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Book
Introduction to elliptic curves and modular forms
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ISBN: 0387960295 1468402579 1468402552 9780387960296 Year: 1984 Volume: 97 Publisher: New York

A course in number theory and cryptography
Author:
ISBN: 0387965769 3540965769 9780387965765 Year: 1987 Volume: 114 Publisher: New York (N.Y.): Springer

A course in number theory and cryptography
Author:
ISBN: 0387942939 1461264421 1441985921 Year: 2006 Volume: 114 Publisher: New York Springer


Book
Number theory related to Fermat's last theorem : proceedings of the conference sponsored by the Vaughn Foundation
Authors: ---
ISBN: 3764331046 Year: 1982 Volume: 26 Publisher: Boston : Birkhäuser,

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Book
Random Curves
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ISBN: 9783540740780 3540740775 9783540740773 3540740783 Year: 2008 Publisher: Berlin, Heidelberg Springer Berlin Heidelberg

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These autobiographical memoirs of Neal Koblitz, coinventor of one of the two most popular forms of encryption and digital signature, cover many topics besides his own personal career in mathematics and cryptography - travels to the Soviet Union, Latin America, Vietnam and elsewhere, political activism, and academic controversies relating to math education, the C. P. Snow two-culture problem, and mistreatment of women in academia. The stories speak for themselves and reflect the experiences of a student and later a scientist caught up in the tumultuous events of his generation.


Book
A Course in Mathematical Logic for Mathematicians
Authors: --- ---
ISBN: 1461424798 1441906142 9786613569103 1280391189 1441906150 Year: 2010 Publisher: New York, NY : Springer New York : Imprint: Springer,

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A Course in Mathematical Logic for Mathematicians, Second Edition offers a straightforward introduction to modern mathematical logic that will appeal to the intuition of working mathematicians. The book begins with an elementary introduction to formal languages and proceeds to a discussion of proof theory. It then presents several highlights of 20th century mathematical logic, including theorems of Gödel and Tarski, and Cohen's theorem on the independence of the continuum hypothesis. A unique feature of the text is a discussion of quantum logic. The exposition then moves to a discussion of computability theory that is based on the notion of recursive functions and stresses number-theoretic connections. The text present a complete proof of the theorem of Davis–Putnam–Robinson–Matiyasevich as well as a proof of Higman's theorem on recursive groups. Kolmogorov complexity is also treated. Part III establishes the essential equivalence of proof theory and computation theory and gives applications such as Gödel's theorem on the length of proofs. A new Chapter IX, written by Yuri Manin, treats, among other things, a categorical approach to the theory of computation, quantum computation, and the P/NP problem. A new Chapter X, written by Boris Zilber, contains basic results of model theory and its applications to mainstream mathematics. This theory has found deep applications in algebraic and diophantine geometry. Yuri Ivanovich Manin is Professor Emeritus at Max-Planck-Institute for Mathematics in Bonn, Germany, Board of Trustees Professor at the Northwestern University, Evanston, IL, USA, and Principal Researcher at the Steklov Institute of Mathematics, Moscow, Russia. Boris Zilber, Professor of Mathematical Logic at the University of Oxford, has contributed the Model Theory Chapter for the second edition.

Gauge field theory and complex geometry
Authors: --- ---
ISBN: 3540613781 3642082564 3662073862 Year: 1997 Publisher: Berlin : Springer,

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From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.

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