An Introduction to Diophantine Equations

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

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.

Inhaltsverzeichnis

Diophantine Equations.- Elementary Methods for Solving Diophantine Equations.- Some Classical Diophantine Equations.- Pell-Type 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 Pell-Type Equations.- Solutions to Some Advanced Methods in Solving Diophantine Equations.

Details

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xi 345 S.
ISBN-13:	9780817645489
ISBN-10:	0817645489
Sprache:	Englisch
Herstellernummer:	11732259
Einband:	Gebunden
Autor:	Andreescu, Titu Andrica, Dorin Cucurezeanu, Ion
Auflage:	2010 edition
Hersteller:	Birkhauser Boston Birkhuser Boston
Maße:	245 x 164 x 30 mm
Von/Mit:	Titu Andreescu (u. a.)
Erscheinungsdatum:	13.09.2010
Gewicht:	0,688 kg

Artikel-ID: 107448850

Zusammenfassung

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xi 345 S.
ISBN-13:	9780817645489
ISBN-10:	0817645489
Sprache:	Englisch
Herstellernummer:	11732259
Einband:	Gebunden
Autor:	Andreescu, Titu Andrica, Dorin Cucurezeanu, Ion
Auflage:	2010 edition
Hersteller:	Birkhauser Boston Birkhuser Boston
Maße:	245 x 164 x 30 mm
Von/Mit:	Titu Andreescu (u. a.)
Erscheinungsdatum:	13.09.2010
Gewicht:	0,688 kg