Category: Number Theory

Download e-book for kindle: Liebe und Mathematik: Im Herzen einer verborgenen by Edward Frenkel,Thomas Filk

By Edward Frenkel,Thomas Filk

ISBN-10: 3662434202

ISBN-13: 9783662434208

Eine Liebeserklarung an die Mathematik und eine Autobiographie wie ein grosser russischer Roman der "New York Times"-Bestseller des brillanten Mathematikers Edward Frenkel

"Zwei faszinierende Erzahlungen die eine mathematischer Natur, die andere personlich sind in "Liebe und Mathematik" miteinander verwoben Geschickt fuhrt Frenkel den Leser an die Rander unserer gegenwartigen Kenntnis. Sein Ziel ist es, die Schonheit der Mathematik fur jeden sichtbar zu machen." Nature

"Edward Frenkels Buch "Liebe und Mathematik" ist im Kern eine Liebesgeschichte, die romantische Beschreibung und Liebeserklarung eines Mannes an jene Gefahrtin, die ihm das Schicksal zugeteilt hat. Wenn ich das Buch in einem Wort zusammenfassen sollte, dann ware dieses Wort Leidenschaft. Die romantische, stellenweise poetische Prosa, der breite Bogen tiefer und profunder menschlicher Ideen und der ewige Reigen fundamentaler Fragen, die bestandig in neuem Gewand wieder auftauchen, lassen quickly unweigerlich an die grossen russischen Romane von Dostojewski, Pasternak, Scholochow und all den anderen denken. "Keith Devlin, Huffington submit

Liebe und Mathematik" ist zugleich eine Autobiographie, ein Eingangstor zum Verstandnis der Mathematik, die so oft Furcht einflosst, und der erste allgemein verstandliche Bericht uber das Langlands-Programm, eines der zentralen schopferischen Projekte der heutigen Menschheit. In diesem Buch geht es in fundamentaler Weise um unser Wissen von der Realitat auf allen Ebenen." Jaron Lanier, Autor von "Wem gehort die Zukunft?"

Liebe und Mathematik "ist nicht etwa ein abgehobener philosophischer Uberblick uber die Mathematik, sondern ein Bericht direkt aus dem Leben eines praktizierenden Mathematikers an der vordersten entrance der Forschung. Und als solcher ist das Buch kraftvoll, ""leidenschaftlich und inspirierend." long island occasions

"In der Uberzeugung, dass manche von uns sich nicht mit der Mathematik einlassen, weil wir sie nicht sehen konnen, setzt Professor Frenkel sie unermudlich in Beziehung zu Dingen, die wir sehen konnen. Ein farbensattes Lob der Zahlen. "The dad or mum

"Wenn guy dieses Buch liest, fuhlt guy den Drang, alles fallen zu lassen und der Mathematik eine neue probability zu geben; teilzuhaben am ultimativ Geheimnisvollen." Chris Carter, Schopfer von "Akte X "("The X Files")

"Ein atemberaubendes landscape der modernen Mathematik." Mario Livio, Astrophysiker und Autor von "Ist Gott ein Mathematiker?" und "B""rilliant errors"

"Sollten Sie kein Mathematiker sein dieses Buch weckt den Wunsch, einer zu werden." Nassim Nicholas Taleb, Autor von "Der schwarze Schwan" und "Antifragilitat "

"_____ "

Stellen Sie sich vor, Sie besuchten eine Kunstschule, in der guy Ihnen lediglich beibringt, wie guy einen Gartenzaun streicht. Stellen Sie sich vor, guy hatte Ihnen dort nie die Bilder von Picasso und van Gogh gezeigt, Ihnen noch nicht einmal gesagt, dass es diese Bilder uberhaupt gibt. So ungefahr wird an unseren Schulen Mathematik unterrichtet, und es ist daher kein Wunder, dass sie fur die meisten von uns als eine zutiefst langweilige geistige Ubung erscheint.

In "Liebe und Mathematik" zeigt uns der beruhmtekannte Mathematiker Edward Frenkel eine Seite der Mathematik, die wir noch nie gesehen haben. Hier offenbaren sich die Schonheit und die Eleganz eines grossen Kunstwerks. In seinem leidenschaftlichen Buch beweist Frenkel, dass die Mathematik alles andere ist als nur die Nische einiger Spezialisten: Sie ruhrt vielmehr ans Herz aller Dinge und eint uns uber alle Kulturen, Zeiten und Raume hinweg.

