Number Theory Diophantine And Algebraic

Author : Daniel Duverney
Publisher : World Scientific
Page : 348 pages
File Size : 52,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814307468

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Number Theory by Daniel Duverney Pdf

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 : Henri Cohen
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 43,6 Mb
Release : 2007-05-23
Category : Mathematics
ISBN : 9780387499222

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Number Theory by Henri Cohen Pdf

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 : Róbert Freud,Edit Gyarmati
Publisher : American Mathematical Soc.
Page : 549 pages
File Size : 47,8 Mb
Release : 2020-10-08
Category : Education
ISBN : 9781470452759

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Number Theory by Róbert Freud,Edit Gyarmati Pdf

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 : Kálmán Györy,Gábor Halász
Publisher : North Holland
Page : 508 pages
File Size : 54,7 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018528755

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Number Theory: Diophantine and algebraic by Kálmán Györy,Gábor Halász Pdf

Author : F. Halter-Koch,Robert F. Tichy
Publisher : Walter de Gruyter
Page : 573 pages
File Size : 40,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110801958

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Algebraic Number Theory and Diophantine Analysis by F. Halter-Koch,Robert F. Tichy Pdf

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 : Daniel E. Flath
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 48,8 Mb
Release : 2018-09-27
Category : Number theory
ISBN : 9781470446949

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Introduction to Number Theory by Daniel E. Flath Pdf

Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honors-level undergraduates, Flath's Introduction to Number Theory focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with abstract algebra. The text treats a variety of topics from elementary number theory including the distribution of primes, sums of squares, continued factions, the Legendre, Jacobi and Kronecker symbols, the class group and genera. But the focus is on quadratic reciprocity (several proofs are given including one that highlights the p−q symmetry) and binary quadratic forms. The reader will come away with a good understanding of what Gauss intended in the Disquisitiones and Dirichlet in his Vorlesungen. The text also includes a lovely appendix by J. P. Serre titled Δ=b2−4ac. The clarity of the author's vision is matched by the clarity of his exposition. This is a book that reveals the discovery of the quadratic core of algebraic number theory. It should be on the desk of every instructor of introductory number theory as a source of inspiration, motivation, examples, and historical insight.

Author : Jörn Steuding
Publisher : Birkhäuser
Page : 232 pages
File Size : 47,5 Mb
Release : 2016-12-21
Category : Mathematics
ISBN : 9783319488172

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Diophantine Analysis by Jörn Steuding Pdf

This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject. The topics range from Baker’s method of bounding linear forms in logarithms (authored by Sanda Bujačić and Alan Filipin), metric diophantine approximation discussing in particular the yet unsolved Littlewood conjecture (by Simon Kristensen), Minkowski’s geometry of numbers and modern variations by Bombieri and Schmidt (Tapani Matala-aho), and a historical account of related number theory(ists) at the turn of the 19th Century (Nicola M.R. Oswald). Each of these notes serves as an essentially self-contained introduction to the topic. The reader gets a thorough impression of Diophantine Analysis by its central results, relevant applications and open problems. The notes are complemented with many references and an extensive register which makes it easy to navigate through the book.

Author : W Narkiewicz
Publisher : World Scientific Publishing Company
Page : 384 pages
File Size : 41,8 Mb
Release : 1984-02-01
Category : Mathematics
ISBN : 9789813104099

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Number Theory by W Narkiewicz Pdf

The aim of this book is to familiarize the reader with fundamental topics in number theory: theory of divisibility, arithmetrical functions, prime numbers, geometry of numbers, additive number theory, probabilistic number theory, theory of Diophantine approximations and algebraic number theory. The author tries to show the connection between number theory and other branches of mathematics with the resultant tools adopted in the book ranging from algebra to probability theory, but without exceeding the undergraduate students who wish to be acquainted with number theory, graduate students intending to specialize in this field and researchers requiring the present state of knowledge.

Author : Izabella Grigorʹevna Bashmakova,Joseph H. Silverman
Publisher : Cambridge University Press
Page : 110 pages
File Size : 55,7 Mb
Release : 1997
Category : Mathematics
ISBN : 0883855267

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Diophantus and Diophantine Equations by Izabella Grigorʹevna Bashmakova,Joseph H. Silverman Pdf

Semi-popular maths on an area of number theory related to Fermat.

Author : Jan-Hendrik Evertse,Klmn Gyory
Publisher : Cambridge University Press
Page : 381 pages
File Size : 43,9 Mb
Release : 2015-12-30
Category : Mathematics
ISBN : 9781107097605

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Unit Equations in Diophantine Number Theory by Jan-Hendrik Evertse,Klmn Gyory Pdf

A comprehensive, graduate-level treatment of unit equations and their various applications.

Author : Yuan Wang
Publisher : Springer Science & Business Media
Page : 185 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581717

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Diophantine Equations and Inequalities in Algebraic Number Fields by Yuan Wang Pdf

The circle method has its genesis in a paper of Hardy and Ramanujan (see [Hardy 1])in 1918concernedwiththepartitionfunction andtheproblemofrep resenting numbers as sums ofsquares. Later, in a series of papers beginning in 1920entitled "some problems of'partitio numerorum''', Hardy and Littlewood (see [Hardy 1]) created and developed systematically a new analytic method, the circle method in additive number theory. The most famous problems in ad ditive number theory, namely Waring's problem and Goldbach's problem, are treated in their papers. The circle method is also called the Hardy-Littlewood method. Waring's problem may be described as follows: For every integer k 2 2, there is a number s= s(k) such that every positive integer N is representable as (1) where Xi arenon-negative integers. This assertion wasfirst proved by Hilbert [1] in 1909. Using their powerful circle method, Hardy and Littlewood obtained a deeper result on Waring's problem. They established an asymptotic formula for rs(N), the number of representations of N in the form (1), namely k 1 provided that 8 2 (k - 2)2 - +5. Here

Author : Trygve Nagell
Publisher : American Mathematical Soc.
Page : 309 pages
File Size : 47,8 Mb
Release : 2021-07-21
Category : Education
ISBN : 9781470463243

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Introduction to Number Theory by Trygve Nagell Pdf

A special feature of Nagell's well-known text is the rather extensive treatment of Diophantine equations of second and higher degree. A large number of non-routine problems are given. Reviews & Endorsements This is a very readable introduction to number theory, with particular emphasis on diophantine equations, and requires only a school knowledge of mathematics. The exposition is admirably clear. More advanced or recent work is cited as background, where relevant … [T]here are welcome novelties: Gauss's own evaluation of Gauss's sums, which is still perhaps the most elegant, is reproduced apparently for the first time. There are 180 examples, many of considerable interest, some of these being little known. -- Mathematical Reviews

Author : Jan-Hendrik Evertse,Klmn Gyory
Publisher : Cambridge University Press
Page : 477 pages
File Size : 53,6 Mb
Release : 2016-11-03
Category : Mathematics
ISBN : 9781107097612

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Discriminant Equations in Diophantine Number Theory by Jan-Hendrik Evertse,Klmn Gyory Pdf

The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.

Author : Ethan D. Bolker
Publisher : Courier Corporation
Page : 208 pages
File Size : 49,6 Mb
Release : 2012-06-14
Category : Mathematics
ISBN : 9780486153094

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Elementary Number Theory by Ethan D. Bolker Pdf

This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and more.

Author : Kalman Gyoery,Attila Pethoe,Vera T. Sos
Publisher : Walter de Gruyter
Page : 617 pages
File Size : 52,5 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110809794

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Number Theory by Kalman Gyoery,Attila Pethoe,Vera T. Sos Pdf

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.