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Titu Andreescu
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An Introduction to Diophantine Equations: A Problem-Based Approach 2010th Edition

by Titu Andreescu (Author), Dorin Andrica (Author), Ion Cucurezeanu (Author)
4.3 4.3 out of 5 stars 10 ratings
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This book is an introduction to the study of Diophantine equations. The book, organized in two parts, introduces the reader to the main elementary methods necessary in solving Diophantine equations, presents some classical Diophantine equations, and contains complete solutions to all of the exercises. The book is intended for undergraduates, high school students and their teachers, mathematics contests participants (including Olympiad and Putnam competitors), as well as any person interested in essential mathematics. This work uniquely presents unconventional and non-routine examples, ideas, and techniques.
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  1. ISBN-10
    0817645489
  2. ISBN-13
    978-0817645489
  3. Edition
    2010th
  4. Publisher
    Birkhäuser
  5. Publication date
    September 13, 2010
  6. Language
    English
  7. Dimensions
    6.25 x 1 x 9.5 inches
  8. Print length
    356 pages
  9. See all details
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Editorial Reviews

Review

From the reviews:

“This book is devoted to problems from mathematical competitions involving diophantine equations. … Each chapter contains a large number of solved examples and presents the reader with problems whose solutions can be found in the book’s second part. This volume will be particularly interesting for participants in mathematical contests and their coaches. It will also give a lot of pleasure to everyone who likes to tackle elementary, yet nontrivial problems concerning diophantine equations.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 167 (3-4), September, 2012)

“This book explains methods for solving problems with Diophantine equations that often appear in mathematical competitions at various levels. … The book can be recommended to mathematical contest participants, but also to undergraduate students, advanced high school students and teachers.” (Andrej Dujella, Mathematical Reviews, Issue 2011 j)

“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 attackDiophantine 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

  • Publisher ‏ : ‎ Birkhäuser; 2010th edition (September 13, 2010)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 356 pages
  • ISBN-10 ‏ : ‎ 0817645489
  • ISBN-13 ‏ : ‎ 978-0817645489
  • Item Weight ‏ : ‎ 3.33 pounds
  • Dimensions ‏ : ‎ 6.25 x 1 x 9.5 inches
  • Customer Reviews:
    4.3 4.3 out of 5 stars 10 ratings

About the author

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Titu Andreescu

Titu Andreescu

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Dr. Titu Andreescu is an associate professor of mathematics in the Science and Mathematics Education department at the University of Texas at Dallas (UTD). Much of his career has been devoted to competition math, an efficient medium for teaching creative problem-solving for a wide-range of math topics. With over 30 years of experience teaching, coaching, and mentoring the brightest mathematical minds of our age, Dr. Andreescu's books are essential for every math enthusiast's library. Here are just a few highlights from his distinguished career:

-Authored, co-authored, and edited more than 40 math books and publications

-Head coach and leader of the USA International Mathematical Olympiad (IMO) for 8 years

-Director of the Mathematical Association of American (MAA) American Mathematics -Competitions for 5 years

-Has contributed hundreds of problems to various math competitions including and up to the IMO

-Co-founder of the Purple Comet! Math Meet, the first international team based math competition, http://www.purplecomet.org/

-Founder and Director of AwesomeMath, an organization that provides enriching experiences in mathematics to intellectually curious learners, https://www.awesomemath.org/

Customer reviews

4.3 out of 5 stars
4.3 out of 5
We don’t use a simple average to calculate the overall star rating and percentage breakdown by star. Our system gives more weight to certain factors—including how recent the review is and if the reviewer bought it on Amazon. Learn more
10 global ratings

Top reviews from the United States

eddie salazar gamboa
5.0 out of 5 stars Nivel
Reviewed in the United States on July 19, 2019
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Magnifico de equstion Dophanyino con ejemplos de alto mivel
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Dolaur
5.0 out of 5 stars Five Stars
Reviewed in the United States on July 30, 2017
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kind of irritating and addicting. Well presented logical progression.. Make me curse.. at time !Goda... :-)
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Robert Allen
1.0 out of 5 stars ABSOLUTELY ROTTEN!
Reviewed in the United States on November 4, 2021
As the authors merely state their computations and conclusion without explaining how they arrived at them, the book is completely useless.
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mathematicsOnline
5.0 out of 5 stars An excellent book for IMOs
Reviewed in the United States on June 25, 2012
The scope of the book is to present methods and ways of thinking to solve Diophantine Equations. The main subjects that have been discussed in the present work are classical Diophantine equations, Pell-type equations as well as some advanced methods for solving Diophantine equations (in the Ring of Gaussian integers, in the Ring of integers, quadratic reciprocity and divisors of certain forms). Each one of these subjects has been presented in a self-contained and methodological manner. The book contains several interesting problems which are solved rigorously.

The authors have succeeded in providing an essential contribution for students and teachers who are preparing for IMOs.
4 people found this helpful
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Nick
5.0 out of 5 stars Ottimo
Reviewed in Italy on March 6, 2021
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Ottimo prodotto, spedizione perfetta! A++
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Aary SB
1.0 out of 5 stars One Star
Reviewed in India on March 11, 2018
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Damaged product
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