Elementary Number Theory: Primes, Congruences, and Secrets
William Stein
November 2008
November 2008
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This is a textbook about classical elementary number theory and
elliptic curves. The first part discusses elementary topics such as
primes, factorization, continued fractions, and quadratic forms, in
the context of cryptography, computation, and deep open research
problems. The second part is about elliptic curves, their applications
to algorithmic problems, and their connections with problems in number
theory such as Fermats Last Theorem, the Congruent Number Problem, and
the Conjecture of Birch and Swinnerton-Dyer. The intended audience of
this book is an undergraduate with some familiarity with basic
abstract algebra, e.g. rings, fields, and finite abelian groups.
On November 2008, this book was published by Springer-Verlag and can be purchased from Amazon.com. If your university has Springer-Link, you may be able to download a PDF version of the book for fee. Also, I will be making the PDF of the book free to everybody starting May 2010 (thanks to a generous contract with Springer-Verlag). |