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Jones & Bartlett Publishers, 1995. — 415 p. This text presents the principal ideas of classical number theory emphasizing the historical development of these results and the important figures who worked on them. It is intended to introduce third or fourth-year undergraduates to mathematical proofs by presenting them in a clear and simple way and by providing complete,...
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Sudbury: Jones and Bartlett, 1995. — 402 p. — ISBN 0-86720-472-9. International edition. This book presents the principal ideas of classical elementary number theory, emphasizing the historical development of these results and the important figures who worked on them. This book is also intended to introduce students to mathematical prooves by presenting them in a clear and...
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Springer, 2002. — 314 Pages. — ISBN: 3034894813 This volume contains the proceedings of the International Conference on Number Theory and Discrete Mathematics in honour of Srinivasa Ramanujan, held at the Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India, in October 2000, as a contribution to the International Year of Mathematics. It collects 29...
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Eine Einführung mit Übungen, Hinweisen und Lösungen. — Vieweg+Teubner Verlag, 2012. — 160 S. Zahlentheorie, neben Geometrie wohl das älteste Gebiet der Mathematik, hat im Lauf der Zeit nichts von ihrem Reiz eingebüßt - ganz im Gegenteil: Die Faszination zeitloser Probleme wie der Fermatschen Vermutung genau so wie aktuelle Anwendungen in Kryptographie lassen sie lebendiger denn...
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Springer, 2008. — 193 p. — ISBN: 0387785094 Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and...
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Kluwer Academic Publishers, 1998. — 298 p. This volume contains a collection of papers in Analytic and Elementary Number Theory in memory of Professor Paul Erdos, one of the greatest mathematicians of this century. Written by many leading researchers, the papers deal with the most recent advances in a wide variety of topics, including arithmetical functions, prime numbers, the...
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Springer, 2012. — 236 pages. ISBN: 1461400279 This book contains a unique collection of both research and survey papers written by an international group of some of the world's experts on partitions, q-series, and modular forms, as outgrowths of a conference held at the University of Florida, Gainesville in March 2008. The success of this conference has led to annual year-long...
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The J29 Project, 2012. - 165 с. This problem set is my main source for writing a book. It is nothing but a set of problems posted by active users of AoPS/MathLinks, and it will be a really good source for preparing for mathematical olympiads. Problems Amir Hossein. Andrew. Goutham. Orlando. Valentin. Darij. Vesselin. Gabriel. April. Arne. Kunihiko. Solutions
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Учебное пособие:Zalau(Romania), GIL Publishing House, , 2002,198 pp. Пособие посвящено диофантовым уравнениям и методам их решений.Предназначено старшеклассникам и студентам младших курсов, прежде всего, для их математического образования. Пособие будет незаменимым помощником учащихся при подготовке их к участию в математических олимпиадах различного уровня, а также поможет...
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Birkhauser Boston, 2009. — 384 p. Number theory, an ongoing rich area of mathematical exploration, is noted for its theoretical depth, with connections and applications to other fields from representation theory, to physics, cryptography, and more. While the forefront of number theory is replete with sophisticated and famous open problems, at its foundation are basic,...
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Springer, 2015. — 232 p. — ISBN: 0387351566 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...
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Springer, 2015. — 232 p. — ISBN: 0387351566. 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...
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Birkhauser Boston, 2010. — 344 p. 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...
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Birkhäuser Boston, 2006. — 204 p. This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas,...
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N.-Y., Springer, 2005. - 436p. Считавшийся утерянным сборник заметок гениального индийского математика Раманужана. Аннотация издателя: "In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the...
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N.-Y., Springer, 2010. - 422p. Считавшийся утерянным сборник заметок гениального индийского математика Раманужана. Аннотация издателя: "In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the...
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N.-Y., Springer, 2012. - 439p. Считавшийся утерянным сборник заметок гениального индийского математика Раманужана. Аннотация издателя: "In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the...
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N.-Y., Springer, 2013. - 439p. Считавшийся утерянным сборник заметок гениального индийского математика Раманужана. Аннотация издателя: "In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the...
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Springer, 2018. — 430 p. — ISBN 978-3-319-77832-7, 3319778323. Считавшийся утерянным сборник заметок гениального индийского математика Раманужана. Для изучающих теорию чисел, теорию функций, историю математики, психологию математического творчества. In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine...
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Springer-Science+Business Media, 1995. — 390 Pages. ISBN: 9401041261 Like other introductions to number theory, this one includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange's Four Square Theorem, the theorem behind Lucas's test for perfect numbers, the...
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Singapore: World Scientific, 2010. — 267 p. This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory -...
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Springer, 1976. - 350 pages. OCR This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include...
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Springer, 1976. — 350 pages. This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include Dirichlet's...
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New York: Springer-Verlag. – 1990. – 216 p. (Graduate Texts in Mathematics 41). This volume is a textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. The volume presupposes a background in number theory comparable to that provided in the first volume, together with a knowledge of the basic concepts of...
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N.-Y.: Springer, 2014. — 274p. Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that...
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New York; Toronto: John Wiley & Sons, 1988. — 262 p. The complete ordered field R The Concept of a Field: Algebraic Preliminaries Order Relations, Completeness Ordered Groups and Fields Recognition of R On Properties Equivalent to Completion Cantor's Characterisation of (Q, ≤) Constructions of R Decimal Representations of the Real Numbers Constructions of R with Decimal Sequences...
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Princeton University Press, 2012, 275 pp., ISBN: 978-0-691-15119-9, Eng., PDF Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics- the Birch and Swinnerton-Dyer Conjecture . The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general...
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Princeton University Press, 2008. — 312 p. — ISBN 0691138710. The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and...
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Princeton: Princeton University Press, 2016. — 249 p. We use addition on a daily basis--yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer...
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Singapore, World Scientific Publishing Co. Pte. Ltd., 2002. - 330 p. ISBN-10: 9812381147 Научно-популярная книга, посвящённая числам Фибоначчи и их обобщениям. Рассматриваются, среди прочего, задачи о перечислениях деревьях, код Грэя, треугольник Паскаля, геометрические и теоретико-групповые аспекты чисел Фибоначчи, связь "золотого сечения" и фракталов. Для любителей...
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The MIT Press, 1996. — 496 p. — ISBN: 0262024055 Algorithmic Number Theory provides a thorough introduction to the design and analysis of algorithms for problems from the theory of numbers. Although not an elementary textbook, it includes over 300 exercises with suggested solutions. Every theorem not proved in the text or left as an exercise has a reference in the notes section...
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Cambridge, 2016. — 339 p. — ISBN 10 1107552370. Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic...
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Cambridge University Press, 1985. — 107 p. — ISBN: 0521286549, 0521243831 Number theory has a long and distinguished history and the concepts and problems relating to the subject have been instrumental in the foundation of much of mathematics. In this book, Professor Baker describes the rudiments of number theory in a concise, simple and direct manner. Though most of the text...
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Clarendon Press, 1986. — 275 pages. — (London Mathematical Society Monographs New Series) ISBN: 0198535457 ISBN-13: 9780198535454 This book launches the prestigious new series London Mathematical Society Monographs. The author, noted for his work throughout the mathematical community, here presents an overview of the theory of nonlinear Diophantine approximation. He has...
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Springer, 2008. — 522 p. — (Universitext). — ISBN-13: 978-3-540-69199-0. In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding...
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Springer, 2003. — 227 p. — ISBN 0-387-95529-1. Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields. It is an ideal topic to lead college students, as well as some talented and motivated high school students, to a better appreciation of the power of mathematical...
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Springer International Publishing, Switzerland, 2016. — 331 p. — ISBN: 3319468308 This book is based on lectures given originally at Reading University and more recently at Oxford as part of the Continuing Education program of Oxford University in England. In a sense it is a sequel to Gems of Geometry (now in its second edition) and which is also based on lectures given at...
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Singapore: World Scientific Publishing, 2004. — 375p. — ISBN 981-238-938-5; 981-256-080-7 Introduction Calculus of Arithmetic Functions Summatory Functions The Distribution of Prime Numbers An Elementary Proof of the P.N.T. Dirichlet Series and Mellin Transforms Inversion Formulas The Riemann Zeta Function Primes in Arithmetic Progressions Applications of Characters Oscillation...
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Singapore: World Scientific Publishing CompanyWorld, 2004. -375p. This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable ("elementary") and complex variable ("analytic") methods are...
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New York: Springer, 2014. - 497p. This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are...
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Proceedings of The Seventh International Research Conference on Fibonacci Numbers and Their Applications', Technische Universitat, Graz, Austria, July 15-19, 1996 Springer, 1998. - 520 pages. ISBN-10: 9401061076 This volume contains the proceedings of the Seventh International Research Conference on Fibonacci Numbers and their Applications. It includes a carefully refereed...
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N.-Y.: Springer-Verlag, 1997. - 321 p. Записные книжки гениального индийского математика Сринавасы Раманужана. В пятой части (четыре предыдущие на сайте имеются) результаты касающиеся непрерывных дробей, теории эллиптических функций, тэта-функции и некоторые другие вопросы. Для изучающих математику, историю математики и психологию математического творчества.
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American Mathematical Society, 2006. — 187 p. — ISBN 0821841785. Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important...
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Springer, 1985. - 372 Pages. ISBN: 0387961100 Srinivasa Ramanujan is, arguably, the greatest mathematician that India has produced. His story is quite unusual: although he had no formal education inmathematics, he taught himself, and managed to produce many important new results. With the support of the English number theorist G. H. Hardy, Ramanujan received a scholarship to go...
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Springer-Verlag, 1998. - 359 Pages. ISBN: 354096794X This book is the second of four Volumes devoted to the editing of Ramanu-Ramanujan's notebooks. Part I, published in 1985, contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan's quarterly reports. In this volume, we examine Chapters 10-15 in Ramanujan's second notebook. If a result...
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Springer, 1991. - 528 pages. ISBN: 0387975039 During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N....
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Springer-Verlag, 1993. - 451 pages. ISBN: 0387941096 This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results...
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American Mathematical Society, 1999. — 393 pages. ISBN: 0821812009 This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme...
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New York: Springer, 2014. — 251 p. In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In this book we give a complete and (almost) self-contained exposition of Mihăilescu’s...
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Springer Netherlands, 2008 - 374 p. This book presents a fully scientific account of the use of the golden ratio. It explores the observation that stable nucleides obey a number theory based general law. The discovery described in this book could be of seminal significance, also in other fields where the golden ratio is known to be of fundamental importance.
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W.A. Benjamin, 1970. — 180 p. 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 the Fermat conjecture for exponents three and four. The text contains abundant numerical examples and a particularly helpful collection of...
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N.-Y.: Springer, 2012. - 579p. Number theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve. In the past, a variety of very different techniques has been applied to further its understanding. Classical...
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Berlin, Springer, 2007. - 588p. Введение в проблематику "гипотезы Римана" - одной из "проблем тысячелетия", а также хрестоматия классических работ по этой теме. Включает в себя описание проблемы, методы вычисления дзета-функции, следствия и обобщения гипотезы Римана, изложение неудачных попыток доказательства и 24 статьи по этой теме (некоторые в оригинале, на французском и...
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Madison: University of Wisconsin, 2003. — 140 p. This book will describe the recent proof of Fermat’s Last Theorem by Andrew Wiles, aided by Richard Taylor, for graduate students and faculty with a reasonably broad background in algebra. It is hard to give precise prerequisites but a first course in graduate algebra, covering basic groups, rings, and fields together with a passing...
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CRC Press, 1999 - 303 p. This study demonstrates the key manipulations surrounding Brauer groups, graded rings, group representations, ideal classes of number fields, p-adic differential equations, and rationality problems of invariant fields - displaying a command of the most advanced methods in algebra. It describes new developments in noncommutative valuation theory and p-adic...
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New York: Springer, 2018. — 218 p. Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists...
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John Wiley & Sons, 2008. - 384 Pages. ISBN: 0470412151 A Course in Computational Number Theory uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers....
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Монография. Серия "Undergraduate Texts in Mathematics". New York: Springer-Verlag, 1989. - xiii + 237 p. ISBN: 0-387-97040-1. Эта книга сфокусирована на единственной проблеме: как факторизовать большое целое число или доказать его простоту. От древнего решета Эратосфена до многократного полиномиального квадратичного решета (MPQS) и методов эллиптической кривой, открытых...
