An Introduction To Diophantine Equations

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An Introduction To Diophantine Equations

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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02

An Introduction To Diophantine Equations written by Titu Andreescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-02 with Mathematics categories.

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.

An Introduction To Diophantine Equations

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Author : Titu Andreescu
language : en
Publisher: Birkhäuser
Release Date : 2010-09-13

An Introduction To Diophantine Equations written by Titu Andreescu and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-13 with Mathematics categories.

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.

Diophantine Geometry

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Author : Marc Hindry
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Diophantine Geometry written by Marc Hindry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Diophantine Equations And Power Integral Bases

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Author : Istvan Gaal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Diophantine Equations And Power Integral Bases written by Istvan Gaal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This monograph investigates algorithms for determining power integral bases in algebraic number fields. It introduces the best-known methods for solving several types of diophantine equations using Baker-type estimates, reduction methods, and enumeration algorithms. Particular emphasis is placed on properties of number fields and new applications. The text is illustrated with several tables of various number fields, including their data on power integral bases. Good resource for solving classical types of diophantine equations. Aimed at advanced undergraduate/graduate students and researchers.

Diophantine Analysis

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Author : Jorn Steuding
language : en
Publisher: CRC Press
Release Date : 2005-05-19

Diophantine Analysis written by Jorn Steuding and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-19 with Mathematics categories.

While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain. Diophantine Analysis examines the theory of diophantine ap

Number Theory

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Author : Daniel Duverney
language : en
Publisher: World Scientific
Release Date : 2010

Number Theory written by Daniel Duverney and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory. These topics are covered in 12 chapters and more than 200 solved exercises. Clear, concise, and self-contained, this textbook may be used by undergraduate and graduate students, as well as highschool mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, this fascinating branch of mathematics.

An Introduction To Diophantine Equations

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Author : Titu Andreescu
language : en
Publisher:
Release Date : 2002

An Introduction To Diophantine Equations written by Titu Andreescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Diophantine equations categories.

Fundamentals Of Diophantine Geometry

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Author : S. Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Fundamentals Of Diophantine Geometry written by S. Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.

The Algorithmic Resolution Of Diophantine Equations

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Author : Nigel P. Smart
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-12

The Algorithmic Resolution Of Diophantine Equations written by Nigel P. Smart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-12 with Mathematics categories.

A coherent account of the computational methods used to solve diophantine equations.

Exponential Diophantine Equations

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Author : T. N. Shorey
language : en
Publisher: Cambridge University Press
Release Date : 1986-11-27

Exponential Diophantine Equations written by T. N. Shorey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-11-27 with Mathematics categories.

This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations, the generalised hyperelliptic equation, and the Fermat and Catalan equations. The necessary preliminaries are given in the first three chapters. Each chapter ends with a section giving details of related results.