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Author: John William Scott Cassels
Publisher: Cambridge University Press
Published: 1991-11-21
Total Pages: 148
ISBN-13: 9780521425308
DOWNLOAD EBOOK →A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.
Author: J. W. S. Cassels
Publisher:
Published: 1991
Total Pages: 146
ISBN-13: 9781107094505
DOWNLOAD EBOOK →A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 292
ISBN-13: 1475742525
DOWNLOAD EBOOK →The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
Author: J. Coates
Publisher: Springer
Published: 2006-11-14
Total Pages: 269
ISBN-13: 3540481605
DOWNLOAD EBOOK →This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.
Author: Dale Husemoller
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 363
ISBN-13: 1475751192
DOWNLOAD EBOOK →The book divides naturally into several parts according to the level of the material, the background required of the reader, and the style of presentation with respect to details of proofs. For example, the first part, to Chapter 6, is undergraduate in level, the second part requires a background in Galois theory and the third some complex analysis, while the last parts, from Chapter 12 on, are mostly at graduate level. A general outline ofmuch ofthe material can be found in Tate's colloquium lectures reproduced as an article in Inven tiones [1974]. The first part grew out of Tate's 1961 Haverford Philips Lectures as an attempt to write something for publication c10sely related to the original Tate notes which were more or less taken from the tape recording of the lectures themselves. This inc1udes parts of the Introduction and the first six chapters The aim ofthis part is to prove, by elementary methods, the Mordell theorem on the finite generation of the rational points on elliptic curves defined over the rational numbers. In 1970 Tate teturned to Haverford to give again, in revised form, the originallectures of 1961 and to extend the material so that it would be suitable for publication. This led to a broader plan forthe book.
Author: J. W. S. Cassels
Publisher: Cambridge University Press
Published: 1991-11-21
Total Pages: 0
ISBN-13: 9780521425308
DOWNLOAD EBOOK →The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.
Author: Christof Paar
Publisher: Springer Science & Business Media
Published: 2009-11-27
Total Pages: 372
ISBN-13: 3642041019
DOWNLOAD EBOOK →Cryptography is now ubiquitous – moving beyond the traditional environments, such as government communications and banking systems, we see cryptographic techniques realized in Web browsers, e-mail programs, cell phones, manufacturing systems, embedded software, smart buildings, cars, and even medical implants. Today's designers need a comprehensive understanding of applied cryptography. After an introduction to cryptography and data security, the authors explain the main techniques in modern cryptography, with chapters addressing stream ciphers, the Data Encryption Standard (DES) and 3DES, the Advanced Encryption Standard (AES), block ciphers, the RSA cryptosystem, public-key cryptosystems based on the discrete logarithm problem, elliptic-curve cryptography (ECC), digital signatures, hash functions, Message Authentication Codes (MACs), and methods for key establishment, including certificates and public-key infrastructure (PKI). Throughout the book, the authors focus on communicating the essentials and keeping the mathematics to a minimum, and they move quickly from explaining the foundations to describing practical implementations, including recent topics such as lightweight ciphers for RFIDs and mobile devices, and current key-length recommendations. The authors have considerable experience teaching applied cryptography to engineering and computer science students and to professionals, and they make extensive use of examples, problems, and chapter reviews, while the book’s website offers slides, projects and links to further resources. This is a suitable textbook for graduate and advanced undergraduate courses and also for self-study by engineers.
Author: A. Robert
Publisher: Springer
Published: 2009-02-27
Total Pages: 272
ISBN-13: 3540469168
DOWNLOAD EBOOK →Author: John William Scott Cassels
Publisher:
Published: 2014-05-14
Total Pages: 146
ISBN-13: 9781107088290
DOWNLOAD EBOOK →A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.
Author: Spencer J. Bloch
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 114
ISBN-13: 0821829734
DOWNLOAD EBOOK →This is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more).