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1990, North-Holland, 331 p. Pade approximants and continued fractions are typical examples of old domains (since continued fractions can be traced back at least to Euclid's g.c.d. algorithm more that 2000 years ago) which are nou in full vitality. Thi is due to their numerous applications in number theory, cryptography, statistics, numerical analysis, special functions, digital...
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559 p. Berlin - 1991. The book is devoted to the history of continued fractions since the early ages till the last century. Contents: Introduction . The Early ages . Euclid's algorithm. The square root. Indeterminate equations. History of notations. The First Steps . Ascending continued fractions. The birth of continued fractions. Miscellaneous contributions....
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American Mathematical Society, 2006. - 236 pages. Introduction to the ShortTables. Convenient Short Tables. ntroduction to the Main Tables. The Cunningham-Woodall Tables and Their Influence. The Cunningham Project. Developments Contributing to the Present Tables. Developments in Technology. Developments in Factorization. Developments in Primality Testing. (a) The Theory....
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Zurich: European Mathematical Society, 2015. - 200p. This book arose from courses given at the International Summer School organized in August 2012 by the number theory group of the Department of Mathematics at the University of Würzburg. It consists of four essentially self-contained chapters and presents recent research results highlighting the strong interplay between number...
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Cambridge: Cambridge University Press, 2017. — 348 p. The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The books are gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of...
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Cambridge: Cambridge University Press, 2017. — 512 p. The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the...
  • №64
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Cambridge: Cambridge University Press, 2004. — 292 p. To help the reader access the current state of research in this branch of number theory, Yann Bugeaud combines the most important results previously scattered throughout the research literature and also includes a number of significant open questions. Although written for graduates who wish to pursue research, the collection...
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Cambridge: Cambridge University Press, 2012. — 318 p. This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral...
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Paris: European Mathematical Society, 2018. — 242 p. The aim of this book is to serve as an introductory text to the theory of linear forms in the logarithms of algebraic numbers, with a special emphasis on a large variety of its applications. We wish to help students and researchers to learn what is hidden inside the blackbox ‚Baker's theory of linear forms in logarithms' (in...
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Mathematical Sciences Research Institute, 2008. — 660 p. — (MRSI Publications, Volume 44). Our subject arises out of two roots of mathematical thought: fascination with properties of whole numbers and the urge to compute. Number theory and computer science flowered vividly during the last quarter of the twentieth century, and the synergy at their intersection was striking....
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AMS, 2000. — 151 p. Welcome to diophantine analysis-an area of number theory in which we attempt to discover hidden treasures and truths within the jungle of numbers by exploring rational numbers. Diophantine analysis comprises two different but interconnected domains-diophantine approximation and diophantine equations. This highly readable book brings to life the fundamental...
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Cambridge: Cambridge University Press, 1997. — 280 p. A sequence of exercises which will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves.
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7th ed. — McGraw-Hill Science/Engineering/Math, 2010. — 448 p. — ISBN 0073383147, 9780073383149. Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a...
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Boston: Allyn and Bacon, Inc., 1976, — 390 p. Elementary number theory revised edition is written for undergraduate students, students who are preparing for math Olympiads, teachers. This book gives simple account of classical number theory, as well as to impart some of historical background in which the subject involved. This book will introduce you with many parts of modern...
  • №72
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Providence, Rhode Island, USA: American Mathematical Society, 2018. — 297 p. — (Series: AMS / MAA, volume 39). — ISBN-10 1470443481. A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well...
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New York: Springer, 2017. — 277 p. With a specific focus on the mathematical life in small undergraduate colleges, this book presents a variety of elementary number theory insights involving sequences largely built from prime numbers and contingent number-theoretic functions. Chapters include new mathematical ideas and open problems, some of which are proved in the text. Vector...
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John Wiley & Sons, 1914. - 94 pages. The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The arrangement of the material is as follows: The first five chapters are devoted to the development of those elements which are essential to any...
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Cambridge University Press, Macmillan, 1957. - 166 pages. Cambridge tracts in mathematics and mathematical physics, volume 45. This issue sets out to give some idea of the basic techniques and of some of the most striking results of Diophantine approximation. A selection of theorems with complete proofs are presented, and Cassels also provides a precise introduction to each...
  • №76
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Cambridge: Cambridge University Press, 1986. — 372 p. — (London Mathematical Society Student Texts, No. 3). — ISBN 978-0-521-30484-9. The p-adic numbers, the earliest of local fields, were introduced by Hensel some 70 years ago as a natural tool in algebra number theory. Today the use of this and other local fields pervades much of mathematics, yet these simple and natural...
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World Scientific Publishing Company, 2011. - 236 pages. Цель данных лекций - представление самодостаточного изложения некоторых замечательных формул, открытых С. Рамануджаном(гениальным индийским математиком, наиболее известным благодаря своим работам в области теории чисел). В данных лекциях в основном рассматриваются результаты по непрерывным дробям Роджерса-Рамануджана и...
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World Scientific, 2009. — 128 p. — (Monographs in Number Theory, Volume 3). — ISBN: 9814271357, 9814271365 This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression. The materials in this book are...
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Bookboon, 2016. — 88 p. — ISBN 978-87-403-1559-2. This book consists of the lecture notes, problems and solutions from the author’s Coursera course “Fibonacci numbers and the golden ratio.” YouTube links to the course’s videos are provided at the top of each lecture. In these lectures, we learn the origin of the Fibonacci numbers and the golden ratio, and derive a formula to...
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Tampa: University of South Florida, 2002. — 129 p. At first blush one might think that of all areas of mathematics certainly arithmetic should be the simplest, but it is a surprisingly deep subject. We assume that students have some familiarity with basic set theory, and calculus. To a great extent the book is self-contained. It requires only a certain amount of mathematical...
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Cambridge: Cambridge University Press, 2015. - 320p. There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to...
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Bordeaux: Universite de Bordeaux, 2010. — 294 p. This book is an expanded version of a course that I gave at ICTP in Trieste in the summer 2012, preceding a conference on “hypergeometric motives”, and in Rennes in April 2014 at the Journ´ees Louis Antoine. The goal of this book is to present a number of analytic and arithmetic numerical methods used in number theory, with a...
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Springer. — 563 p. Fundamental Number-Theoretic Algorithms. Algorithms for Linear Algebra and Lattices. Algorithms on Polynomials. Algorithms for Algebraic Number Theory I. Algorithms for Quadratic Fields. Algorithms for Algebraic Number Theory II. Introduction to Elliptic Curves. Factoring in the Dark Ages. Modern Primality Tests. Modern Factoring Methods. Appendix A...
  • №84
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Springer, 1999. — 599 p. — (Graduate Texts in Mathematics). — ISBN: 0387987274, 9780387987279 Скан. The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine...
  • №85
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Springer, Graduate texts of Mathematics 240, 2007. - 596 pages. This book deals with several aspects of what is now called explicit number theory, not including the essential algorithmic aspects, which are for the most part covered by two other books of the author [Coh0] and [Coh1]. The central (although not unique) theme is the solution of Diophantine equations, i.e.,...
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Springer, 2007. — 650 p. 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...
  • №87
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Dover Publications, 1980. — 288 p. Eminent mathematician, teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, theories have evolved during last 2 centuries. Abounds with numerical examples, over 200 problems, many concrete, specific theorems. Numerous graphs, tables.
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Springer, 1995. — 311 pages. The Book of Numbers lets readers of all levels of mathematical sophistication (or lack thereof) understand the origins, patterns, and interrelationships of different numbers. Whether it is a visualization of the Catalan numbers or an explanation of how the Fibonacci numbers occur in nature, there is something in here to delight everyone. The...
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Springer International Publishing AG, 2017. — 696 p. — ISBN 3319561715. Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at...
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2nd edition. — New York: Springer, 2009. — 610 p. — ISBN 9780387894850. Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of...
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Springer, 2006. — 377 pages. Undergraduate courses in mathematics are commonly of two types. On the one hand are courses in subjects - such as linear algebra or real analysis - with which it is considered that every student of mathematics should be acquainted. On the other hand are courses given by lecturers in their own areas of specialization, which are intended to serve as a...
  • №92
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Springer, 2006. — 359 pages. ISBN: 0387298533 Undergraduate courses in mathematics are commonly of two types. On the one hand are courses in subjects - such as linear algebra or real analysis - with which it is considered that every student of mathematics should be acquainted. On the other hand are courses given by lecturers in their own areas of specialization, which are...
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Springer, 2005. — 597 p. Prime numbers beckon to the beginner, the basic notion of primality being accessible to a child. Yet, some of the simplest questions about primes have stumped humankind for millennia. In this book, the authors concentrate on the computational aspects of prime numbers, such as recognizing primes and discovering the fundamental prime factors of a given...
  • №94
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Springer, 2008. — 431 pages. Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these...
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  • 3,61 МБ
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8th edition. — Cambridge University Press, 2008. — 250 p. — ISBN 9780521722360. Now into its Eighth edition, The Higher Arithmetic introduces the classic concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers The theory of numbers is considered to be the purest branch of pure mathematics and is...
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Cambridge University Press, 2003. — 154 p. — (London Mathematical Society Student Texts 55). — ISBN 978-0521531436. This text is a self-contained study of expander graphs, specifically, their explicit construction. Expander graphs are highly connected but sparse, and while being of interest within combinatorics and graph theory, they can also be applied to computer science and...
  • №97
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American Mathematical Association, 1983. — 176 p. In order to make some important mathematical ideas interesting and understandable to a large audience of high school students and laymen. Most of the volumes in the New Mathematical Library cover topics not usually included in the high school curriculum; they vary in difficulty, and, even within a single book, some parts require a...
  • №98
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2003. - 119 pages. A Riemann zeta function is a function which is analytic in the complex plane, with the possible exception of a simple pole at one, and which has characteristic Euler product and functional identity. Riemann zeta functions originate in an adelic generalization of the Laplace transformation which is de ned using a theta function. Hilbert spaces, whose elements...
  • №99
  • 622,09 КБ
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Providence: American Mathematical Society, 2012. — 434 p. The authors assemble a fascinating collection of topics from analytic number theory that provides an introduction to the subject with a very clear and unique focus on the anatomy of integers, that is, on the study of the multiplicative structure of the integers. Some of the most important topics presented are the global and...
  • №100
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Providence: American Mathematical Society, 2016. — 258 p. “Generalized numbers” is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study...
  • №101
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Published by the Carnegie Institution of Washington, Washington, 1919. - 486 pages. The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This first volume in the...
  • №102
  • 33,68 МБ
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Published by the Carnegie Institution of Washington, Washington, 1920. - 803 pages. The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the...
  • №103
  • 39,35 МБ
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Published by the Carnegie Institution of Washington, Washington, 1923. - 313 pages. The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This third volume in the...
  • №104
  • 36,76 МБ
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Dover Publications, 1929. — 193 p. — ISBN: 0486603423, 9780486603421 The aim of this book is not technique, but the central ideas of the subject. Topics are not abandoned just at the point when they become most interesting, but are carried to fruition with attention to both classic and recent literature. Topics are excluded if their full treatment requires results capable of...
  • №105
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Учебное пособие. Series: Lecture Notes in Computer Science, Vol. 3000. Berlin, Heidelberg: Springer-Verlag, 2004. – X+147 p. ISBN: 3-540-40344-2. Книга посвящена алгоритмам для решения древней задачи о простоте: определить, яляется ли данное натуральное число N простым или составным. Эта задача является одной из базовых в теории чисел, и эффективные алгоритмы для её решения,...
  • №106
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Wiley, 2010. — 523 p. — ISBN: 0470496363 Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra...
  • №107
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New York: Palgrave McMillan, 2011. — 272 p. — ISBN-10: 0230113842; ISBN-13: 978-0230113848 — (MacSci) Every time we download music, take a flight across the Atlantic or talk on our cell phones, we are relying on great mathematical inventions. In The Number Mysteries, one of our generation's foremost mathematicians Marcus du Sautoy offers a playful and accessible examination of...
