An Introduction to Diophantine Equations: A Problem-Based Approach [Hardcover]

Titu Andreescu (Author), Dorin Andrica (Author), Ion Cucurezeanu (Author)

Book Description

ISBN-10: 0817645489 | ISBN-13: 978-0817645489 | Publication Date: September 13, 2010 | Edition: 1st Edition.

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

Editorial Reviews

Review

From the reviews: “Diophantus’ Arithmetica is a collection of problems each followed by a solution...The book at hand is intended for high school students, undergraduates and math teachers. It is written in a language that everyone in these groups will be familiar with. The exposition is very lucid and the proofs are clear and instructive. The book will be an invaluable source for math contest participants and other math fans. It will be an excellent addition to any math library.” (Alex Bogomolny, The Mathematical Association of America, October, 2010) “Diophantine analysis, the business of solving equations with integers, constitutes a subdiscipline within the larger field of number theory. One problem in this subject, Fermat's last theorem, till solved, topped most lists of the world's most celebrated unsolved mathematics problems, so the subject attracted much attention from mathematicians and even the larger public. Nevertheless, sophisticated 20th-century tools invented to attack Diophantine equations (algebraic number fields, automorphic forms, L-functions, adelic groups, etc.) have emerged as proper objects of study in their own right. So for a popular subject, modern lower-level works focused on the individual Diophantine equation (and not on big machines aimed generally at classes of such equations) are relatively rare. The present volume…fills this need...Summing Up: Recommended. Lower- and upper-division undergraduates and general readers.” (D.V. Feldman, Choice, July, 2010)

From the Back Cover

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The material is organized in two parts: Part I introduces the reader to elementary methods necessary in solving Diophantine equations, such as the decomposition method, inequalities, the parametric method, modular arithmetic, mathematical induction, Fermat's method of infinite descent, and the method of quadratic fields; Part II contains complete solutions to all exercises in Part I. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions.   An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

Product Details

• Hardcover: 356 pages
• Publisher: Birkhäuser Boston; 1st Edition. edition (September 13, 2010)
• Language: English
• ISBN-10: 0817645489
• ISBN-13: 978-0817645489
• Product Dimensions: 9.3 x 6.4 x 1.4 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #951,706 in Books (See Top 100 in Books)