Number Theory

e-books in this category

A Computational Introduction to Number Theory and Algebra
by Victor Shoup - Cambridge University Press , 2005
This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes. It is accessible to a broad audience. Prerequisites are a typical undergraduate course in calculus and some experience in doing proofs.
(12728 views)

A Course In Algebraic Number Theory
by Robert B. Ash - University of Illinois , 2003
Basic course in algebraic number theory. It covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer’s theorem, the factorization of prime ideals in Galois extensions, local and global fields, etc.
(5398 views)

A set of new Smarandache functions, sequences and conjectures in number theory
by Felice Russo - American Research Press , 2000
The fascinating Smarandache's universe is halfway between the recreational mathematics and the number theory. This book presents new Smarandache functions, conjectures, solved and unsolved problems, new type sequences and new notions in number theory.
(2213 views)

Algebraic Number Theory
by J.S. Milne , 2008
Contents: Preliminaries From Commutative Algebra; Rings of Integers; Dedekind Domains; Factorization; The Finiteness of the Class Number; The Unit Theorem; Cyclotomic Extensions; Fermat's Last Theorem; Valuations; Local Fields; Global Fields.
(2689 views)

Algorithmic Number Theory
by J.P. Buhler, P. Stevenhagen - Cambridge University Press , 2008
This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students. It covers the fundamental algorithms of elementary number theory, lattice basis reduction, elliptic curves, algebraic number fields, etc.
(6545 views)

Algorithms for Modular Elliptic Curves
by J. E. Cremona - Cambridge University Press , 1992
The author describes the construction of modular elliptic curves giving an algorithm for their computation. Then algorithms for the arithmetic of elliptic curves are presented. Finally, the results of the implementations of the algorithms are given.
(3709 views)

An Introduction to the Smarandache Function
by Charles Ashbacher - Erhus Univ Pr , 1995
In the 1970's a Rumanian mathematician Florentin Smarandache created a new function in number theory, which consequences encompass many areas of mathematics.The purpose of this text is to examine some of those consequences.
(2017 views)

An Introduction to the Theory of Numbers
by Leo Moser - The Trillia Group , 2007
The book on elementary number theory: compositions and partitions, arithmetic functions, distribution of primes, irrational numbers, congruences, Diophantine equations; combinatorial number theory, and geometry of numbers.
(3822 views)

Arithmetic Duality Theorems
by J.S. Milne - BookSurge Publishing , 2006
This book, intended for research mathematicians, proves the duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry, for example, in the proof of Fermat's Last Theorem.
(2116 views)

Circulants
by Alun Wyn-jones , 2008
The goal of this book is to describe circulants in an algebraic context. It oscillates between the point of view of circulants as a commutative algebra, and the concrete point of view of circulants as matrices with emphasis on their determinants.
(2878 views)

Collections of Problems on Smarandache Notions
by Charles Ashbacher - Erhus University Press , 1996
This text deals with some advanced consequences of the Smarandache function. The reading of this book is a form of mindjoining, where the author tries to create the opportunity for a shared experience of an adventure.
(1860 views)

Comments and topics on Smarandache notions and problems
by Kenichiro Kashihara - Erhus University Press , 1996
An examination of some of the problems posed by Florentin Smarandache. The problems are from different areas, such as sequences, primes and other aspects of number theory. The problems are solved in the book, or the author raises new questions.
(1871 views)

Complex Multiplication
by J. S. Milne , 2006
These are preliminary notes for a modern account of the theory of complex multiplication. The reader is expected to have a good knowledge of basic algebraic number theory, and basic algebraic geometry, including abelian varieties.
(101 views)

Computer analysis of number sequences
by Henry Ibstedt - American Research Press , 1998
This is a book on empirical number theory concentrating on the analysis of number sequences. Its focus is on a small part of integer sequences defined by Florentin Smarandache. The author has also included some other results of his research.
(2406 views)

Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry
by Florentin Smarandache - Amer Research Pr , 2000
A collection of definitions, questions, and theorems such as Smarandache type conjectures, problems, numerical bases, T-numbers, progressions, series, functions, Non-Euclidean geometries, paradoxes, linguistic tautologies, and more.
(3881 views)