  • №108
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Dover, 2008. — 272 pages. Minimal prerequisites make this text ideal for a first course in number theory. Written in a lively, engaging style by the author of popular mathematics books, it features nearly 1,000 imaginative exercises and problems. Solutions to many of the problems are included, and a teacher's guide is available. 1978 edition.
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2nd Edition. — New York: W.H. Freeman and Company, 1978. — 260 p. — ISBN: 071670076X. Designed for a first course in number theory with minimal prerequisites, the book is designed to stimulates curiosity about numbers and their properties. Includes almost a thousand imaginative exercises and problems.
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Clay Mathematics Institute, 2007. - 256 pages ISBN 0821843079 Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Göttingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life...
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Springer, 1990. - 438 pages. ISBN: 0387974970. This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the...
  • №112
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Academic Press, 1974. - 315 Pages. ISBN: 0122327500 Vol. 58 (Pure and Applied Mathematics) Superb, high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled On the Number of Primes Less Than a Given Magnitude, and traces developments in theory inspired by it. Topics include Riemann’s main formula, the prime number...
  • №113
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Harvard: N.D. Elkies, 2015. — 163 p. Introduction: What is analytic number theory? Distribution of primes before complex analysis: classical techniques (Euclid, Euler); primes in arithmetic progressions via Dirichlet characters and L-series; Cebyˇsev’s estimates on ˇ π(x). Distribution of primes using complex analysis: ζ(s) and L(s, χ) as functions of a complex variable, and the...
  • №114
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Springer, 2003. — 287 p. — ISBN 0-387-95320-5. Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and...
  • №115
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American Mathematical Society, 2003. — 318 p. — (Mathematical Surveys and Monographs 104). — ISBN 0-8218-3387-1 Definitions and Techniques Zeros, Multiplicity and Growth Periodicity Operations on Power Series and Linear Recurrence Sequences Character Sums and Solutions of Congruences Arithmetic Structure of Recurrence Sequences Distribution in Finite Fields and Residue Rings...
  • №116
  • 3,57 МБ
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Springer, 2006. — 297 p. — ISBN: 1852339179, 1849969590 "An Introduction to Number Theory" provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the...
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Leiden: Leiden University, 2014. - 144p. Contents : Notation Introduction Complex analysis Dirichlet series and arithmetic functions Characters and Gauss sums The Riemann zeta function and L-functions Tauberian theorems The Prime Number Theorem for arithmetic progressions Euler's gamma function The functional equation for the Riemann zeta function
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Leiden: Leiden University, 2015. - 156p. Contents : Introduction Geometry of numbers Some algebra Transcendence results Linear forms in logarithms Approximation to algebraic numbers by rationals The subspace theorem P-adic numbers The p-adic subspace theorem
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Cambridge University Press, UK, 2017. — 478 p. — (new mathematical monographs 32) — ISBN-10: 1107097614 Discriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings...
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Cambridge: Cambridge University Press, 2015. — 375 p. Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects,...
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Wiley-Interscience,2006, 307 p. A balanced and clearly explained treatment of infinity in mathematics.The concept of infinity has fascinated and confused mankind for centuries with concepts and ideas that cause even seasoned mathematicians to wonder. For instance, the idea that a set is infinite if it is not a finite set is an elementary concept that jolts our common sense and...
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Second Edition. — Boston - Basel - Berlin: Birkhäuser, 2016 — 422 p. — ISBN 978-3-319-43875-7 (eBook). A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem. Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique...
  • №123
  • 3,54 МБ
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Birkhäusеr Bоston, 2007. — 349 p. — ISBN 0-8176-4545-1 (eBook) This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic,...
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De Gruyter, 2017. — 342 p. — ISBN 978-3110515848 This two-volume set collects and presents some fundamentals of mathematics in an entertaining and performing manner. The present volume examines many of the most important basic results in algebra and number theory, along with their proofs, and also their history. Contents The natural, integral and rational numbers Division and...
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Springer, 2005. - 230 Pages. The square root of 2 is a fascinating number – if a little less famous than such mathematical stars as pi, the number e, the golden ratio, or the square root of – 1. (Each of these has been honored by at least one recent book. ) Here, in an imaginary dialogue between teacher and student, readers will learn why v2 is an important number in its own...
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N.-Y.: John Wiley & Sons Inc, 2003. - 228p. On historical and mathematical grounds alike, number theory has earned a place in the curriculum of every mathematics student. This clear presentation covers the elements of number theory, with stress on the basic topics concerning prime numbers and Diophantine equations (especially quadratic equations in two variables). Topics...
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Springer, 2015. — 282 p. — ISBN: 3319110349 The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number...
  • №128
  • 2,48 МБ
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Springer, 2015. — 282 p. — ISBN: 3319110349. The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory....
  • №129
  • 1,49 МБ
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Dover Publications, Inc., 2004. — 115 p. — ISBN 10 0486495884. A concise work on important topics in number theory, this classic text was devised by a prominent mathematician to explain the essentials of mathematics in a manner accessible to high school and college students as well as to other readers. Clear-cut explanations cover natural numbers as cardinals, with discussions of...
  • №130
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American Mathematical Society, 2017. — 213 p. — (Mathematical Surveys and Monographs 227). — ISBN 1470441462. The theory of bounded cohomology, introduced by Gromov in the late 1980s, has had powerful applications in geometric group theory and the geometry and topology of manifolds, and has been the topic of active research continuing to this day. This monograph provides a...
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Dover, 2001. — 226 p. — ISBN: 0486414493 Support text for a first course in number theory features the use of algebraic methods for studying arithmetic functions. Subjects covered include the Erdös-Selberg proof of the Prime Number Theorem, an introduction to algebraic and geometric number theory—the former by studying Gaussian and Jacobian integers, the latter through...
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Pearson, 2005. — 240 p. — ISBN 978-0-321-26842-3. Решебник к Rosen K.H. Elementary Number Theory And Its Applications. 5th ed. Chapters: The Integers. Integer Representations and Operations. Primes and Greatest Common Divisors. Congruences. Applications of Congruences. Some Special Congruences. Multiplicative Functions. Cryptology. Primitive Roots. Applications of Primitive Roots...
  • №133
  • 1,77 МБ
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Montreal: McGill University, 2013. - 363p. We present a modern introduction to number theory, aimed both at students who have little experience of university level mathematics, as well as those who are completing an undergraduate degree. Like most introductions to number theory, our contents are largely inspired by Gauss’s Disquisitiones Arithmeticae (1801), though we also...
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Springer, 2003. — 505 p. Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols,...
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  • 3,14 МБ
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Springer, 2018. — 404 p. — ISBN 3319909142. Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions...
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John Wiley & Sons, 2012. — 380 p. — ISBN: 0470631570 Discover the properties and real-world applications of the Fibonacci and the Catalan numbers With clear explanations and easy-to-follow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers. Beginning with a historical...
  • №137
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Springer-Verlag, 1994. — 302 p. — ISBN 0387942890. This book contains discussions of hundreds of open questions in number theory, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To...
  • №138
  • 6,60 МБ
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Springer-Verlag, 1994. — 302 p. — ISBN 0387942890. This book contains discussions of hundreds of open questions in number theory, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent...
  • №139
  • 3,48 МБ
  • добавлен
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Third Edition. — New York: Springer-Verlag, 2004. — 456 p. — (Problem Books in Mathematics) — ISBN 978-1-4419-1928-1. В книге обсуждаются сотни нерешенных задач теории чисел, рассортированных по 185 различным темам. Они представляют многочисленные разделы теории чисел и организованы в шесть категорий: простые числа, делимость, аддитивная теория чисел, диофантовы уравнения,...
  • №140
  • 4,07 МБ
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Third Edition. — New York: Springer-Verlag, 2004. — 456 p. — (Problem Books in Mathematics) — ISBN 978-1-4419-1928-1. В книге обсуждаются сотни нерешенных задач теории чисел, рассортированных по 185 различным темам. Они представляют многочисленные разделы теории чисел и организованы в шесть категорий: простые числа, делимость, аддитивная теория чисел, диофантовы уравнения,...
  • №141
  • 5,33 МБ
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September 17, 2007 - Hut, Hyfs och Hallning Productions This textbook presents the most crucial topics in elementary number theory that appear in mathematical contests, therefore this book will be helpfull for those preparing for mathematical contests in both national and international levels.
  • №142
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CRC Press, 2013. — 431 p. — ISBN: 1466591838 Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms,...
  • №143
  • 6,77 МБ
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Springer, 2018. — 504 p. — (CMS Books in Mathematics). — ISBN 978-3-030-01402-5. The objective of this book is to provide tools for solving problems which involve cubic number fields. Many such problems can be considered geometrically; both in terms of the geometry of numbers and geometry of the associated cubic Diophantine equations that are similar in many ways to the Pell...
  • №144
  • 7,40 МБ
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Cambridge at the University Press, 1915 - 84 p. This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the...
  • №145
  • 12,99 МБ
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Cambridge: Cambridge University Press, 1927. - 387p. Сборник опубликованных (с 1911 по 1918 годы) работ гениального индийского математика Сринавасы Раманужана. Также включает некоторые результаты, приведенные Раманужаном в письмах к Харди. Для изучающих теорию чисел, математический анализ, историю математики и психологию математического творчества.
  • №146
  • 8,54 МБ
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Oxford University Press, 1971. - 421 pages. This book has developed gradually from lectures delivered in a number of universities during the last ten years, and, like many books which have grown out of lectures, it has no very definite plan. It is not in any sense (as an expert can see by reading the table of contents) a systematic treatise on the theory of numbers. It does...
  • №147
  • 9,87 МБ
  • дата добавления неизвестна
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Oxford University Press, 2008. - 621 Pages. An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the...
  • №148
  • 11,08 МБ
  • дата добавления неизвестна
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Oxford: At the Clarendon Press, 1971. — 421 p. This book has developed gradually from lectures delivered in a number of universities during the last ten years, and, like many books which have grown out of lectures, it has no very definite plan. It is not in any sense (as an expert can see by reading the table of contents) a systematic treatise on the theory of numbers. It does not...
  • №149
  • 5,75 МБ
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Clarendon Press, 1998. — 320 pages. ISBN-10: 0198500831 This book examines the number-theoretic properties of the real numbers. It collects a variety of new ideas and develops connections between different branches of mathematics. An indispensable compendium of basic results, the text also includes important theorems and open problems. The book begins with the classical results...
  • №150
  • 2,26 МБ
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2018. - 174 p. This book provides an introduction to Number Theory from a point of view that is more geometric than is usual for the subject, inspired by the idea that pictures are often a great aid to understanding. The title of the book Topology of Numbers is intended to express this visual slant, where we are using the term “Topology" with its general meaning of “the spatial...
  • №151
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Cornell University, 2019. — 213 p. The plan is for this to be an introductory textbook on elementary number theory from a geometric point of view, as opposed to the usual strictly algebraic approach. The title "Topology of Numbers" is intended to convey this idea of a more geometric slant, where we are using the word "Topology" in the general sense of "geometrical arrangement"...
  • №152
  • 2,84 МБ
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2017. — 147 p. This book provides an introduction to Number Theory from a somewhat unusual geometric point of view. It might have been called “Geometry of Numbers" if this phrase did not already have a well-established meaning rather different from what we have in mind here. Instead we have chosen the title Topology of Numbers where we are using the term “Topology" with its general...
  • №153
  • 2,01 МБ
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World Scientific, 2006. - 260 pages. ISBN-10: 9812564772, 9812566015 The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Legendre. While our understanding of continued fractions and related methods for simultaneous diophantine approximation has burgeoned over the course of...
  • №154
  • 12,71 МБ
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N.-Y.: A K Peters/CRC Press, 2012. — 444p. Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago,...
  • №155
  • 12,21 МБ
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Springer, 1998. — 359 p. — ISBN: 3540627790, 9783540627791. David Hilbert, I.T. Adamson, F. Lemmermeyer, N. Schappacher, R. Schoof. OCR. This book is a translation into English of Hilbert's "Theorie der algebraischen Zahlkrper" best known as the "Zahlbericht", first published in 1897, in which he provided an elegantly integrated overview of the development of algebraic...
