## Elliptic Tales

Author: Avner Ash
Publisher: Princeton University Press
ISBN: 0691151199
Size: 50.82 MB
Format: PDF, Docs
View: 154

## Elliptic Curves

Author: Dale Husemöller
Publisher: Springer Science & Business Media
ISBN: 0387215778
Size: 71.20 MB
Format: PDF, Docs
View: 4505

First Edition sold over 2500 copies in the Americas; New Edition contains three new chapters and two new appendices

## Elliptic Curves

Author: J. S. Milne
Publisher: Createspace Independent Pub
ISBN: 9781419652578
Size: 45.69 MB
Format: PDF, Docs
View: 282

This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in advanced undergraduate or first-year graduate courses. Reviews Indeed, the book is affordable (in fact, the most affordable of all references on the subject), but also a high quality work and a complete introduction to the rich theory of the arithmetic of elliptic curves, with numerous examples and exercises for the reader, many interesting remarks and an updated bibliography. Mathematical Reviews, Álvaro Lozano-Robledo J. S. Milne's lecture notes on elliptic curves are already well-known … The book under review is a rewritten version of just these famous lecture notes from 1996, which appear here as a compact and inexpensive paperback that is now available worldwide. Zentralblatt MATH, Werner Kleinert

## Rational Points On Elliptic Curves

Author: Joseph H. Silverman
Publisher: Springer
ISBN: 3319185888
Size: 19.75 MB
Format: PDF, Mobi
View: 7040

The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.

## The Queen Of Mathematics

Author: Jay Goldman
Publisher: CRC Press
ISBN: 1439864624
Size: 65.62 MB
Format: PDF, Docs
View: 4461

This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries. It leads to an understanding of today's research problems on the basis of their historical development. This book is a contribution to cultural history and brings a difficult subject within the reach of the serious reader.

## The Irrationals

Author: Julian Havil
Publisher: Princeton University Press
ISBN: 1400841704
Size: 33.28 MB
Format: PDF, ePub, Mobi
View: 4559

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.