Diophantine Analysis
by R. D. Carmichael - John Wiley & Sons , 1915
The author's purpose has been to supply the reader with a convenient introduction to Diophantine Analysis. No attempt has been made to include all special results, but a large number of them are to be found both in the text and in the exercises.
(141 views)

Distribution of Prime Numbers
by W W L Chen - Macquarie University , 2003
These notes were used by the author at Imperial College, University of London. The contents: arithmetic functions, elementary prime number theory, Dirichlet series, primes in arithmetic progressions, prime number theorem, Riemann zeta function.
(2247 views)

Elementary Number Theory
by William Stein - Springer , 2004
Textbook on number theory and elliptic curves. It discusses primes, factorization, continued fractions, quadratic forms, computation, elliptic curves, their applications to algorithmic problems, and connections with problems in number theory.
(3005 views)

Elementary Number Theory
by William Edwin Clark - University of South Florida , 2002
One might think that of all areas of mathematics arithmetic should be the simplest, but it is a surprisingly deep subject. It is assumed that students have some familiarity with set theory, calculus, and a certain amount of mathematical maturity.
(2669 views)

Elementary Number Theory
by W W L Chen - Macquarie University , 2003
An introduction to the elementary techniques of number theory: division and factorization, arithmetic functions, congruences, quadratic residues, sums of integer squares, elementary prime number theory, Gauss sums and quadratic reciprocity.
(2174 views)

Elementary Theory of Numbers
by Waclaw Sierpinski - ICM , 1964
The variety of topics covered here includes divisibility, diophantine equations, prime numbers, the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, and more.
(2139 views)

Elliptic Curves
by J. S. Milne - BookSurge Publishing , 2006
This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in undergraduate courses.
(2459 views)

Essays on the Theory of Numbers
by Richard Dedekind - The Open Court Publishing , 1901
This is a book combining two essays: "Continuity and irrational numbers" - Dedekind's way of defining the real numbers from rational numbers; and "The nature and meaning of numbers" where Dedekind offers a precise explication of the natural numbers.
(189 views)

Geometric Theorems and Arithmetic Functions
by Jozsef Sandor - American Research Press , 2002
Contents: on Smarandache's Podaire theorem, Diophantine equation, the least common multiple of the first positive integers, limits related to prime numbers, a generalized bisector theorem, values of arithmetical functions and factorials, and more.
(3551 views)

Modular Forms: A Computational Approach
by William A. Stein - American Mathematical Society , 2007
This book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments.
(419 views)

On Some of Smarandache's Problems
by Krassimir Atanassov - Erhus Univ Pr , 1999
A collection of 27 Smarandache's problems which the autor solved by 1999. 22 problems are related to different sequences, 4 problems are proved, modifications of two problems are formulated, and counterexamples to two of the problems are constructed.
(1801 views)

Pluckings from the tree of Smarandache: Sequences and functions
by Charles Ashbacher - American Research Press , 1998
The third book in a series exploring the set of problems called Smarandache Notions. This work delves more deeply into the mathematics of the problems, the level of difficulty here will be somewhat higher than that of the previous books.
(1784 views)

Predicative Arithmetic
by Edward Nelson - Princeton Univ Pr , 1987
The book based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, and more.
(3260 views)

Surfing on the ocean of numbers
by Henry Ibstedt - Erhus University Press , 1997
The author uses computers to explore the solutions to some problems in number theory. The emphasis is on the statement of a problem and the examination of the solutions for numbers in a selected range. Many of the problems are very hard.
(2218 views)

The Smarandache Function
by C. Dumitrescu, V. Seleacu - Erhus University Press , 1996
The function in the title is originated from the Romanian mathematician Florentin Smarandache, who has significant contributions in mathematics and literature. This text introduces the Smarandache function and discusses its generalisations.
(1882 views)

The Theory of Numbers
by R. D. Carmichael - John Wiley & Sons , 1914
The purpose of this book is to give the reader a convenient introduction to the theory of numbers. The treatment throughout is made as brief as is possible consistent with clearness and is confined entirely to fundamental matters.
(2129 views)