Birth of a Theorem

A Mathematical Adventure

Author: Cédric Villani

Publisher: Farrar, Straus and Giroux

ISBN:

Category: Biography & Autobiography

Page: 272

View: 393

In 2010, the French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof that 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 a collaboration. Villani's diaries, e-mails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You're privy to 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.

Birth of a Theorem

A Mathematical Adventure

Author: Cédric Villani

Publisher: Random House

ISBN:

Category: Mathematics

Page: 272

View: 137

“This man could plainly do for mathematics what Brian Cox has done for physics” — Sunday Times How does a genius see the world? Where and how does inspiration strike? Cédric Villani takes us on a mesmerising adventure as he wrestles with the Boltzmann equation – a new theorem that will eventually win him the most coveted prize in mathematics and a place in the mathematical history books. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair. Of ordinary family life blurring with the abstract world of mathematical physics, of theories and equations that haunt your dreams and seeking the elusive inspiration found only in a locked, darkened room. Blending science with history, biography with myth, Villani conjures up an inimitable cast: the omnipresent Einstein, mad genius Kurt Godel, and Villani’s personal hero, John Nash. Step inside the magical world of Cédric Villani...

Euleriana

Author: Beitrage Zu Leben Und Werk

Publisher: Birkhäuser

ISBN:

Category: Juvenile Nonfiction

Page: 555

View: 683

Das vorliegende Buch ist keine «Festschrift» im gewohnten Sinne, d. h. keine mehr oder weniger willkurliche Sammlung von Fachabhandlungen ohne wechselseitigen inneren Zusammenhang, sondern es unterliegt einer ganz bestimmten Konzeption: Die hier vereinigten Beitdige sollen Leben und Werk Leonhard Eulers etwa im MaBstab seiner breitgefacherten Aktivitaten in synoptischer Sicht abdecken und die nachhaltige Wirkung seines wissenschaft­ lichen Schaff ens auf die heutige Zeit aufzeigen. Das Inhaltsverzeichnis lasst leicht folgende Gliederung des Buches erkennen: Der erste Beitrag steht fUr sich al1ein und solI unter BerUcksichtigung der neuen Forschungen einen Uberblick Uber Leben und Wirken Eulers bieten, der einen weiteren Leser­ kreis ansprechen mage. Die nachsten neun Aufsatze (Gelfond bis Schoenberg) umspannen die Gebiete Zahlentheorie, Algebra und Analysis, wahrend die nachfolgenden sechs Beitrage (Speiser bis Fellmann) der Physik gewidmet sind. Den drei Arbeiten zur Astronomie (Cross, Yolk, Nevskaja) schliessen sich sechs Uber Eulers Beziehungen zu Akademien und markanten Einzelpersan­ lichkeiten an (Kopelevic bis Jaquel), gefolgt von drei Beitragen zur Philoso­ phie, Theologie und Biographie Eulers (Breidert, Raith, Bernoulli). Den Abschluss bilden drei Darstellungen zur Editionsgeschichte der Opera omnia und zur Bibliographie (Biermann, Burckhardt). Jeder Beitrag kann unabhan­ gig von der getroffenen Reihenfolge gelesen werden. Einheitlich im ganzen Band werden die BezUge auf die Werke Eulers abgekUrzt zitiert, und zwar in der Reihenfolge: Nummer des Enestram­ Verzeichnisses, Serie der Opera omnia, Band, evtl. Seitenangabe. Ein Beispiel mage dies verdeutlichen: E. 65/0. I,24, p. 23lf. , verweist auf Eulers Methodus inveniendi lineas curvas . . . im Band 24 der Series prima, Seiten 23lf.

The Birth of Model Theory

Löwenheim's Theorem in the Frame of the Theory of Relatives

Author: Calixto Badesa

Publisher: Princeton University Press

ISBN:

Category: Mathematics

Page: 256

View: 767

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.

Euler's Gem

The Polyhedron Formula and the Birth of Topology

Author: David S. Richeson

Publisher: Princeton University Press

ISBN:

Category: Mathematics

Page: 317

View: 961

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 formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. 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. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula'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.

The Birth of Model Theory

Lowenheim's Theorem in the Frame of the Theory of Relatives

Author: Calixto Badesa

Publisher: Princeton University Press

ISBN:

Category: Mathematics

Page: 256

View: 129

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.

Queueing Theory

Arrival Theorem, Balance Equation, Bcmp Network, Birth-Death Process, Bulk Queue, Burke's Theorem, Buzen's Algorithm, Cumulative Flow

Author: Source Wikipedia

Publisher: University-Press.org

ISBN:

Category:

