Share
Fr. 135.60
Tit Andreescu, Titu Andreescu, Dori Andrica, Dorin Andrica, Ion Cucurezeanu
An Introduction to Diophantine Equations  A ProblemBased Approach
English · Hardback
Shipping usually within 4 to 7 working days
Description
This problemsolving 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 ProblemBased 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 nonroutine examples, ideas, and techniques.
List of contents
Diophantine Equations. Elementary Methods for Solving Diophantine Equations. Some Classical Diophantine Equations. PellType Equations. Some Advanced Methods for Solving Diophantine Equations. Solutions to Exercises and Problems. Solutions to Elementary Methods for Solving Diophantine Equations. Solutions to Some Classical Diophantine Equations. Solutions to PellType Equations. Solutions to Some Advanced Methods in Solving Diophantine Equations.
Summary
This problemsolving book is an introduction to the study of Diophantine equations. It introduces the reader to elementary methods necessary in solving Diophantine equations and contains complete solutions to all exercises
Additional text
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 (34), 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 20thcentury tools invented to attackDiophantine equations (algebraic number fields, automorphic forms, Lfunctions, adelic groups, etc.) have emerged as proper objects of study in their own right. So for a popular subject, modern lowerlevel 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 upperdivision undergraduates and general readers.” (D.V. Feldman, Choice, July, 2010)
Report
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 (34), 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 20thcentury tools invented to attackDiophantine equations (algebraic number fields, automorphic forms, Lfunctions, adelic groups, etc.) have emerged as proper objects of study in their own right. So for a popular subject, modern lowerlevel 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 upperdivision undergraduates and general readers." (D.V. Feldman, Choice, July, 2010)
Product details
Authors  Tit Andreescu, Titu Andreescu, Dori Andrica, Dorin Andrica, Ion Cucurezeanu 
Publisher  Springer, Basel 
Languages  English 
Product format  Hardback 
Released  05.10.2010 
EAN  9780817645489 
ISBN  9780817645489 
No. of pages  345 
Dimensions  160 mm x 239 mm x 26 mm 
Weight  692 g 
Illustrations  XI, 345 p. 
Subject 
Natural sciences, medicine, IT, technology
> Mathematics
> Arithmetic, algebra

Customer reviews
No reviews have been written for this item yet. Write the first review and be helpful to other users when they decide on a purchase.
Write a review
Thumbs up or thumbs down? Write your own review.