Number theory Books

An engaging treatment of an 800-year-old problem explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. Its entertaining style will appeal to recreational readers and students alike.

A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for...

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...

A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a...

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no...

Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a...

Peter Higgins distills centuries of work into one delightful narrative that celebrates the mystery of numbers and explains how different kinds of numbers arose and why they are useful. Full of historical snippets and interesting examples, the book ranges...

Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of...

Discovered at the turn of the 20th century, p-adic numbers are frequently used by mathematicians and physicists. This text is a self-contained presentation of basic p-adic analysis with a focus on analytic topics. It offers...

Problems.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.-...

Getting to the Root of the Mystery; 2 Irrationality and its Consequences; 3 The Power of a Little Algebra; 4 Witchcraft; 5 Odds and Ends

Algebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of an Elliptic Curve.- Elliptic Curves over Finite Fields.- Elliptic Curves over C.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields.-...

Problems.- Elementary Number Theory.- Euclidean Rings.- Algebraic Numbers and Integers.- Integral Bases.- Dedekind Domains.- The Ideal Class Group.- Quadratic Reciprocity.- The Structure of Units.- Higher Reciprocity Laws.- Analytic Methods.- Density...

Introduction ������ l'�����tude de la th�����orie des nombres et de l'alg�����bre sup�����rieure est un livre �����crit par Emile Borel et publi����� en 1895. Il s'agit d'un ouvrage de r�����f�����rence en math�����matiques qui aborde les concepts...

""Einleitung In Die Theorie Der Elliptischen Funktionen"" ist ein Buch von Karl Bobek, das erstmals im Jahr 1884 ver������ffentlicht wurde. Das Buch ist eine Einf�����hrung in die Theorie der elliptischen Funktionen und richtet sich an Studenten und...

""Einleitung in die Theorie der bin�����ren Formen"" ist ein Buch von Francesco Faa di Bruno, das im Jahr 1881 ver������ffentlicht wurde. Das Buch besch�����ftigt sich mit der Theorie der bin�����ren Formen, die sich mit der algebraischen Struktur von...

Die Elemente der Arithmetik als Vorbereitung auf die Funktionentheorie ist ein Buch von Max Simon, das im Jahr 1884 ver������ffentlicht wurde. Das Buch behandelt die Grundlagen der Arithmetik und deren Anwendung in der Funktionentheorie. Es ist ein...

Introduction to Math Olympiad Problems aims to introduce high school students to all the necessary topics that frequently emerge in international Math Olympiad competitions. In addition to introducing the topics, the book will also provide several...

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquim series established to honor Professors A. J. Coleman and H. W. Ellis and to acknow­ ledge their long lasting...

Total Domination in Graphs gives a clear understanding of this topic to any interested reader who has a modest background in graph theory. This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured...

Introduction.-1. Notable Elements.-2. Numerical Semigroups with Maximal Embedding Dimension.-3. Irreducible Numerical Semigropus.-4. Proportionally Modular Numerical Semigroups.-5. The Quotient of a Numerical Semigroup by a Positive Integer.-6. Families...

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.Throughout Geometry, Complex Dimensions and Zeta Functions, Second...

This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior...

The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to...

"THE RULE OF NINE" IS A FASCINATING BOOK BY IYESIS MITCHELL-TIBERE THAT DELVES INTO THE MYSTICAL AND MATHEMATICAL SIGNIFICANCE OF THE NUMBER NINE. THE BOOK ARGUES THAT THE CREATOR'S SIGNATURE IS HIDDEN IN DIVINE MULTIPLICATION THROUGH THE RULE OF NINE,...

* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation* Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty* A special feature is a selection of...

Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects...

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some...

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 in mathematical research in number...

This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve...

Das Buch ""Das Pythagor�����ische Dreieck und die ungerade Zahl"" von Karl Thomas, ver������ffentlicht im Jahr 1859, besch�����ftigt sich mit der mathematischen Beziehung zwischen dem Pythagor�����ischen Dreieck und ungeraden Zahlen. Der Autor untersucht...

Das Buch ""Das Fortschreitungsgesetz Der Primzahlen: Durch Eine Transcendente Gleichung Exakt Dargestellt"" wurde im Jahr 1899 von Julius Von Braun ver������ffentlicht. Es besch�����ftigt sich mit der Mathematik der Primzahlen und stellt eine...

Este libro es una guía completa y accesible para entender los diferentes sistemas de numeración y la teoría de los números primos. Mateo Tuñón y Lara, quien fue un destacado matemático y profesor español del siglo XIX, ofrece lecciones claras y precisas...

WORK IS IN FRENCHThis book is a reproduction of a work published before 1920 and is part of a collection of books reprinted and edited by Hachette Livre, in the framework of a partnership with the National Library of France, providing the opportunity to...

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are...