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Author : Jan-Hendrik Evertse,Klmn Gyory
Publisher : Cambridge University Press
Page : 381 pages
File Size : 42,9 Mb
Release : 2015-12-30
Category : Mathematics
ISBN : 9781107097605
A comprehensive, graduate-level treatment of unit equations and their various applications.
Author : Jan-Hendrik Evertse,Klmn Gyory
Publisher : Cambridge University Press
Page : 477 pages
File Size : 54,9 Mb
Release : 2016-11-03
Category : Mathematics
ISBN : 9781107097612
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 51,8 Mb
Release : 2007-05-23
Category : Mathematics
ISBN : 9780387499222
The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.
Author : Daniel Duverney
Publisher : World Scientific
Page : 348 pages
File Size : 46,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814307468
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 : Open University M381/Number theory/Unit 8,Alan Best
Publisher : Unknown
Page : 48 pages
File Size : 55,9 Mb
Release : 2009-05-16
Category : Diophantine equations
ISBN : 0749222786
Topics covered in this unit include Pell's equation, The Pythagorean equation, Fermat's last Theorem, and Sums of squares.To order all 8 units in the Number Theory series please see produc M381/PP02
Author : Róbert Freud,Edit Gyarmati
Publisher : American Mathematical Soc.
Page : 549 pages
File Size : 55,9 Mb
Release : 2020-10-08
Category : Education
ISBN : 9781470452759
Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.
Author : István Gaál
Publisher : Springer Nature
Page : 326 pages
File Size : 54,5 Mb
Release : 2019-09-03
Category : Mathematics
ISBN : 9783030238650
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 : F. Halter-Koch,Robert F. Tichy
Publisher : Walter de Gruyter
Page : 573 pages
File Size : 55,5 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110801958
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author : Istvan Gaal
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200857
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 : Kálmán Györy,Gábor Halász
Publisher : North Holland
Page : 508 pages
File Size : 50,8 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018528755
Author : Tristin Cleveland
Publisher : Scientific e-Resources
Page : 328 pages
File Size : 52,5 Mb
Release : 2018-04-11
Category : Electronic
ISBN : 9781839473265
In spite of the fact that arithmetic majors are generally familiar with number hypothesis when they have finished a course in conceptual polynomial math, different students, particularly those in training and the human sciences, regularly require a more essential prologue to the theme. In this book the writer takes care of the issue of keeping up the enthusiasm of understudies at the two levels by offering a combinatorial way to deal with basic number hypothesis. In concentrate number hypothesis from such a point of view, arithmetic majors are saved reiteration and furnished with new bits of knowledge, while different understudies advantage from the subsequent effortlessness of the verifications for some hypotheses. Of specific significance in this content is the creator's accentuation on the estimation of numerical cases in number hypothesis and the part of PCs in getting such illustrations. The point of this book is to acquaint the reader with essential subjects in number hypothesis: hypothesis of distinctness, arithmetrical capacities, prime numbers, geometry of numbers, added substance number hypothesis, probabilistic number hypothesis, hypothesis of Diophantine approximations and logarithmic number hypothesis.
Author : Wolfgang M. Schmidt
Publisher : Springer
Page : 224 pages
File Size : 43,7 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540473749
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
Author : Michael Jacobson,Hugh Williams
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 53,7 Mb
Release : 2008-12-04
Category : Mathematics
ISBN : 9780387849232
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.
Author : Umberto Zannier
Publisher : Springer
Page : 239 pages
File Size : 45,7 Mb
Release : 2015-05-05
Category : Mathematics
ISBN : 9788876425172
These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several supplements, hinted exercises and an appendix on recent work on heights.
Author : Titu Andreescu,Dorin Andrica,Ion Cucurezeanu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 53,7 Mb
Release : 2010-09-02
Category : Mathematics
ISBN : 9780817645496
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.
