[PDF] An Introduction To Diophantine Equations eBook

Author : Titu Andreescu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 35,41 MB
Release : 2010-09-02
Category : Mathematics
ISBN : 0817645497

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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.

Author : Titu Andreescu
Publisher : Birkhäuser
Page : 345 pages
File Size : 41,2 MB
Release : 2011-03-02
Category : Mathematics
ISBN : 9780817672034

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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.

Author : Nigel P. Smart
Publisher : Cambridge University Press
Page : 264 pages
File Size : 36,71 MB
Release : 1998-11-12
Category : Mathematics
ISBN : 9780521646338

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

Author : Istvan Gaal
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 49,55 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461200857

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Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.

Author : Titu Andreescu
Publisher : Springer
Page : 224 pages
File Size : 32,53 MB
Release : 2015-06-29
Category : Mathematics
ISBN : 0387541098

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This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell’s equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.

Author : Daniel Duverney
Publisher : World Scientific
Page : 348 pages
File Size : 49,59 MB
Release : 2010
Category : Mathematics
ISBN : 9814307467

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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. Clear, concise, and self-contained, the topics are covered in 12 chapters with more than 200 solved exercises. The textbook may be used by undergraduates and graduate students, as well as high school mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, the fascinating branch of mathematics.

Author : H. Davenport
Publisher : Cambridge University Press
Page : 160 pages
File Size : 22,5 MB
Release : 2005-02-07
Category : Mathematics
ISBN : 9780521605830

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Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.

Author : Marc Hindry
Publisher : Springer Science & Business Media
Page : 574 pages
File Size : 33,85 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461212103

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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.

Author : Michael Jacobson
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 18,11 MB
Release : 2008-12-02
Category : Mathematics
ISBN : 038784922X

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Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell’s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation. The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell’s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.