"Liebe und Mathematik" erzahlt zwei miteinander verwobene Geschichten: eine von den Wundern der Mathematik und eine von der Reise eines jungen Mannes, der diese career erlernt und sie lebt. Nachdem er ein repressives Ausbildungssystem gemeistert hat, entwickelt er sich zu einem der fuhrenden Mathematiker des 21. Jahunderts. Heute arbeitet Frenkel an einer der grossten Ideen, die der Mathematik in den letzten 50 Jahren entsprungen sind: dem Langlands-Programm. Viele sehen darin die grosse vereinheitlichte Theorie der Mathematik. Das Langlands-Programm ermoglicht es Forschern, ihre Entdeckungen aus einem Gebiet in ein vollkommen anderes zu ubertragen und somit Probleme zu losen, die zuvor als unlosbar galten, wie etwa den Grossen Fermat schen Satz.

Im Kern ist "Liebe und Mathematik" eine Geschichte uber eine andere paintings des Denkens, die unser Leben bereichern und uns in die Lage versetzen kann, die Welt und unseren Platz in ihr besser zu verstehen. Es ist eine Einladung, das geheimnisvolle, verborgene Universum der Mathematik zu entdecken. "

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Elementary Number Theory - download pdf or read online

By James K. Strayer

ISBN-10: 0534936725

ISBN-13: 9780534936723

during this student-friendly textual content, Strayer offers the entire subject matters helpful for a primary path in quantity idea. also, chapters on primitive roots, Diophantine equations, and endured fractions permit teachers the pliability to tailor the fabric to fulfill their very own lecture room wishes. every one bankruptcy concludes with seven pupil initiatives, one among which consistently includes programming a calculator or desktop. all the initiatives not just have interaction scholars in fixing number-theoretical difficulties but additionally support familiarize them with the appropriate mathematical literature.

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Field Theory: 158 (Graduate Texts in Mathematics) by Steven Roman PDF

By Steven Roman

ISBN-10: 0387276777

ISBN-13: 9780387276779

ISBN-10: 1441920951

ISBN-13: 9781441920959

"Springer has simply published the second one version of Steven Roman’s box concept, and it is still the best graduate-level introductions to the topic out there....Every component to the booklet has a few sturdy routines that will make this e-book very good to exploit both as a textbook or to profit the fabric by yourself. All in all...a well-written expository account of a really interesting sector in mathematics." --THE MAA MATHEMATICAL SCIENCES electronic LIBRARY

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Download e-book for iPad: Number Theory: A Historical Approach by John J. Watkins

By John J. Watkins

ISBN-10: 0691159408

ISBN-13: 9780691159409

The normal numbers were studied for hundreds of thousands of years, but so much undergraduate textbooks current quantity thought as a protracted record of theorems with little point out of ways those effects have been found or why they're very important. This e-book emphasizes the historic improvement of quantity conception, describing tools, theorems, and proofs within the contexts within which they originated, and offering an obtainable advent to 1 of the main interesting topics in mathematics.

Written in an off-the-cuff type via an award-winning instructor, Number Theory covers top numbers, Fibonacci numbers, and a number of alternative crucial subject matters in quantity idea, whereas additionally telling the tales of the nice mathematicians at the back of those advancements, together with Euclid, Carl Friedrich Gauss, and Sophie Germain. This distinctive introductory textbook positive factors an in depth set of difficulties that let scholars to actively make stronger and expand their realizing of the cloth, in addition to absolutely labored recommendations for lots of of those difficulties. it's also useful tricks for whilst scholars are uncertain of ways to start on a given problem.

  • Uses a distinct historic method of educating quantity theory
  • Features a number of difficulties, beneficial tricks, and entirely labored solutions
  • Discusses enjoyable themes like Pythagorean tuning in tune, Sudoku puzzles, and mathematics progressions of primes
  • Includes an creation to Sage, an easy-to-learn but robust open-source arithmetic software program package deal
  • Ideal for undergraduate arithmetic majors in addition to non-math majors
  • Digital suggestions guide (available purely to professors)

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Download e-book for kindle: Analytic Number Theory: In Honor of Helmut Maier’s 60th by Carl Pomerance,Michael Th. Rassias

By Carl Pomerance,Michael Th. Rassias

ISBN-10: 3319222392

ISBN-13: 9783319222394

ISBN-10: 3319355511

ISBN-13: 9783319355511

This quantity encompasses a selection of study and survey papers written by means of probably the most eminent mathematicians within the foreign group and is devoted to Helmut Maier, whose personal examine has been groundbreaking and deeply influential to the sphere. particular emphasis is given to themes relating to exponential and  trigonometric sums and their habit in brief durations, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted major numbers, oscillation theorems for primes in mathematics progressions, inequalities on the topic of the distribution of primes in brief periods, the Möbius functionality, Euler’s totient functionality, the Riemann zeta functionality and the Riemann speculation. Graduate scholars, examine mathematicians, in addition to desktop scientists and engineers who're drawn to natural and interdisciplinary learn, will locate this quantity an invaluable resource.

Contributors to this volume:

Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de los angeles Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.

