Introduction to Number Theory (Textbooks in Mathematics) - Hardcover

Vazzana, Anthony; Erickson, Martin; Garth, David

Hardcover

ISBN 10: 1584889373 ISBN 13: 9781584889373

Publisher: Chapman and Hall/CRC, 2007

Synopsis

One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics.

This classroom-tested, student-friendly text covers a wide range of subjects, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments that include cryptography, the theory of elliptic curves, and the negative solution of Hilbert’s tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Euler’s theorem in RSA encryption, and quadratic residues in the construction of tournaments. The book interweaves the theoretical development of the material with Mathematica^® and Maple™ calculations while giving brief tutorials on the software in the appendices.

Highlighting both fundamental and advanced topics, this introduction provides all of the tools to achieve a solid foundation in number theory.

About this title

About the Author

Truman State University, Kirksville, Missouri, USA Truman State University, Kirksville, Missouri, USA

Review

Introduction to Number Theory is a well-written book on this important branch of mathematics. ... The authors succeed in presenting the topics of number theory in a very easy and natural way, and the presence of interesting anecdotes, applications, and recent problems alongside the obvious mathematical rigor makes the book even more appealing. I would certainly recommend it to a vast audience, and it is to be considered a valid and flexible textbook for any undergraduate number theory course.
―IACR Book Reviews, May 2011

Erickson and Vazzana provide a solid book, comprising 12 chapters, for courses in this area ... All in all, a welcome addition to the stable of elementary number theory works for all good undergraduate libraries.
―J. McCleary, Vassar College, CHOICE, Vol. 46, No. 1, August 2009 

... reader-friendly text ... 'Highlighting both fundamental and advanced topics, this introduction provides all of the tools to achieve a solid foundation in number theory.'
―L’Enseignement Mathématique, Vol. 54, No. 2, 2008

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2007
• Language: English
• ISBN 10: 1584889373
• ISBN 13: 9781584889373
• Binding: Hardcover
• Edition number: 1
• Number of pages: 536