Number theory Books

This book presents a printed testimony for the fact that George Andrews, one of the world's leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the...

This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south...

Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational...

These proceedings collect several number theory articles, most of which were written in connection to the workshop WIN4: Women in Numbers, held in August 2017, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. It collects...

The theory of numbers continues to occupy a central place in modern mathematics because of both its long history over many centuries as well as its many diverse applications to other fields such as discrete mathematics, cryptography, and coding theory...

George Andrews is one of the most influential figures in number theory and combinatorics. In the theory of partitions and q-hypergeometric series and in the study of Ramanujan's work, he is the unquestioned leader. To suitably honor him during his 70th...

This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive...

"Number Theory and Related Fields" collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia...

In recent years, research in K3 surfaces and Calabi-Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics-in particular, in string...

Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions...

Surveys.- Multiples of forms.- On Saltman's p-Adic Curves Papers.- Serre's Conjecture II: A Survey.- Field Patching, Factorization, and Local-Global Principles.- Deformation Theory and Rational Points on Rationally Connected Varieties.- Recent Progress...

Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental...

This volume contains the proceedings of the very successful second China-Japan Seminar held in lizuka, Fukuoka, Japan, during March 12-16, 2001 under the support of the Japan Society for the Promotion of Science (JSPS) and the...

This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for...

Children's Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that...

Der Autor ist zu diesem kleinen Büchlein gekommen wie die Jungfrau zum Kinde. Nicht, dass es hier keine "Schwangerschaft" gegeben hätte, während derer man über die Grundidee und die Nützlichkeit dieses Werks intensiv nachgedacht hätte. Vielmehr in dem...

"Searching for N" is a captivating collection of articles that takes readers on a journey through the fascinating world of number theory and beyond. Written by a mathematics enthusiast, this book presents classic topics like prime numbers and...

"Computing with Fermat" is a fascinating collection of math articles that pay tribute to the great Pierre de Fermat, exploring various math problems using computational number theory that relate to his work. With chapters such as "On Fermat's...

Die Theorie und Aufl������sung der h������heren algebraischen und der transzendenten Gleichungen (1850) von Schnuse, C. H. ist ein mathematisches Buch, das sich mit der Theorie und L������sung von h������heren algebraischen und transzendenten Gleichungen...

Das Buch ""Briot und Bouquet's: Theorie der doppelt-periodischen Funktionen und insbesondere der elliptischen Transzendenten (1862)"" von Hermann Fischer ist eine umfassende Abhandlung �����ber die Theorie der doppelt-periodischen Funktionen und...

""�����l�����ments de la th�����orie des d�����terminants"" (1883) de Dostor, G. est un livre qui traite de la th�����orie des d�����terminants en math�����matiques. Le livre explore les propri�����t�����s des d�����terminants, y compris leur calcul,...

""�����l�����ments d'arithm�����tique th�����orique et pratique"" est un livre �����crit par E. A. Tarnier et publi����� en 1853. Il s'agit d'un ouvrage qui aborde les principes fondamentaux de l'arithm�����tique, tels que les nombres premiers, les...

""�����ber eine besondere Klasse irrationaler Modulargleichungen der elliptischen Funktionen"" ist ein mathematisches Buch von Ernst Wilhelm Fiedler, das im Jahr 1885 ver������ffentlicht wurde. Das Buch besch�����ftigt sich mit einer speziellen Art von...

Das Buch ""�����bersicht der Theorie der elliptischen Funktionen"" wurde im Jahr 1863 von Hermite, Charles ver������ffentlicht. Es handelt sich um eine umfassende Darstellung der Theorie der elliptischen Funktionen, die zu dieser Zeit ein wichtiger...

Verhandeling: Over De Primitieve Wortels Van Alle Getallen, En Hunne Toepassing Op De Decimale Breuken (1855) geschreven door Hennekeler, G. Van is een boek dat zich richt op de primitieve wortels van alle getallen en hun toepassing op decimale breuken...

This book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem. It covers many of the familiar topics of elementary number theory, all with an algorithmic...

The first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnotes give an historical background to the text, in...

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...

Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra...

With plenty of new material not found in other books, Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying...

고대 수학자들은 난제에 직면했습니다. 2의 제곱근에 어떤 숫자를 사용해야 할까요? 고대 바빌로니아인들은 분수 305470/216000을 사용했습니다. 이는 소수점 여섯 자리까지 정확했습니다. 고대 인도인들은 분수 577/408을 사용했습니다. 이 분수는 소수점 다섯 자리까지 정확했습니다. 오늘날 수학자들은 2의 제곱근이 무리수이며, 그 숫자는 반복되지 않고 영원히 이어진다는 것을 알고 있습니다. 무한 계열을 사용하여 계산됩니다. 이 책에서는 2의...

소수는 1보다 크고 자신과 1만 인수로 갖는 정수입니다. 예를 들어, 5는 2, 3 또는 4를 인수로 갖지 않으므로 소수입니다. 5의 유일한 인수는 1과 5입니다. 소수는 고대부터 연구되어 왔습니다. 키레네의 에라토스테네스는 기원전 276년에서 기원전 194년 사이에 살았습니다. 그는 오늘날에도 여전히 가르쳐지고 있는 소수를 찾는 방법을 개발했습니다. 이를 에라토스테네스의 체라고 합니다. 소수는 오늘날에도 수학자들을 매료시키고 있습니다. 소수는 수론과...

Through a set of related yet distinct texts, the author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions: Ideal- and valuation-theoretic aspects, L functions and class field theory, with a presentation...

The Fundamental Principle of Digits of a Number is a new mathematical idea for which the author received a copyright from the United States Library of Congress. Two related concepts make it easy to understand and apply the principle. The first...

This book explains how to analyze statistical models with hidden (latent) variables. It takes a systematic, geometric approach to studying the semialgebraic structure of latent tree models. The first part of the book introduces key concepts in algebraic...

Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good...

This comprehensive study traces the historic development of division in extreme and mean ratio (""the golden number"") from its first appearance in Euclid's Elements through the 18th century. Features numerous illustrations.

Die Kryptologie, eine jahrtausendealte "Geheimwissenschaft", gewinnt für den Informatiker zusehends praktische Bedeutung in Verbindung mit Datenbanken und Telekommunikation. Neben ihre Nutzung in rechnergestützten öffentlichen...

I. Integer Points.- §1. Statement of the Problem, Auxiliary Remarks, and the Simplest Results.- §2. The Connection Between Problems in the Theory of Integer Points and Trigonometric Sums.- §3. Theorems on Trigonometric Sums.- §4. Integer Points in a...

1. The Circle Method and Waring's Problem.- 1.1 Introduction.- 1.2 Farey Division.- 1.3 Auxiliary Lemmas.- 1.4 Major Arcs.- 1.5 Singular Integral.- 1.6 Singular Series.- 1.7 Proof of Lemma 1.12.- 1.8 Proof of Theorem 1.1.- Notes.- 2. Complete Exponential...

For many years, Serge Lang has given talks on selected items in mathematics which could be extracted at a level understandable by those who have had calculus. Written in a conversational tone, Lang now presents a collection of...

The Rogers--Ramanujan identities are a pair of infinite series-infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory,...