  • №156
  • 2,06 МБ
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Springer, 2011. - 340 pages. ISBN: 1447121309 Number theory is a branch of mathematics which draws its vitality from a rich historical background. It is also traditionally nourished through interactions with other areas of research, such as algebra, algebraic geometry, topology, complex analysis and harmonic analysis. More recently, it has made a spectacular appearance in the...
  • №157
  • 3,51 МБ
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Rehoboth, USA: American Research Press, 2003. — 97 pages. — ISBN: 193123373X Which is the smallest integer that can be expressed as a sum of consecutive integers in a given number of ways? Alternating iterations of the Smarandache function and the Euler phi-function respectively the sum of divisors function. Some light is thrown on loops and invariants resulting from these...
  • №158
  • 3,56 МБ
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Springer, 1990, 389 p., second edition. Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant...
  • №159
  • 4,70 МБ
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New York: American Mathematical Society, 2014. - 119p. The Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the...
  • №160
  • 737,66 КБ
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Springer, 2009. — 520 p. — ISBN: 038784922X 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...
  • №161
  • 4,62 МБ
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Cambridge: Cambridge university press, 2003. — 264 p. At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells (in an approximate but well-defined sense) how many primes can be found that are less than any integer. The prime number theorem tells what this formula is and it is...
  • №162
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Springer, 2014. — 298 p. — (Springer Undergraduate Mathematics Series). — ISBN: 9783319075440, 9783319075457 The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number...
  • №163
  • 2,32 МБ
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Addison Wesley, 1980. — 428 p. This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods. Any commentary upon the present volume by Professors Jones and Thron on the analytic theory of continued fractions must begin with the remarkable fact that it is the first systematic treatment of the...
  • №164
  • 3,44 МБ
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Singapore: World Scientific Publishing, 2015. — 316 p. This is a book on zeta-functions as viewed from their symmetry—functional equations. There is an eternal conflict between the viewpoints on whether one assumes the Euler product or not. Without the Euler product, the class is wider and with it, the class gives rise to some more delicate information. Here we take the former...
  • №165
  • 6,92 МБ
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Singapore: World Scientific, 2013. — 272 p. This volume is based on the successful 6th China - Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory - additive...
  • №166
  • 1,74 МБ
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Springer-Verlag, 1989. — 169 p. This book deals with various systems of "numbers" that can be constructed by adding "imaginary units" to the real numbers. The complex numbers are a classical example of such a system.
  • №167
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Walter de Gruyter, Berlin, 1992. — xii + 396 p. This monograph is devoted to a systematic exposition of the theory of the Riemann zeta-function. This type of project is not new. One need only recall Titchmarsh's The Theory of the Riemann Zeta-Function , first published in 1951 and then reissued by Oxford University Press in 1986. Titchmarsh's book has not lost its special...
  • №168
  • 2,78 МБ
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Springer, 2013. — 403 p. — ISBN-10: 3642393675 Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to...
  • №169
  • 3,12 МБ
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Providence: American Mathematical Society, 2000. — 157 p. This is the English translation of the original Japanese book. In this volume, “Fermat's Dream”, core theories in modern number theory are introduced. Developments are given in elliptic curves, pp-adic numbers, the ζζ-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number...
  • №170
  • 993,90 КБ
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Providence: American Mathematical Society, 2000. — 157 p. This is the English translation of the original Japanese book. In this volume, “Fermat's Dream”, core theories in modern number theory are introduced. Developments are given in elliptic curves, pp-adic numbers, the ζζ-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number...
  • №171
  • 6,52 МБ
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Providence: American Mathematical Society, 2011. — 250 p. This book, the second of three related volumes on number theory, is the English translation of the original Japanese book. Here, the idea of class field theory, a highlight in algebraic number theory, is first described with many concrete examples. A detailed account of proofs is thoroughly exposited in the final chapter....
  • №172
  • 8,37 МБ
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Providence: American Mathematical Society, 2011. — 250 p. This book, the second of three related volumes on number theory, is the English translation of the original Japanese book. Here, the idea of class field theory, a highlight in algebraic number theory, is first described with many concrete examples. A detailed account of proofs is thoroughly exposited in the final chapter....
  • №173
  • 1,98 МБ
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Berlin: de Gruyter, 2016. — 206 p. By connecting dynamical systems and number theory this graduate textbook on ergodic theory covers a highly active area of mathematics, where a variety of strands of research open up. After introducing number-theoretical dynamical systems, the text touches on foundations and renewal theory before covering infinite ergodic theory. Applications such...
  • №174
  • 2,34 МБ
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Dover Publications, Mineola, New York, 1998. — 62 p. Translated by F. Bagemihl, H.Komm and W. Seidel. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. The author, one of the leading Russian mathematicians of the post-war period, attempts to present three important results in number theory in such a way as to promote interest in the...
  • №175
  • 399,67 КБ
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Providence: American Mathematical Society, 2004. — 329 p. This volume contains a collection of articles from the meeting of the Canadian Number Theory Association held at the Centre de Recherches Mathematiques (CRM) at the University of Montreal. The book represents a cross section of current research and new results in number theory. Topics covered in this book include algebraic...
  • №176
  • 9,68 МБ
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The Mathematical Association of America, 1991. — 353 p. Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each...
  • №177
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R. Knott, 2001. — 293 p. The Fibonacci sequence is named after Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics. By modern convention, the sequence begins either with F0=0 or with F1= 1. The Liber Abaci began the sequence with F1=1, without an initial 0....
  • №178
  • 1,88 МБ
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Addison-Wesley, 1974. - 119 pages. Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E. Knuth, in appreciation of this revolutionary system, took a week off from work on The Art of Computer Programming to write an introduction to Conway's method. Never content with the ordinary, Knuth wrote this introduction as a work of fiction-a...
  • №179
  • 10,64 МБ
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2nd edition. — Springer, 1994. — 235 p. — ISBN 0-387-94293-9. The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. No background in algebra or number theory is assumed, and the book begins with a discussion of the basic number...
  • №180
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Oxford: Oxford University Press, 2009. - 440p. Like the intriguing Fibonacci and Lucas numbers, Catalan numbers are also ubiquitous. "They have the same delightful propensity for popping up unexpectedly, particularly in combinatorial problems," Martin Gardner wrote in Scientific American. "Indeed, the Catalan sequence is probably the most frequently encountered sequence that is...
  • №181
  • 3,29 МБ
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Academic Press, 2007. — 800 pages. Second Edition ISBN: 0123724872 This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique...
  • №182
  • 8,10 МБ
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Wiley-Interscience, 2001. — 648 p. The first comprehensive survey of mathematics' most fascinating number sequences Fibonacci and Lucas numbers have intrigued amateur and professional mathematicians for centuries. This volume represents the first attempt to compile a definitive history and authoritative analysis of these famous integer sequences, complete with a wealth of...
  • №183
  • 16,68 МБ
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John Wiley & Sons, Inc., 2017. — xx+680 p. — (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs, and Tracts). — ISBN 978-1118742129. The first comprehensive survey of mathematics most fascinating number sequences Fibonacci and Lucas numbers have intrigued amateur and professional mathematicians for centuries. This volume represents the first attempt to compile a...
  • №184
  • 4,20 МБ
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Wiley, 2019. — 731 p. — ISBN 9781118742082. Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshev polynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and...
  • №185
  • 7,04 МБ
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Springer Science+Business Media, New York, 2014. — 444 p. — ISBN 978-1-4614-8488-2. Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis,...
  • №186
  • 10,57 МБ
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Cambridge University Press, 2008. — 316 p. — ISBN: 978-0521888516, e-ISBN: 978-0511398872. Series: Cambridge Tracts in Mathematics (Book 175). Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that...
  • №187
  • 1,55 МБ
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New York, Chulsea Publishing Company, 1958. - 256 pages. Professor Landau gave a six-semester course on Number Theory at the University of Gottingen, which was published in three volumes as Vorlesungen uber Zahlentheorie (Leipzig, 1927). When Vorlesungen uber Zahlentheorie was reprinted in 1947, the part on Elementary Number Theory was issued separately as Elementare...
  • №188
  • 2,45 МБ
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Combined 2nd edition. — Springer Science & Business Media, 2012. — 436 p. Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper...
  • №189
  • 23,06 МБ
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Cambridge: Cambridge University Press, 2015. — 344p. Harald Niederreiter's pioneering research in the field of applied algebra and number theory has led to important and substantial breakthroughs in many areas. This collection of survey articles has been authored by close colleagues and leading experts to mark the occasion of his 70th birthday. The book provides a modern...
  • №190
  • 2,82 МБ
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Elsevier, 1987 year - 731 p. This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc. This second edition was prepared jointly by P.M....
  • №191
  • 7,35 МБ
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Dover edition, 2002. — 511 p. Volume 1 Introduction The Euclidean Algorithm and Its Consequences Congruences Primitive Roots and Indices Quadratic Residues Number-Theoretic Functions and the Distribution of primes Sums of Squares Pell’s Equation and Some Applications Rational Approximations to Real Numbers Volume 2 Binary Quadratic Forms Algebraic Numbers...
  • №192
  • 23,76 МБ
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Wiley, 2015. — 210 p. A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the...
  • №193
  • 1,56 МБ
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John Wiley & Sons, 2015. — 224 p. — ISBN: 1119062764 A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by...
  • №194
  • 1,76 МБ
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North Holland, 1992. — 606 p. — Studies in Computational Mathematics. This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and...
  • №195
  • 15,11 МБ
  • дата добавления неизвестна
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Mexico: Universidad Nacional Autonoma de Mexico. 2009. — 81 p. Continued Fractions De nitions Properties In nite continued fractions Convergentes Quadratic Irrationalities Pell Equations Problems Notes Binary recurrent sequences Examples of binary recurrent sequences Lucas sequences The Primitive Divisor Theorem Applications Lehmer sequences Problems Notes Lower bounds for linear...
  • №196
  • 500,02 КБ
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Springer, 2007. — 520 p. — ISBN 3540203648, 9783540203643, 9783540276920 Series: Encyclopaedia of Mathematical Sciences, Vol. 49 This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development...
  • №197
  • 2,49 МБ
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2nd ed. — Springer, 2018. — 213 p. — (Universitext). — ISBN 9783319902326, 3319902326. Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to...
  • №198
  • 1,94 МБ
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Washington: MAA, 2007. — 135 p. — ISBN 9780883857519, 0883857510. Intro Divisibility in the Natural Numbers Linear Equations Through the Ages Prime Numbers From Antiquity to the Internet Thinking Cyclically Prince & Master Abstracting the Ordinary Fermat, Wilson & Leibniz Public Key Codes & RSA Hard Problems Higher Order Congruences Sophie Germain is Germane 1 Quadratic...
  • №199
  • 650,12 КБ
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Washington, D.C.: Mathematical Association of America, 2007. — 150 p. — (MAA textbooks). — ISBN 978-0-88385-983-4. This innovative textbook leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. The first is to help students develop mathematical thinking skills, particularly theorem-proving skills. The other goal...
  • №200
  • 620,72 КБ
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Scholarly Publishing Office, 2005. - 29 pages. This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the...
  • №201
  • 1,19 МБ
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Penguin, 2004. — 275 p. Imagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who take delight in the imaginative work of reading poetry, but may have no background in math, to make a leap of the imagination in mathematics. Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success,...
  • №202
  • 2,49 МБ
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Cambridge: Cambridge University Press, 2015. — 154 p. — ISBN 1-107101-2-1. Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis, which remains to be one of the most important unsolved problems in mathematics. Through the deep insights of...
  • №203
  • 20,86 МБ
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Cambridge University Press, 2008. — 364 p. — ISBN-10: 0521714672 Many areas of active research within the broad field of number theory relate to properties of polynomials, and this volume displays the most recent and most interesting work on this theme. The 2006 Number Theory and Polynomials workshop in Bristol drew together international researchers with a variety of...
  • №204
  • 3,27 МБ
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CRC Press, 2009. - 440 pages. Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and...
  • №205
  • 3,80 МБ
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Chapman and Hall/CRC, 2008. - 384 Pages. Second Edition An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and...
  • №206
  • 6,18 МБ
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Providence: American Mathematical Society, 1990. — 237 p. This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either...
