-29
Category : Computers
ISBN : 9783662226469

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Automated Theorem Proving in Software Engineering by Johann M. Schumann Pdf

Growing demands for the quality, safety, and security of software can only be satisfied by the rigorous application of formal methods during software design. This book methodically investigates the potential of first-order logic automated theorem provers for applications in software engineering. Illustrated by complete case studies on protocol verification, verification of security protocols, and logic-based software reuse, this book provides techniques for assessing the prover's capabilities and for selecting and developing an appropriate interface architecture.

Author : Hans Christian Von Baeyer
Publisher : Harvard University Press
Page : 284 pages
File Size : 52,8 Mb
Release : 2004
Category : Science
ISBN : 0674013875

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Information by Hans Christian Von Baeyer Pdf

In this primer for the information age, von Baeyer presents a clear description of what information is; how concepts of its measurement, meaning, and transmission evolved; and what its ever-expanding presence portends for the future.

Author : Calixto Badesa
Publisher : Princeton University Press
Page : 256 pages
File Size : 46,6 Mb
Release : 2009-01-10
Category : Mathematics
ISBN : 9781400826186

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The Birth of Model Theory by Calixto Badesa Pdf

Löwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Löwenheim--appears to have attributed to him. In The Birth of Model Theory, Calixto Badesa provides both the first sustained, book-length analysis of Löwenheim's proof and a detailed description of the theoretical framework--and, in particular, of the algebraic tradition--that made the theorem possible. Badesa's three main conclusions amount to a completely new interpretation of the proof, one that sharply contradicts the core of modern scholarship on the topic. First, Löwenheim did not use an infinitary language to prove his theorem; second, the functional interpretation of Löwenheim's normal form is anachronistic, and inappropriate for reconstructing the proof; and third, Löwenheim did not aim to prove the theorem's weakest version but the stronger version Skolem attributed to him. This book will be of considerable interest to historians of logic, logicians, philosophers of logic, and philosophers of mathematics.

Author : Jean-Marie De Koninck,Nicolas Doyon
Publisher : American Mathematical Soc.
Page : 329 pages
File Size : 48,8 Mb
Release : 2021-05-19
Category : Education
ISBN : 9781470464899

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The Life of Primes in 37 Episodes by Jean-Marie De Koninck,Nicolas Doyon Pdf

This book is about the life of primes. Indeed, once they are defined, primes take on a life of their own and the mysteries surrounding them begin multiplying, just like living cells reproduce themselves, and there seems to be no end to it. This monograph takes the reader on a journey through time, providing an accessible overview of the numerous prime number theory problems that mathematicians have been working on since Euclid. Topics are presented in chronological order as episodes. These include results on the distribution of primes, from the most elementary to the proof of the famous prime number theorem. The book also covers various primality tests and factorisation algorithms. It is then shown how our inability to factor large integers has allowed mathematicians to create today's most secure encryption method. Computer science buffs may be tempted to tackle some of the many open problems appearing in the episodes. Throughout the presentation, the human side of mathematics is displayed through short biographies that give a glimpse of the lives of the people who contributed to the life of primes. Each of the 37 episodes concludes with a series of problems (many with solutions) that will assist the reader in gaining a better understanding of the theory.

Author : Daniel J. Velleman
Publisher : Cambridge University Press
Page : 401 pages
File Size : 43,7 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780521861243

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How to Prove It by Daniel J. Velleman Pdf

This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.

Author : Robert A. Wilson
Publisher : OUP Oxford
Page : 153 pages
File Size : 52,8 Mb
Release : 2002-01-24
Category : Electronic
ISBN : 9780191583605

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Graphs, Colourings and the Four-Colour Theorem by Robert A. Wilson Pdf

The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.