Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) 2nd Edition by Joseph H. Silverman (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is well written, and to be honest, it is very easy to understand. Usually an author of a math book likes to say: “the prerequisite is very modest…” but later you will find that this is only true for Chapter 1. This book is different. It tries to omit some technical details but still provides useful information. The 2015 new edition adds Fermat theorem and cryptology. Highly recommended to anyone interested in Number Theory.

⭐Instead of using a proper binding method such as smyth-sewn binding, the pages are simply glued together. It’s very easy to crack the binding.

⭐In theory, I should be pretty good at math… but I chose CS as my calling instead of math. Alas, given the importance of elliptic curve cryptography, I thought it is about time that I read up on the subject. Not having gone into any graduate level math of any type, this subject proved quite challenging — until I discovered this book. OK, so it isn’t rigorous in terms of proving everything. But for the reader interested in self-study and looking for an entry ticket, this book is the answer. When I finish, I will decide whether to pursue a more rigorous treatment. But to get started, this is a great “intro”. (I put that in quotes because it still requires quite an investment.)

⭐Interesting material, carefully put together, and readable.

⭐This book, as intended, is aimed at bright undergraduates, and is successful at making the material accessible. There are some theorems which aren’t proved in full generality, but the special cases chosen are more than sufficient to give an overview of the theory of elliptic curves, in particular the group of rational points on such curves. A reader with a background in some very basic projective/algebraic geometry will be able to put the first chapter into a broader context, and this will dispense with some of the worries you might otherwise have left over. A reader with good experience of undergraduate algebra may find the presentation of some proofs a little long, but they can easily skip over the details they’re happy with and enjoy a very readable introduction to the subject. There are exercises to help you get to grips with the theorems and explore some of the motivations for the subject. I would highly recommend using these as an opportunity to learn how to use some computer software for dealing with elliptic curves, as otherwise you could spend many days doing calculations!

⭐Sehr gute Einführung in die Theorie elliptischer Kurven. Es werden erst einmal wichtige Ideen und Grundlagen vorgestellt, ohne zu sehr in die Tiefe zu gehen. Geeignet für Leser, die sich erst einmal einen Überblick verschaffen wollen.

⭐

⭐Really great book. Perfectly understandable and good exercises. As a somebody who is pretty young, finding good and well written resources may be a hard task, but this book is one of the few that I would recommend to everyone.The product in itself is really clean and good-looking, I’m really happy with it.

⭐Une introduction aux courbes elliptiques abordable pour les étudiants dès la licence.C’est une référence, écrit par John Tate (Prix Abel 2010) et Joseph Silverman, qui est une ouverture à unautre bouquin de J.Silverman “The Arithmetic of elliptic curve”.

⭐

⭐A very classical brilliant books on rational points on elliptic curves written by two leading mathematicians on this subject. A book that every number theorist must become acquainted with this wonderful book. It deserves to be acquired by every specialist of this area of mathematics.

Keywords

Free Download Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) 2nd Edition in PDF format
Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) 2nd Edition PDF Free Download
Download Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) 2nd Edition 2015 PDF Free
Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) 2nd Edition 2015 PDF Free Download
Download Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) 2nd Edition PDF
Free Download Ebook Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) 2nd Edition