  • №207
  • 28,28 МБ
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New York: Cambridge University Press, 2006. — 552 p. — ISBN-13 978-0-511-25746-9 Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the...
  • №208
  • 4,99 МБ
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103 p. - National Council of Teachers of Mathematics - 1964. Provided is an introduction to the properties of continued fractions for intellectually curious high school student. Also included are proofs that show new relationships between bits of familiar mathematics, exercises that demonstrate the properties under investigations, answers to exercises in the appendix, and...
  • №209
  • 2,77 МБ
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Taylor & Francis Group, 2005. — 368 p. — (Discrete Mathematics and Its Applications). — ISBN: 1584884568 Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a...
  • №210
  • 24,09 МБ
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West Lafayette: The Trillia Group, 2004. — 95 p. — ISBN 1-931705-01-1 These lectures are intended as an introduction to the elementary theory of numbers. Contents Compositions and Partitions Arithmetic Functions Distribution of Primes Irrational Numbers Congruences Diophantine Equations Combinatorial Number Theory Geometry of Numbers Classical Unsolved Problems...
  • №211
  • 402,97 КБ
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Cambridge University Press, 2008. — 393 p. This volume presents an authoritative, up-to-date review of analytic number theory. It contains outstanding contributions from leading international figures in this field. Core topics discussed include the theory of zeta functions, spectral theory of automorphic forms, classical problems in additive number theory such as the Goldbach...
  • №212
  • 2,18 МБ
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2 edition. — Springer, 2005. — 503 p. The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject. Includes various levels of problems - some are easy and straightforward, while others are more challenging. All problems are elegantly solved.
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Springer, 2001. — 460 p. — ISBN: 3540662898 This book presents the development of Prime Number Theory from its beginnings until the end of the first decade of the XXth century. Special emphasis is given to the work of Cebysev, Dirichlet, Riemann, Vallée-Poussin, Hadamard and Landau. The book presents the principal results with proofs and also gives, mostly in short...
  • №214
  • 4,47 МБ
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Springer, 2000. — 518 pages. ISBN: 0387989129 This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proof for one of the most famous results in mathematics, the prime number theorem. With...
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  • 3,30 МБ
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Springer Science & Business Media, 1996. — 342 p. The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to learn, not for experts who already know it. For this...
  • №216
  • 15,26 МБ
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Springer, 1999. — 574 p. — ISBN 978-3-642-08473-7. This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically...
  • №217
  • 45,34 МБ
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Graduate texts in Mathematics Springer-Verlag, New York, 1998, 81 pages The initial step in the investigation of a number theoretic item is the formulation of the generating function. This formulation inevitably moves us away from the designated subject to a consideration of complex variables. Having wandered away from our subject, it becomes necessary to effect a return....
  • №218
  • 297,31 КБ
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N.-Y.: Springer, 2015. - 442p. This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the...
  • №219
  • 4,68 МБ
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The Mathematical Association of America, 1955. — 176 p. In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational...
  • №220
  • 4,10 МБ
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John Wiley & Sons, 1991. — 541 pages. ISBN: 0471625469 The Fifth Edition of one of the standard works on number theory, written by internationally-recognized mathematicians. Chapters are relatively self-contained for greater flexibility. New features include expanded treatment of the binomial theorem, techniques of numerical calculation and a section on public key cryptography....
  • №221
  • 3,35 МБ
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Yale University, 1961. — 145 pages. A superb development that starts with the natural numbers and carries the reader through the rationals and their decimal representations to algebraic numbers and then to the real numbers. Along the way, you will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. This material is basic to all of...
  • №222
  • 1,74 МБ
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American Mathematical Association, 1973 - 149 p. This book is one of a series written by professional mathematicians in order to make some important mathematical ideas interesting and under- standable to a large audience of high school students and laymen. Most of the volumes in the New Mathematical L i h y cover topics not usually included in the high school curriculum; they vary...
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Изд-во: Nanyang Technological University, 2010 г. 95 с. These are lecture notes for the class on introduction to algebraic number theory, given at Nanyang Technological University from January to April 2009 and 2010. Contents: Algebraic Numbers and Algebraic Integers Ideals Ramification Theory Ideal Class Group and Units p-adic numbers Valuations p-adic fields
  • №224
  • 562,80 КБ
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169 p. - Random House "New Mathematical Library" series - 3rd edition - 1963. This book is one of a series written by professional mathematicians in order to make some important mathematical ideas interesting and understandable to a large audience of high school students and laymen. Contents: Prefrace . Expansion of Rational Functions . Introduction. Definitions and...
  • №225
  • 1,16 МБ
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American Mathematical Society, 1962 - 193 p. The geometry of numbers is a branch of number theory that originated with the publication of Minkowski’s seminal work in 1896 and ultimately established itself as an important field of study in its own right. Its focus is the conversion of arithmetic questions into geometric contexts, with the result that certain difficult questions in...
  • №226
  • 1,03 МБ
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Dover Publications, 2018. — 298 p. — (Dover Books on Mathematics). — ASIN 048682764X. Concise but thorough and systematic, this categorical discussion of the real number system presents a series of step-by-step axioms, each illustrated by examples. The highly accessible text is suitable for readers at varying levels of knowledge and experience: advanced high school students and...
  • №227
  • 16,48 МБ
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2nd. ed. — Washington: The Mathematical Association of America, 2016. — 146 p. — (Anneli Lax New Mathematical Library). Revised and Updated by John J. Watkins and Robin Wilson. In preparing this edition we have endeavored to remain as closely as possible to Oystein Ore’s original intentions. We have felt free, however, to make changes in the presentation and layout of the...
  • №228
  • 4,06 МБ
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Dover Publications, 1988. - 380 pages. Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
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  • 7,92 МБ
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Sрringer, 1984. - 556 pages. After an eclipse of some 50 years, Number Theory, that is to say the study of the properties of the integers, has regained in France a vitality worthy o£ its distinguished past. More and more researchers have been attracted by problems which, though it is possible to express in simple statements, whose solutions require all their ingenuity and...
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  • 2,90 МБ
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Birkhäuser, 2015. — 456 p. — ISBN-10: 1493930907 Offers a self-contained treatment of progress and problems related to the Eulerian numbers Covers a topic that plays an important role in combinatorics, number theory, and topology Provides previously-unpublished coverage of gamma-nonnegativity of a simplicial complex and its results in combinatorial terms Includes discussion...
  • №231
  • 10,68 МБ
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3rd Edition. — New York, London, Sydney, Toronto: John Wiley & Sons, Inc., 1971. — 339 p. — ISBN 0-471-68320-5. The fine work of both the Mathematical Association of America and the National Council of Teachers of Mathematics through support from the National Science Foundation is beginning to be evidenced in the improved mathematics background of the students entering the...
  • №232
  • 8,52 МБ
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Springer, 2018. — 220 p. — ISBN 978-3-319-92777-0. This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired...
  • №233
  • 2,32 МБ
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Springer, 2018. — 196 p. — ISBN 978-3-319-92777-0. This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired...
  • №234
  • 3,66 МБ
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New York: M. Dekker, 1993. - 319 p. Presenting the proceedings of a recently held conference in Provo, Utah, this reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum.;Detailing the integration of geometric, algebraic, analytic and arithmetic ideas, Number Theory with an Emphasis on the Markoff Spectrum...
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  • 2,14 МБ
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171 pages. Contents . Introduction. Prime Numbers. Congruences. Multiplicative Number Theoretic Functions. Primitive Roots and Quadratic Residues. Introduction to Continued Fractions. Introduction to Analytic Number Theory. Other Topics in Number Theory. These notes serve as course notes for an undergraduate course in number theory. Most if not all universities...
  • №236
  • 695,01 КБ
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Springer, 2012. — 186 pages. ISBN: 8132207696. Srinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. But what is missing in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12...
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  • 3,51 МБ
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New Dehli: Hindustan Book Agency, 2009. — 229 p. This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute in February~2005. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and...
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  • 1,15 МБ
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Springer, 2010. — 341 p. — ISBN: 1441904948, 1489981942 The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as...
  • №239
  • 1,75 МБ
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The Macmillan Company, 1910. - 474 pages. This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We...
  • №240
  • 2,44 МБ
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Springer-Verlag, 1979. — 317 p. Fermat's problem, also called Fermat's last theorem, has attracted the attention of mathematicians far more than three centuries. Many clever methods have been devised to attack the problem, and many beautiful theories have been treated with the aim of proving the theorem. Yet, despite all the attempts, the question remains unanswered.
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  • 13,54 МБ
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Sрringer, 2000. - 392 pages. This selection of expository essays by Paulo Ribenboim should be of interest to mathematicians from all walks. Ribenboim, a highly praised author of several popular titles, writes each essay in a light and humorous language without secrets, making them thoroughly accessible to everyone with an interest in numbers. This new collection includes essays...
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  • 1,58 МБ
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New Jersey (USA): World Scientific Publishing Co., 2016. — 321 p. — ISBN 978-9814725811. Prime Numbers, Friends Who Give Problems is written as a trialogue, with two persons who are interested in prime numbers asking the author, Papa Paulo, intelligent questions. Starting at a very elementary level, the book advances steadily, covering all important topics of the theory of prime...
  • №243
  • 1,45 МБ
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Springer, 1991. - 237 pages. The immensely popular Guinness Book of World Records lacked a chapter on prime numbers. The author's popular "The Book of Prime Number Records", however, filled this need. It is devoted to presenting records concerning prime numbers, but it also explores the interface between computations and the theory of prime numbers. The book contains an...
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  • 1,53 МБ
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Springer, 2004. - 373 pages. 2nd edition A deep understanding of prime numbers is one of the great challenges in mathematics. In this new edition, fundamental theorems, challenging open problems, and the most recent computational records are presented in a language without secrets. The impressive wealth of material and references will make this book a favorite companion and a...
  • №245
  • 1,19 МБ
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Springer, 1996. - 541 pages. The Guinness Book made records immensely popular. This book is devoted, at first glance, to present records concerning prime numbers. But it is much more. It explores the interface between computations and the theory of prime numbers.
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  • 10,97 МБ
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Монография (англ. яз.) N.-Y.: Springer, 2012. - XVIII, 464 p. 20 ill. (Modern Birkhäuser Classics) ISBN 978-08176-8297-2 e-ISBN 978-0-8176-8298-9 Является переизданием одноименной книги, изданной в 1994 г. издательством Birkhäuser (Boston, Birkhäuser, 1994, серия "Progress in Mathematics Vol, 126). Из предисловия бумажного издания книги: В наше время почти поголовного...
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  • 4,38 МБ
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The MIT Press, 1977. — 672 p. — ISBN-10 0262680289; ISBN-13 978-0262680288. Elementary number theory : a problem oriented approach by Joe Roberts, a professor in the Reed College math department. This book was published by MIT Press in the late 1970s. Visually, it's an amazing book: it is not typeset, but rather is photographically reproduced from a handwritten manuscript. Book...
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  • 21,67 МБ
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World Scientific Publishing Company, 1992. - 200 Pages. This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of...
  • №249
  • 1,46 МБ
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New York, 2005. — 304 p. This is one of the rarest books dedicated to give an intellectual thought to the Riemann Hypothesis. As it is well known among mathematicians the Riemann Hypothesis is one of the unresolved problems of the millennim. The book helps a reader to understand underlying problems and ideas of the hypothesis to be able to give a further thought to the problem...
  • №250
  • 21,12 МБ
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Birkhäuser Basel, 2015. — 119 p. — ISBN-10: 3319221434 A short, compact yet comprehensive introduction to Catalan numbers and their applications Designed to be as accessible for students as possible Includes exercises with hints and solutions to help students gain a better grasp on the material This textbook provides an introduction to the Catalan numbers and their...
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  • 4,47 МБ
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Pearson, 2011. — 766 p. — 6th ed. — ISBN: 0321500318, 9780321500311 Выложен также Instructor's Solutions Manual с решениями задач. Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps readers explore key concepts and push their...
  • №252
  • 36,41 МБ
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5th ed. — Addison Wesley, 2004. — 744 pages. Elementary Number Theory and Its Applications is noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to years of use and professor feedback, the fifth edition...