Page: 96

View: 751

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 32. Chapters: Arrival theorem, Balance equation, BCMP network, Birth-death process, Bulk queue, Burke's theorem, Buzen's algorithm, Cumulative flow diagram, Ehrenfest model, Erlang (unit), Fluid queue, Fork-join queue, G-network, Gordon-Newell theorem, Jackson network, Kendall's notation, Kingman's formula, Lindley equation, Little's law, M/G/1 queue, M/M/1 queue, M/M/c queue, Markovian arrival processes, Mean value analysis, Offered load, Palm calculus, Palm-Khintchine theorem, Pollaczek-Khinchine formula, Product form solution, Punctuality, Quasi-birth-death process, Quasireversibility, Queueing model, Queuing delay, Teletraffic engineering, Traffic equations, Traffic generation model, Uniformization (probability theory). Excerpt: In queueing theory, a discipline within the mathematical theory of probability a Jackson network (sometimes Jacksonian network) is a class of queueing network where the equilibrium distribution is particularly simple to compute as the network has a product-form solution. It was the first significant development in the theory of networks of queues, and generalising and applying the ideas of the theorem to search for similar product-form solutions in other networks has been the subject of much research, including ideas used in the development of the Internet. The networks were first identified by James R. Jackson and his paper was re-printed in the journal Management Science's 'Ten Most Influential Titles of Management Sciences First Fifty Years.' Jackson was inspired by the work of Burke and Reich, though Walrand notes "product-form results ... a much less immediate result of the output theorem than Jackson himself appeared to believe in his fundamental paper." An earlier product-form solution was found by R. R. P. Jackson for tandem queues (a finite chain of queues where each...

The Birth of Model Theory

Author: Calixto Badesa

Publisher:

ISBN:

Category: Mathematics

Page: 256

View: 624

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.

Uniformization of Riemann Surfaces

Revisiting a Hundred-year-old Theorem

Author: Henri Paul de Saint-Gervais

Publisher:

ISBN:

Category: Curves, Algebraic

Page: 482

View: 270

The Birth of Numerical Analysis

Author: Adhemar Bultheel

Publisher: World Scientific

ISBN:

Category: Electronic books

Page: 240

View: 604

The 1947 paper by John von Neumann and Herman Goldstine, OC Numerical Inverting of Matrices of High OrderOCO ( Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years. Sample Chapter(s). Chapter 1: Some pioneers of extrapolation methods (323 KB). Contents: Some Pioneers of Extrapolation Methods (C Brezinski); Very Basic Multidimensional Extrapolation Quadrature (J N Lyness); Numerical Methods for Ordinary Differential Equations: Early Days (J C Butcher); Interview with Herbert Bishop Keller (H M Osinga); A Personal Perspective on the History of the Numerical Analysis of Fredholm Integral Equations of the Second Kind (K Atkinson); Memoires on Building on General Purpose Numerical Algorithms Library (B Ford); Recent Trends in High Performance Computing (J J Dongarra et al.); Nonnegativity Constraints in Numerical Analysis (D-H Chen & R J Plemmons); On Nonlinear Optimization Since 1959 (M J D Powell); The History and Development of Numerical Analysis in Scotland: A Personal Perspective (G Alistair Watson); Remembering Philip Rabinowitz (P J Davis & A S Fraenkel); My Early Experiences with Scientific Computation (P J Davis); Applications of Chebyshev Polynomials: From Theoretical Kinematics to Practical Computations (R Piessens). Readership: Mathematicians in numerical analysis and mathematicians who are interested in the history of mathematics.

Asymptotic Properties of Permanental Sequences

Related to Birth and Death Processes and Autoregressive Gaussian Sequences

Author: Michael B. Marcus

Publisher: Springer Nature

ISBN:

Category: Mathematics

Page: 114

View: 184

This SpringerBriefs employs a novel approach to obtain the precise asymptotic behavior at infinity of a large class of permanental sequences related to birth and death processes and autoregressive Gaussian sequences using techniques from the theory of Gaussian processes and Markov chains. The authors study alpha-permanental processes that are positive infinitely divisible processes determined by the potential density of a transient Markov process. When the Markov process is symmetric, a 1/2-permanental process is the square of a Gaussian process. Permanental processes are related by the Dynkin isomorphism theorem to the total accumulated local time of the Markov process when the potential density is symmetric, and by a generalization of the Dynkin theorem by Eisenbaum and Kaspi without requiring symmetry. Permanental processes are also related to chi square processes and loop soups. The book appeals to researchers and advanced graduate students interested in stochastic processes, infinitely divisible processes and Markov chains.

Discrete Geometry and Topology

On the 100th Anniversary of the Birth of Boris Nikolaevich Delone : Collection of Papers

Author: Boris Nikolaevich Delone

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 193

View: 548

This collection of papers honors the 100th anniversary of the birth of Boris Nikolaevich Delone, whose mathematical interests centered on the geometry of positive quadratic forms. After an initial paper presenting an account of Delone's life, including his scientific work, the book centers on discrete geometry and combinatorics. The book presents new methods that permit a description of the structure of some $L$-bodies and $L$-partitionings and that, in many cases, provide a definitive description. Also studied are combinatorial-topological problems arising in the statistical Ising model, the disposition of finite point sets in convex bodies of high dimension under certain conditions, and investigations of regular partitionings of spaces of constant curvature.

Exploring the Riemann Zeta Function

190 years from Riemann's Birth

Author: Hugh Montgomery

Publisher: Springer

ISBN:

Category: Mathematics

Page: 298

View: 931

Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.

17 Lectures on Fermat Numbers

From Number Theory to Geometry

Author: Michal Krizek

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 257

View: 108

The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.