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Noncommutative Geometry and Cayley-smooth Orders (Chapman & - download pdf or read online

By Lieven Le Bruyn

ISBN-10: 1420064223

ISBN-13: 9781420064223

Noncommutative Geometry and Cayley-smooth Orders explains the idea of Cayley-smooth orders in significant uncomplicated algebras over functionality fields of types. particularly, the ebook describes the étale neighborhood constitution of such orders in addition to their primary singularities and finite dimensional representations.

After an advent to partial desingularizations of commutative singularities from noncommutative algebras, the e-book offers the invariant theoretic description of orders and their facilities. It proceeds to introduce étale topology and its use in noncommutative algebra in addition to to gather the mandatory fabric on representations of quivers. the following chapters clarify the étale neighborhood constitution of a Cayley-smooth order in a semisimple illustration, classify the linked imperative singularity to tender equivalence, describe the nullcone of those marked quiver representations, and relate them to the research of all isomorphism periods of n-dimensional representations of a Cayley-smooth order. the ultimate chapters learn Quillen-smooth algebras through their finite dimensional representations.

Noncommutative Geometry and Cayley-smooth Orders presents a steady creation to at least one of arithmetic' and physics' preferred topics.

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Arithmetic Geometry: Lectures given at the C.I.M.E. Summer by Jean-Louis Colliot-Thélène,Peter Swinnerton-Dyer,Paul PDF

By Jean-Louis Colliot-Thélène,Peter Swinnerton-Dyer,Paul Vojta,Pietro Corvaja,Carlo Gasbarri

ISBN-10: 3642159443

ISBN-13: 9783642159442

mathematics Geometry should be outlined because the a part of Algebraic Geometry attached with the research of algebraic kinds via arbitrary earrings, particularly via non-algebraically closed fields. It lies on the intersection among classical algebraic geometry and quantity thought. A C.I.M.E. summer season university dedicated to mathematics geometry was once held in Cetraro, Italy in September 2007, and awarded one of the most fascinating new advancements in mathematics geometry. This ebook collects the lecture notes that have been written up by means of the audio system. the most issues hindrance diophantine equations, local-global ideas, diophantine approximation and its kinfolk to Nevanlinna conception, and rationally attached kinds. The booklet is split into 3 components, akin to the classes given via J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.

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H. Salzmann,T. Grundhöfer,H. Hähl,R. Löwen's The Classical Fields: Structural Features of the Real and PDF

By H. Salzmann,T. Grundhöfer,H. Hähl,R. Löwen

ISBN-10: 0521865166

ISBN-13: 9780521865166

The classical fields are the genuine, rational, complicated and p-adic numbers. every one of those fields contains numerous in detail interwoven algebraical and topological constructions. This finished quantity analyzes the interplay and interdependencies of those various elements. the genuine and rational numbers are tested also with recognize to their orderings, and those fields are in comparison to their non-standard opposite numbers. commonplace substructures and quotients, correct automorphism teams and lots of counterexamples are defined. additionally mentioned are crowning glory systems of chains and of ordered and topological teams, with functions to classical fields. The p-adic numbers are positioned within the context of common topological fields: absolute values, valuations and the corresponding topologies are studied, and the category of all in the neighborhood compact fields and skew fields is gifted. workouts are supplied with tricks and suggestions on the finish of the publication. An appendix reports ordinals and cardinals, duality concept of in the community compact Abelian teams and diverse buildings of fields.

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Download e-book for kindle: Algebraic Geometry and Arithmetic Curves (Oxford Graduate by Qing Liu,Reinie Erne

By Qing Liu,Reinie Erne

ISBN-10: 0198502842

ISBN-13: 9780198502845

ISBN-10: 0199202494

ISBN-13: 9780199202492

This booklet is a normal advent to the speculation of schemes, through functions to mathematics surfaces and to the speculation of relief of algebraic curves.

The first half introduces uncomplicated gadgets similar to schemes, morphisms, base switch, neighborhood houses (normality, regularity, Zariski's major Theorem). this is often via the extra worldwide point: coherent sheaves and a finiteness theorem for his or her cohomology teams. Then follows a bankruptcy on sheaves of differentials, dualizing sheaves, and Grothendieck's duality thought. the 1st half ends with the concept of Riemann-Roch and its program to the research of gentle projective curves over a field.
Singular curves are handled via an in depth learn of the Picard group.

The moment half begins with blowing-ups and desingularisation (embedded or now not) of fibered surfaces over a Dedekind ring that leads directly to intersection idea on mathematics surfaces. Castelnuovo's criterion is proved and likewise the lifestyles of the minimum standard version. This results in the examine of relief of algebraic curves. The case of elliptic curves is studied intimately. The booklet concludes with the funadmental theorem of sturdy aid of Deligne-Mumford.

The publication is largely self-contained, together with the mandatory fabric on commutative algebra. the must haves are for that reason few, and the e-book may still go well with a graduate scholar. It includes many examples and approximately six hundred exercises.

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