  • №253
  • 33,45 МБ
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Pearson, 2011. — 268 p. Решение задач из Rosen K.H. Elementary Number Theory, 2011. 6th ed. The Integers. Integer Representations and Operations. Primes and Greatest Common Divisors. Congruences. Applications of Congruences. Some Special Congruences. Multiplicative Functions. Cryptology. Primitive Roots. Applications of Primitive Roots and the Order of an Integer. Quadratic...
  • №254
  • 2,29 МБ
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Princeton (New Jersey, USA): Princeton University Press, 2000. — 241 p. — ISBN 978-0-691-05076-8. One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in...
  • №255
  • 12,19 МБ
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Dover Publications, 2008. - 106 pages. Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970...
  • №256
  • 1,06 МБ
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Kluwer Academic Publishers, 2004. 635 p. ISBN:1-4020-2546-7 (HB) ISBN:1-4020-2547-5 (e-book) Contents Preface Basic Symbols Basic Notations Perfect Numbers: Old and New Issues; Perspectives ntroduction Some historical facts Even perfect numbers Odd perfect numbers Perfect, multiperfect and multiply perfect numbers Quasiperfect, almost perfect, and pseudoperfect...
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  • 2,15 МБ
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Springer, 2005. - 637 pages. ISBN: 1402042159 This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical...
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Выходные данные отсутствуют. August 13, 2005, 98 pages These notes started in the summer of 1993 when I was teaching Number Theory at the Center for Talented Youth Summer Program at the Johns Hopkins University. The pupils were between 13 and 16 years of age. The purpose of the course was to familiarise the pupils with contest-type problem solving. Thus the majority of the...
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  • 792,13 КБ
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Schleich W.P., Maier H., 2014. — 140 p. — ISBN-10: 0470053658 Recently, the fields of number theory and prime numbers have had enormous impact on disciplines such as computing, communications, and physics. However, many of the theorems related to prime numbers remain the exclusive domain of mathematicians. This book is designed to educate non-mathematicians on the connections...
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  • 4,54 МБ
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5th edition. — Springer, 2008. — 432 p. — ISBN-13: 978-3-540-85297-1. "Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio,...
  • №261
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Chelsea Pub. Co, 1978. - 255 pages. The investigation of three problems, that of perfect numbers, that of periodic decimals, and that of Pythagorean numbers has given rise to much of elementary number theory, and the author shows how each result gives rise to further results and conjectures. He treats not only results and theorems ("solved problems") but also questions that are...
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  • 11,66 МБ
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Chelsea Publishing, 1962. — 305 p. — ISBN-10 082182824X; ISBN-13 978-0821828243. The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome...
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  • 12,21 МБ
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New York: Dover Publications, 2008. — 481 p. Starting with the fundamentals of number theory, this text advances to an intermediate level. Author Harold N. Shapiro, Professor Emeritus of Mathematics at New York University's Courant Institute, addresses this treatment toward advanced undergraduates and graduate students. Selected chapters, sections, and exercises are appropriate...
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Cambridge University Press, 2008. — 252 p. — ISBN-10: 0521091705, 0521268265 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....
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Mumbai, India, Tata Institute of Fundamental Research, 241 p. Kronecker’s Limit Formulas . The first limit formula. The Dedekind function. The second limit formula of Kronecker. The elliptic theta-function #1(w, z). The Epstein Zeta-function. Applications of Kronecker’s Limit Formulas to Algebraic Number Theory . Kronecker’s solution of Pell’s equation. Class number of...
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  • 1,36 МБ
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Oxford: Pergamon Press, 1964. - 124 p. On the borders of geometry and arithmetic. What we know and what we do not know about prime numbers. One hundred elementary but difficult problems in arithmetic. References. Quality : 600 dpi..
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Amsterdam: North-Holland, 1988. - 526 p. 2nd. english edition Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised. The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially...
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  • 9,35 МБ
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New York etc.: Elsevier; Warszawa: PWN - Polish Scientific Publishers. — ISBN 0-444-00071-2. "250 Problems in Elementary Number Theory" presents problems and their solutions in five specific areas of this branch of mathe-matics: divisibility of numbers, relatively prime numbers, arithmetic progressions, prime and composite numbers, and Diophantic equations. There is, in...
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Wydanie 3. — Warszawa-Wrocław.: Drukarnia Uniwersytetu i Politechniki, 1950. — 543 stron. Przedmiot Teorii liczb zajmuję się badaniem własności liczb całkowitych, samo zaś pojęcie liczby całkowitej, jak i również teorię działań arytmetycznych na liczbach całkowitych, bierze gotowe z Arytmetyki i Algebry. Spis rzeczy: Podzielność liczb i rozkład na czynniki pierwsze....
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  • 23,65 МБ
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Springer, 2003. — 644 p. Though it is known as an introduction to the Hindu number system and the algorithms of arithmetic that children now learn in grade school, 'Liber abaci' is much more: an encyclopaedia of thirteenth-century mathematics, both theoretical and practical. It develops the tools rigorously, establishing them with Euclidean geometric proofs, and then shows how...
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  • 67,51 МБ
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Pearson, 2012. — 418 p. — 4th ed. — ISBN: 0321816196, 0321816196, 9780321816191 A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce readers to the overall themes and methodology of mathematics through the detailed study of one particular facet—number theory. Starting with nothing more than basic high school algebra, readers are gradually led to...
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New York: Pearson, 2013. — 248 p. This manual contains detailed, worked-out solutions to all exercises in the text.
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Academic Press, 1973. — 218 p. In spite of the large number of existing mathematical tables, until now there has been no table of sequences of integers. Contents. Preface. Acknowledgments. Abbreviations. Description of the Book. Description of a Typical Entry. Arrangement. Number of Terms Given. References. What Sequences Are Included? How Are Arrays of Numbers...
  • №274
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Springer, 2002. - 435 pages. This book takes the reader from elementary number theory, via algorithmic number theory, to applied number theory in computer science. It introduces basic concepts, results, and methods, and discusses their applications in the design of hardware and software, cryptography, and security. It is aimed at undergraduates in computing and information...
  • №275
  • 21,14 МБ
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Computer Science Press, 1982. — 250 p. — ISBN 0914894277, 9780914894278. The purpose of this book is to introduce the reader to computer programming using number theory examples. The book can be used as a supplementary text in a college level number theory course or as a general interest book for anyone interested in computerized number theory.
  • №276
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Lecture Notes in Mathematics 1559. Publisher: Springer, 1994. - 243 pages. The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly...
  • №277
  • 10,07 МБ
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Sprindzuk V.G. 1969, American Mathematical Society, 204 pages. This book deals with the solution of a group of questions related both to the general theory of transcendental numbers and to the metrical theory of diophantine (and also algebraic) approximations. The fundamental problem in this field has been known in the literature since 1932 as Mahler's conjecture, since it arose...
  • №278
  • 3,43 МБ
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Cambridge University Press, 2015. — 216 p. — ISBN: 1107427746 Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book provides, for the first time, a comprehensive collection of their properties and applications in combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. After an...
  • №279
  • 5,79 МБ
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Cambridge University Press, 2015. — 216 p. — ISBN: 1107427746 Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book provides, for the first time, a comprehensive collection of their properties and applications in combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. After an...
  • №280
  • 2,21 МБ
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The MIT Press, 1978. — 360 p. The majority of students who take courses in number theory are mathematics majors who will not become number theorists. Many of them will, however, teach mathematics at the high school or junior college level, and this book is intended for those students learning to teach, In addition to a careful presentation of the standard material usually...
  • №281
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Springer, 2009. — 176 pages. This is a textbook about classical elementary number theory and elliptic curves. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in the context of cryptography, computation, and deep open research problems. The second part is about elliptic curves, their applications to algorithmic...
  • №282
  • 4,00 МБ
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Online ed., 2017. — 172 p. This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergraduate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The reader is strongly encouraged to do every exercise in this book, checking their answers in the back (where many,...
  • №283
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Выходные данные отсутствуют. September, 2004 This textbook presents the most crucial topics in elementary number theory that appear in mathematical contests, therefore this book will be helpfull for those preparing for mathematical contests in both national and international levels.
  • №284
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Springer, 2016. — 239 p. 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...
  • №285
  • 2,67 МБ
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Textbook. — 3rd edition. — no publisher, 2016. — 129 p. An introductory Olympiad Number Theory book for anyone with a passion for number theory and problem-solving. Each section begins by introducing a main concept or idea and then contains many engaging and challenging problems. The goal for the text was to show how several problem-solving skills——experimenting with small cases,...
  • №286
  • 788,32 КБ
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4th ed. — Boca Raton: CRC Press, 2016. — 314 p. — ISBN 978-1-4987-3840-8. Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this...
  • №287
  • 1,57 МБ
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3d edition. — Natick, Massachusetts, 2002. — 334 p. — ISBN 1-56881-119-5. First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last...
  • №288
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Springer, 2013. — 294 p. — (Undergraduate Texts in Mathematics). — ISBN: 3319015761, 9783319015767 While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of...
  • №289
  • 3,51 МБ
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Cambridge University Press, 2003. — 400 p. — ISBN-10 0521012538; ISBN-13 978-0521012539. This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. The author pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs,...
  • №290
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New York: Springer, 2019. — 286 p. This book came out of an attempt to explain to a class of motivated students at the University of Illinois at Chicago what sorts of problems I thought about in my research. In the course, we had just talked about the integral solutions to the Pythagorean Equation and it seemed only natural to use the Pythagorean Equation as the context to...
  • №291
  • 4,15 МБ
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Cambridge University Press, 2005. - 444 Pages. ISBN: 0521850142 Intended to serve as a one-semester introductory course in number theory, this second edition has been revised throughout. In particular, the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler. In addition,...
  • №292
  • 2,88 МБ
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American Mathematical Society, 2000. - 115 pages. We have been curious about numbers--and prime numbers -- since antiquity. One notable new direction this century in the study of primes has been the influx of ideas from probability. The goal of this book is to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a...
  • №293
  • 6,50 МБ
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University of Australia. — Bookboon, 2015. — 76 p. This ebook makes learning "complex" numbers easy through an interactive, fun and personalized approach. Features include: live YouTube video streams and closed captions that translate to 90 languages! Complex numbers "break all the rules" of traditional mathematics by allowing us to take a square root of a negative number. This...
  • №294
  • 3,74 МБ
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Oxford: Oxford University Press, 1986. — 418 p. The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved...
  • №295
  • 3,69 МБ
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Cambridge: Cambridge University Press, 2014. — 249 p. The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between...
  • №296
  • 2,35 МБ
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Wiley, 1984. — 600 p. This book has a remarkable history. The present edition was announced twenty-five years before its publication. The first version of Turân's book was published in 1953 in Hungarian and in German. An improved Chinese edition followed in 1956. The theory was developed so rapidly that only a few years later these editions were out of date. In 1959 Turân...
  • №297
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Pergamon Press, 1955. — 159 p. Translated from the 6th Russian edition published in 1952 (reprinted 1954). The Theory of Divisibility Fundamental Functions of the Theory of Numbers Congruences Linear Congruences Quadratic Congruences Primitive Roots and Indices Solutions to Problems Answers to Numerical Examples Tables of Indices
  • №298
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Berlin: Springer, 2009. - 171p. The famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions) are analyzed through several zeta functions built over those zeros. These ‘second-generation’ zeta functions have surprisingly many explicit, yet largely unnoticed properties, which are surveyed here in an accessible and...
  • №299
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Chelsea Publishing Company, 1967 edition, 433 Pages. The theory of continued fractions has been defined by a small handful of books. This is one of them. The focus of Wall's book is the study of continued fractions in the theory of analytic functions, rather than on arithmetical aspects. There are extended discussions of orthogonal polynomials, power series, infinite matrices...
  • №300
  • 3,36 МБ
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Princeton University Press, 2013.— 592 p. — ISBN: 0691159408, 9780691159409 The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing...
  • №301
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2nd Edition. — Washington, USA: The Mathematical Association of America, 2017. — 148 p. — ISBN 0883856530. Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, ... and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude...
