Talteori

This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. The second volume presupposes a background in number theory com parable to ...

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I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain. It was with these words, written in the 1630s, that Pierre de Fermat intrigued and infuriated the mathematics community. For over 350 years, pr...

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A New York Times Science BestsellerWhat if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how ...

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In 1859, German mathematician Bernhard Riemann presented a paper to the Berlin Academy that would forever change mathematics. The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet prove...

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Uncover the language of our universe - numbers - in this wide-ranging whistle-stop tour of the history and majesty of mathematics. Our world simply wouldn't function if we didn't have numbers. But where do they come from? Why do we cut c...

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Brian Clegg was always fascinated by Isaac Asimov's classic Foundation series of books, in which the future is predicted using sophisticated mathematical modelling of human psychology and behaviour. Only much later did he realise that Asimov&...

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Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math bo...

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Frege presenterar här på ett informellt sätt den del av det logicistiska programmet som består i att definiera de naturliga talen (0, 1, 2, 3 ...) i helt logiska termer. Verket inleds med en djupgående kritik av tidigare matematikfilosofi.

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How do you remember more and forget less? How can you earn more and become more creative just by moving house? And how do you pack a car boot most efficiently? This is your shortcut to the art of the shortcut. Mathematics is full of better ways of...

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The notes in this volume correspond to advanced courses held at the Centre de Recerca Matem tica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p-adic G...

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This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithme...

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Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical alge...

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This book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work. These contributions are presented at the conference on Perfectoid Spaces held at the Int...

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A classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Robert Goldblatt ...

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Number Theory Revealed: A Masterclass acquaints enthusiastic students with the ""Queen of Mathematics''. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and pre...

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Number Theory: A Lively Introduction with Proofs, Applications, and Stories, is a new book that provides a rigorous yet accessible introduction to elementary number theory along with relevant applications. Readable discussions motivate new concept...

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Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book help...

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Number theory is the branch of mathematics primarily concerned with the counting numbers, especially primes. It dates back to the ancient Greeks, but today it has great practical importance in cryptography, from credit card security to national de...

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This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics r...

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Introducing the Collins Modern Classics, a series featuring some of the most significant books of recent times, books that shed light on the human experience classics which will endure for generations to come. Maths is one of the purest forms of t...

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Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide reader...

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In this Very Short Introduction Peter M. Higgins presents an overview of the number types featured in modern science and mathematics. Providing a non-technical account, he explores the evolution of the modern number system, examines the fascinatin...

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We use addition on a daily basis--yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbe...

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Praise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!" Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots t...

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This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for...

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This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique pri...

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This title presents a systematic treatment of results on the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluids. Considered are the linearized stationary case, the nonlinear stationary case, and the full...

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"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of numbe...

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This book features mathematical problems and results that would be of interest to all mathematicians, but especially undergraduates (and even high school students) who participate in mathematical competitions such as the International Math Olympia...

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ThecreationofpublickeycryptographybyDi?eandHellmanin1976andthe subsequent invention of the RSA public key cryptosystem by Rivest, Shamir, and Adleman in 1978 are watershed events in the long history of secret c- munications. It is hard to overesti...

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