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. The intended audience of this book is an undergraduate with some familiarity with basic abstract algebra.
Rezensionen / Stimmen
From the reviews:
"This one treats topics that have become standard in recent years . and it has exercises with selected solutions. . it gives the students a tool to do calculations that illustrate even the most abstract concepts, and, simultaneously, introduces them to an open source software that can later be applied profitably for studying research problems. . introducing the reader to a powerful software system." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1155, 2009)
"The cliché that number theory, ever the purest mathematics, now yields very practical applications barely tells the story. Teach undergraduate number theory today, and students demand to hear about public-key cryptography and related technologies. . Stein (Univ. of Washington) serves undergraduates well by . opening the way by intimating their power. . he frames the sophisticated Birch and Swinnerton-Dyer conjecture as the new canonical challenge for the future. Summing Up: Recommended. All undergraduates students, professionals, and general readers." (D. V. Feldman, Choice, Vol. 47 (2), October, 2009)
"This book is an introduction to elementary number theory with a computational flavor. . Many numerical examples are given throughout the book using the Sage mathematical software. The text is aimed at an undergraduate student with a basic knowledge of groups, rings and fields. Each chapter concludes with several exercises." (Samuel S. Wagstaff Jr., Mathematical Reviews, Issue 2009 i)