  • №302
  • 3,04 МБ
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Springer, 1979. — 70 p. — ISBN: 038790381X He is a well-known analytic number theorist. In reminiscing about Stanley Tennenbaum at the memorial, Mel told of a number theory course he took from Stanley at U. Rochester: "The main text was a magical set of lecture notes by Andr'e Weil, 28 pages of typewritten, double-spaced mimeographed pages. Many years later I was friendly with...
  • №303
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Hoboken, "John Wiley & Sons, Inc", 2005, -291 p. A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers?...
  • №304
  • 1,39 МБ
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World Scientific Publishing, 2018. — 544 p. — ISBN 978-981-3231-52-8 . This book provides a systematic account of several breakthroughs in the modern theory of zeta functions. It contains two different approaches to introduce and study genuine zeta functions for reductive groups (and their maximal parabolic subgroups) defined over number fields. Namely, the geometric one, built up...
  • №305
  • 5,89 МБ
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New York: College of the City of New York, 1912 (2012 edition). — 198 p. — ISBN: 1103311778 A history of the equation x^2—Ay^2=1, table of solutions from A = 1,501 to A = 1,700, bibliography with references to over 300 authors, table of continued fractions for √A.
  • №306
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Cambridge: Cambridge University Press, 2011. — 305 p. Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduction of a powerful new method into elementary number theory. This book provides a gentle introduction to this method, explaining it in a clear and straightforward manner. The many...
  • №307
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Springer International Publishing, Switzerland, 2016. — 300 p. — (Lecture Notes in Mathematics 2171) — ISBN-10 3319459546. This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and...
  • №308
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Oxford University Press, 2002. - 369 pages. ISBN: 0521807999 This book represents the highlights of a conference in 1999 hosted at ETH Zurich. The papers presented here cover a broad spectrum of number theory including geometric, algebrao-geometric and analytic aspects. This volume will appeal to number theorists, algebraic geometers, and geometers with a number theoretic...
  • №309
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Springer, 2002. — 445 p. — ISBN: 3540430725 There are many surprising connections between the theory of numbers, which is one of the oldest branches of mathematics, and computing and information theory. Number theory has important applications in computer organization and security, coding and cryptography, random number generation, hash functions, and graphics. Conversely,...
  • №310
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Учебное пособие. - Самара: Издательство "Самарский университет", 2009. - 72 с. Данное учебное пособие содержит материал теоретического курса и одновременно является задачником по теории чисел. В нем рассматриваются основные определения, понятия, теоремы и алгоритмы теории чисел, а также некоторые прикладные задачи. Расположение теоретического материала соответствует лекционному...
  • №311
  • 572,00 КБ
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Пер. с англ. С.П. Демушкина. Под ред. А.Н. Паршина. — М.: Мир, 1987. — 415 с. Учебное пособие по теории чисел, написанное известными математиками из Канады и США. От читателя не требуется предварительных знаний. Авторы начинают с простейших понятий и примеров и доводят изложение до современных проблем и результатов теории чисел. В книге приведено много задач различной трудности...
  • №312
  • 1,74 МБ
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Электронное издание, качество которого лучше оригинала , но верстка и пагинация с ним не совпадают. Пер. с англ. С.П. Демушкина. Под ред. А.Н. Паршина. — М.: Мир, 1987. — 415 с. Учебное пособие по теории чисел, написанное известными математиками из Канады и США. От читателя не требуется предварительных знаний. Авторы начинают с простейших понятий и примеров и доводят изложение до...
  • №313
  • 5,84 МБ
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Задачи с решениями. К курсу "Алгебра и теория чисел". Москва. Просвещение. 1972 г. – 81 с. По сравнению со 2-м изд. осуществлены след. дополнения: введены упр. на темы «Решение неопр. уравнений 1-й степени с двумя неизвестными в целых числах» и «Конечные цепные дроби»; даны разл. методы обоснования признаков делимости чисел; увеличено кол-во упражнений для самост. решения. В...
  • №314
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М.: МЦНМО, 2003г. - 44с. Содержание: Основные определения. Отступление от функции Эйлера. Таблица групп Эйлера. Группы Эйлера произведений. Гомоморфизм приведения по модулю a, Г(ab)- Г(a). Доказательство теорем о группах Эйлера. Динамическая система Ферма-Эйлера. Статистика геометрических прогрессий. Измерение степени случайности подмножества. Среднее значение...
  • №315
  • 366,83 КБ
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М.: МЦНМО, 2003. — 44 с. — ISBN 5-94057-141-7. Основные определения. Отступление от функции Эйлера. Таблица групп Эйлера. Группы Эйлера произведений. Гомоморфизм приведения по модулю a, Г(ab)- Г(a). Доказательство теорем о группах Эйлера. Динамическая система Ферма-Эйлера. Статистика геометрических прогрессий. Измерение степени случайности подмножества. Среднее значение параметра...
  • №316
  • 911,72 КБ
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М.: Московский центр непрерывного математического образования, 2001. — 40 стр. — Библиотека "Математическое просвещение", выпуск 14. Теория цепных дробей связана с теорией приближений вещественных чисел рациональными, с теорией динамических систем, а также со многими другими разделами математики. В брошюре рассказано о связи цепных дробей с геометрией выпуклых многоугольников....
  • №317
  • 1,66 МБ
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М.: Издательство Московского центра непрерывного математического образования, 2001. — 40 с. — Библиотека "Математическое просвещение", выпуск 14. Теория цепных дробей связана с теорией приближений вещественных чисел рациональными, с теорией динамических систем, а также со многими другими разделами математики. В брошюре рассказано о связи цепных дробей с геометрией выпуклых...
  • №318
  • 261,25 КБ
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Москва: Государственное учебно-педагогическое издательство, 1938. — 480 с. Утверждено Всесоюзным комитетом по делам высшей школы в качестве учебного пособия для физико-математических факультетов педагогических институтов. Предполагается, что читатель владеет элементарной математикой в объеме курса средней школы. Книга состоит из двух частей — учения о числе в его последовательных...
  • №319
  • 7,89 МБ
  • дата добавления неизвестна
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Москва: Государственное учебно-педагогическое издательство, 1938. — 480 с. Предполагается, что читатель владеет элементарной математикой в объеме курса средней школы. Книга состоит из двух частей — учения о числе в его последовательных обобщениях и начальных глав теории чисел. Положенные в основу методологические установки, из которых и вытекал выбор того, а не иного способа...
  • №320
  • 46,55 МБ
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Саратов: СГУ, 1962. — 78 с. Данный специальный курс имеет своей целью ввести слушателей в область математики, называемую аналитической теорией чисел. Предметом ее изучения является, в конечном счете, целое число и его свойства, ряд которых с древнейших времен представляет загадку для человека. Различные области и подразделения, существующие в теории чисел, являются весьма...
  • №321
  • 1,22 МБ
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М.: Наука, 1987. — 368 с. Излагается теория кратных тригонометрических сумм, построенная авторами в последние годы. На основе единого метода получаются оценки этих сумм, подобные классическим оценкам И. М. Виноградова, которые затем применяются к решению ряда проблем аналитической теории чисел. Исследуются тригонометрические интегралы, которые часто встречаются в физике,...
  • №322
  • 4,00 МБ
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Караганда: Карагандинский государственный университет им. Е.А.Букетова, 2009. — 175 с. В учебно-методическом комплексе изложена программа изучения курса «Алгебра и теория чисел». Данная программа охватывает следующие вопросы алгебры и теории чисел: элементы теории множеств, комплексные числа, векторные пространства, системы линейных уравнений, алгебра матриц, определители,...
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М.: МЦНМО, 2013. — 64 с. Теорема о распределении простых чисел утверждает, что доля простых чисел среди чисел от 1 до n примерно равна 1/ ln n. Ее классическое доказательство, предложенное в конце XIX века Адамаром и Валле-Пуссеном, использует комплексный анализ. Элементарное доказательство этой теоремы было найдено только спустя полвека Эрдёшем и Сельбергом. Изложению некоторого...
  • №324
  • 416,20 КБ
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Учебное пособие. — К.: ВПЦ "Київський університет", 2003. — 202 с. У посібнику викладено основи теорії чисел в об’ємі, передбаченому навчальними планами механіко-математичного факультету. Особлива увага приділяється методам розв’язування задач. Наявність великої кількості задач для самостійного розв’язування дозволяє використовувати посібник і як збірник задач.
  • №325
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К.: Вища школа, 1977. - 72 с. В книге освещены некоторые важные вопросы теории чисел. Приведено доказательство теоремы о единственности разложения на простые множители, рассмотрены алгоритм Евклида, диофантовые уравнения, арифметики целых комплексных чисел и классов вычетов, представление чисел в различных позиционных системах и др. Рассчитана на учащихся физико-математических...
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  • 1,40 МБ
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К.: Вища школа, 1977. — 72 с. В книге освещены некоторые важные вопросы теории чисел. Приведено доказательство теоремы о единственности разложения на простые множители, рассмотрены алгоритм Евклида, диофантовые уравнения, арифметики целых комплексных чисел и классов вычетов, представление чисел в различных позиционных системах и др. Рассчитана на учащихся физико-математических...
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М.–Ижевск: НИЦ «Регулярная и хаотическая динамика», Ижевский институт компьютерных исследований, 2012. — 368 с. В течение нескольких последних десятилетий теория автоморфных форм стала основополагающей в развитии теории чисел и алгебраической геометрии и имеет приложения в разнообразных областях, включая комбинаторику и математическую физику. Двенадцать глав этой монографии...
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Минск: Вышэйшая школа, 1980. — 125 c. Книга посвящена одному из самых совершенных творений математиков XVII-XVIII веков ( Гюйгенса, Эйлера, Лагранжа, Лежандра и др.) - теории непрерывных(цепных) дробей , которая фактически переживает свое второе рождение в наше время( 21 век ), находя все новые и новые применения в различных сферах науки и техники. Предисловие . Две исторические...
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К.: Наука, 1986. -176с. Монография посвящена аналитической теории многомерных цепных дробей. Изучены свойства и установлены признаки сходимости числовых и накоторых типов функциональных ветвящихся цепных дробей. Перенесены на многомерный случай основные классические признаки сходимости непрерывных дробей - критерий Зейделя, признак Ворпитского, теорема Слешинского-Прингсгейма,...
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К.: Наукова думка, 1974. — 272 с. У книзі викладено основні результати дослідження нового математичного апарату — гіллястих ланцюгових дробів, а також їх застосування в теорії диференціальних рівнянь, обчислювальній математиці, теорії чисел, теорії ймовірностей, теорії функцій, економіці. Книга може бути корисною для математиків, фізиків, економістів, біологів,...
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3-е изд. доп. — М.: Наука, 1985. — 504 с. Излагается ряд методов современной теории чисел. Изложение иллюстрируется рассмотрением большого числа конкретных теоретико-числовых вопросов, относящихся главным образом к неопределенным уравнениям. Основное внимание уделено алгебраическим методам, но заметное место занимают также геометрический и аналитический методы. В третьем...
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3-е изд. доп. — М.: Наука, 1985. — 504 с. Излагается ряд методов современной теории чисел. Изложение иллюстрируется рассмотрением большого числа конкретных теоретико-числовых вопросов, относящихся главным образом к неопределенным уравнениям. Основное внимание уделено алгебраическим методам, но заметное место занимают также геометрический и аналитический методы. В третьем издании...
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Боро В., Цагир Д., Рольфс Ю., Крафт Х., Янцен Е. Сб. статей 1981 г.: Пер. с нем. — М.: Мир, 1985. — 128 с.: ил. Доступное и занимательное изложение некоторых разделов современной теории чисел: дружественные числа, первые 50 миллионов простых чисел, пифагоровы числа. . . Элементарные факты удачно сочетаются с результатами научных исследований. Авторы - математики из ФРГ. Для всех,...
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Боро В., Цагир Д., Рольфс Ю., Крафт Х., Янцен Е. Сб. статей 1981 г.: Пер. с нем. — М.: Мир, 1985. — 128 с.: ил. Доступное и занимательное изложение некоторых разделов современной теории чисел: дружественные числа, первые 50 миллионов простых чисел, пифагоровы числа. Элементарные факты удачно сочетаются с результатами научных исследований. Авторы - математики из ФРГ. Для всех, кто...
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Учебное пособие. — М: Либроком, 2010. — 216 с. — ISBN 978-5-397-01104-4 Излагаются основы теории чисел (теория делимости, сравнения, вычеты, диофантовы уравнения). Коротко затрагиваются новые веяния и взаимосвязи со смежными дисциплинами (алгебраический ракурс, алгоритмические проблемы, эллиптические кривые). Изложение отличается краткостью и прозрачностью. Для студентов,...
  • №336
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М.: Либроком, 2010. — 216 с. Излагаются основы теории чисел (теория делимости, сравнения, вычеты, диофантовы уравнения). Коротко затрагиваются новые веяния и взаимосвязи со смежными дисциплинами (алгебраический ракурс, алгоритмические проблемы, эллиптические кривые). Изложение отличается краткостью и прозрачностью. Для студентов, преподавателей, инженеров и научных...
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Конспект лекций по курсу "Теория чисел". Волгоград. "Перемена". 2005 Излагаются основы теории правильных конечных и бесконечных цепных дробей. Конечные цепные дроби. Алгоритм Евклида. Свойства конечных цепных дробей. Бесконечные цепные дроби. Представление действительного числа цепной дробью. Оценка погрешности при замене действительного числа его подходящей дробью....
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М.: Московский центр непрерывного математического образования, 2001. — 32 стр. — Библиотека "Математическое просвещение", выпуск 13. Уравнения Пелля представляют собой класс диофантовых уравнений второй степени. Они связаны со многими важными задачами теории чисел. Решение уравнений Пелля - задача непростая, хотя и выполнимая методами элементарной математики. Ключевую роль в...
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М.: Издательство Московского центра непрерывного математического образования, 2001. — 32 с. — (Библиотека "Математическое просвещение", выпуск 13). Уравнения Пелля представляют собой класс диофантовых уравнений второй степени. Они связаны со многими важными задачами теории чисел. Решение уравнений Пелля - задача непростая, хотя и выполнимая методами элементарной математики....
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Теория чисел. А. А. Бухштаб. М.: "Просвещение", 1966. - 385 с. Классический учебник по теории чисел. Книга рассчитана в первую очередь на то, чтобы служить в качестве учебного пособия при прохождении курса теории чисел на физико-математических факультетах педагогических институтов и в университетах. Охватывая полностью учебную программу по теории чисел, книга содержит и...
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М.: Просвещение, 1966 В книге рассмотрены следующие темы: простые числа, НОД, НОК, сравнения, классы, первообразные корни и др. А также каждая из рассмотренных тем сопровождается небольшой исторической справкой. Оглавление: Общие основы теории чисел. Простые числа. Наибольший общий делитель. Наименьшее общее кратное. Функция [x]. Конечные цепные дроби. Иррациональные...
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Одесса: Одесский национальный университет имени И. И. Мечникова, 2013. — 36 с. В книге на примере решения ряда классических проблем излагаются основы аналитических методов теории чисел. Книга будет полезна научным работникам, аспирантам и студентам, желающим усвоить аппарат современной аналитической теории чисел. Введение Теорема И.М. Виноградова о распределении дробных долей...
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М.: МГУ, 1995. — 128 с. Для студентов математических специальностей университетов и пединститутов. Представлены задачи по всем основным разделам теории чисел. В каждом параграфе имеются формулировки необходимых определений и теорем, приводятся теоретические упражнения и численные примеры. Типовые методы решения изложены в виде отдельных задач, снабженных подробными указаниями....
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М.: МГУ, 1995. — 128 с. Для студентов математических специальностей университетов и пединститутов. Представлены задачи по всем основным разделам теории чисел. В каждом параграфе имеются формулировки необходимых определений и теорем, приводятся теоретические упражнения и численные примеры. Типовые методы решения изложены в виде отдельных задач, снабженных подробными...
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М.: Мир, 1972. — 408 с. Монография одного из крупнейших современных математиков, написанная на основе курса лекций, прочитанного автором в Принстонском университете. Содержит изложение теории алгебраических чисел, в том числе теории полей классов, являющееся, по-видимому, на много лет окончательным. Книга представляет интерес не только для специалистов по теории чисел, но и...
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М.: Мир, 1972. - 410 с. Монография одного из крупнейших современных математиков, написанная на основе курса лекций, прочитанного автором в Принстонском университете. Содержит изложение теории алгебраических чисел, в том числе теории полей классов, являющееся, по-видимому, на много лет окончательным. Книга представляет интерес не только для специалистов по теории чисел, но и для...
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M.: Государственное издательство иностранной литературы, 1947. — 226 c. Эта книга представляет собой подлинные записи курса теории чисел, прочитанного автором в Принстоне в течение 1938-1939 гг. В ней описаны основные арифметические понятия и факты, касающиеся алгебраических полей. В главе II автор аксиоматизировал кронекеровский подход к проблеме делимости, которая, по его...
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М.: Наука, 1981. — 448 с. Сборник содержит все основные теоретико-числовые работы выдающегося советского математика профессора Б. А. Венкова. Эти работы относятся к некоммутативной арифметике, теории квадратичных форм, геометрии чисел и теории правильного деления пространства. В них содержится, в частности, замечательное элементарное доказательство формул Дирихле для числа...
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Заглавие "Элементарная теория чисел", данное настоящему реферату, не вполне отражает ту точку зрения, которая была принята при его составлении. В нем собрано все то из классической теории чисел и новых исследований, что осуществляется чисто арифметическим методом (т. е. без введения понятий анализа, геометрии, иррациональных и комплексных чисел). Этот материал удовлетворяет...
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М.: ОНТИ НКПТ СССР, 1937. — 221 с. Заглавие "Элементарная теория чисел", данное настоящему реферату, не вполне отражает ту точку зрения, которая была принята при его составлении. В нем собрано все то из классической теории чисел и новых исследований, что осуществляется чисто арифметическим методом (т. е. без введения понятий анализа, геометрии, иррациональных и комплексных чисел)....
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Числові системи / Л. М. Вивальнюк, В. К. Григоренко, С. С. Левіщенко.— К . : Вища шк. Головне внд-во, 1988.— 272 с.: іл. . Посібник написано відповідно до діючої програми з курсу «Числові системи» для фізико-математичних факультетів педагогічних інститутів. У ньому викладено аксіоматичну теорію всіх числових систем, розглядаються деякі питання основ математики, наведено короткий...
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М.: Наука. 1971. 162с. В книге на ряде фундаментальных проблем аналитической теории чисел дано систематическое изложение основ известного метода автора. Эти проблемы подобраны так, чтобы в возможно более простой форме и достаточно полно отразить существо метода и позволить читателю быстро и основательно усвоить этот метод. Книга будет полезна студентам, аспирантам и научным...
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Учебное пособие. 11-е изд., стер. — СПб.: Лань, 2006. — 176 с. — (Учебники для вузов. Специальная литература). В книге излагаются основы теории чисел в объеме университетского курса. Для студентов математических специальностей университетов и педвузов, аспирантов, научных работников в области математики. Существенно перестроены и дополнены главы первая и вторая. Кроме того, из...
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Москва; Ижевск: Регулярная и хаотическая динамика, 2003. — 176 с. В книге излагаются основы теории чисел в объеме университетского курса. В последнее издание включена новая глава о характерах Дирихле, значительной переработке подвергнута глава о важнейших функциях, встречающихся в теории чисел, внесены изменения в решения ряда задач. Для студентов математических специальностей...
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178с. Содержание: Теория делимости. Важнейшие функции, встречающиеся в теории чисел. Сравнения. Сравнения с одним неизвестным. Сравнения второй степени. Преобразования корня и индексы. Решения задач к каждой главе. Ответы к численным примерам.
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Учебник. Изд. 6-е испр. — М.; Л.: ГИТТЛ, 1952. — 182 с. В книге даётся систематическое изложение основ теории чисел в объёме университетского курса. Значительное количество задач вводит читателя в круг некоторых новых идей в области теории чисел.
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Учебник. Изд. 6-е испр. — М.; Л.: ГИТТЛ, 1952. — 182 с. В книге даётся систематическое изложение основ теории чисел в объёме университетского курса. Значительное количество задач вводит читателя в круг некоторых новых идей в области теории чисел.
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М.: Наука, 1976. - 122 с. В книге рассматриваются центральные проблемы аналитической теории чисел, решающая роль в исследовании которых принадлежит специальным вариантам известного метода автора, изложенного в монографии "Метод тригонометрических сумм в теории чисел". Эти варианты и сами являются мощным средством решения широкого круга задач теории чисел. Книга будет полезна...
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Ленинград: ИАН СССР, 1933. — 36 с. Два доклада из Ноябрьской юбилейной сессии АН СССР, изданные отдельной брошюрой. В первом докладе рассмотрены некоторые проблемы теории чисел, во втором некоторые аспекты теории вероятностей.
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М.: Мир, 1985. — 184 с. Книга известного английского математика, излагающая один из основных методов теории чисел — метод Харди—Литтлвуда. На примерах решения ряда конкретных проблем автор демонстрирует возможности этого метода, приводит изящные и краткие доказательства известных теорем. Приведены задачи разной степени трудности, поставлены новые проблемы. Для математиков...
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2-е изд. — М.: Наука, 1974. — 76 с. Делимость чисел. Делимость сумм и произведений. Признаки равноостаточности и признаки делимости. Делимость степеней. Доказательства теорем. Решения задач.
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Методические рекомендации. – Витебск: Витебский государственный университет имени П.М. Машерова, 2017. – 55 с. Настоящее издание предназначено для первоначального изучения основ теории чисел. В начале каждого параграфа даются основные теоретические сведения (определения, формулировки некоторых теорем). Затем приведены подробно разобранные решения ряда стандартных задач, а также...
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Сборник заданий. – Витебск: Витебский государственный университет имени П.М. Машерова, 2017. – 67 с. Предлагаемое издание адресовано студентам физико-математических специальностей. В начале каждого параграфа даются основные теоретические сведения (определения и формулировки некоторых теорем). Затем приведены подробно разобранные решения ряда задач. В заключение читателю предложены...
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Под ред. А. А. Карацубы. — М.: Изд-во МГТУ, 2006. — 480 с. В настоящее издание вошли все основные работы выдающегося русского математика С. М. Воронина (1946-1997) по теории чисел и анализу, в частности известная теорема об универсальности дзета-функции Римана. Для математиков, интересующихся теорией чисел, теорией квадратурных и интерполяционных формул, а также для аспирантов и...
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М.: Физматлит, 1994. — 376 с. Содержит систематическое изложение теории дзета-функции Римана, одной из важнейших производящих функций теории чисел. Поскольку теория дзета-функции в настоящее время далека от завершенного вида, в книгу включены лишь устоявшиеся классические результаты и недавние достижения теории, имеющие в определенном смысле законченный вид. Необходимые сведения...
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Киев: Издательство Академии наук Украинской ССР, 1952. — 403 с. Исследования Георгия Федосеевича Вороного оказали огромное влияние на развитие теории чисел и в полной мере сохранили свою ведущую роль в настоящее время. Вороной одновременно с Минковским был создателем новой отрасли математики — геометрии чисел и, вместе с тем, дал основополагающие, глубокие результаты в...
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Киев: Издательство Академии наук Украинской ССР, 1952. — 396 с. Во второй том Собрания сочинений Г. Ф. Вороного вошли: а) две его основные работы по аналитической теории чисел: „Об одной задаче из теории асимптотических функций" и „Об одной трансцендентной функции и ее приложениях к суммированию некоторых рядов" вместе с примыкающей ко второй работе статьей „О разложении...
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Киев: Издательство Академии наук Украинской ССР, 1953. — 310 с. Настоящим томом заканчивается издание собрания сочинений Г.Ф. Вороного. Первые два тома содержат все напечатанные при жизни автора монографии и статьи. В третий том вошли научные доклады и сообщения (кроме одного из докладов на III международном съезде математиков, напечатанного во II томе вместе с исследованиями по...
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Львов: Изд-во Львовского университета, 1970. — 169 с. В монографии обосновывается гипотеза Римана о корнях дзета-функции и решается проблема существования вещественных корней L-функций Дирихле. Все нужные понятия из теории чисел приведены в первых трёх главах. Монография рассчитана на научных работников, аспирантов и студентов, занимающихся аналитической теорией чисел и...
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