Recreations in the Theory of Numbers

Author: Albert H. Beiler
Publisher: Courier Corporation
ISBN: 9780486210964
Release Date: 1964
Genre: Games

Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems. Includes divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, more. Solutions to all problems.

Elementary Theory of Numbers

Author: William J. LeVeque
Publisher: Courier Corporation
ISBN: 9780486150765
Release Date: 2014-01-15
Genre: Mathematics

Superb introduction to Euclidean algorithm and its consequences, congruences, continued fractions, powers of an integer modulo m, Gaussian integers, Diophantine equations, more. Problems, with answers. Bibliography.

A Course in Number Theory

Author: H. E. Rose
Publisher: Oxford University Press
ISBN: 0198523769
Release Date: 1995
Genre: Mathematics

The second edition of this undergraduate textbook is now available in paperback. Covering up-to-date as well as established material, it is the only textbook which deals with all the main areas of number theory, taught in the third year of a mathematics course. Each chapter ends with a collection of problems, and hints and sketch solutions are provided at the end of the book, together with useful tables.

Number Theory

Author: Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 0817646450
Release Date: 2009-06-12
Genre: Mathematics

This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.

Elementary Number Theory in Nine Chapters

Author: James J. Tattersall
Publisher: Cambridge University Press
ISBN: 0521850142
Release Date: 2005-06-30
Genre: Mathematics

This textbook is intended to serve as a one-semester introductory course in number theory and in this second edition it has been revised throughout and many new exercises have been added. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.

Ergodic Theory

Author: Manfred Einsiedler
Publisher: Springer Science & Business Media
ISBN: 0857290215
Release Date: 2010-09-11
Genre: Mathematics

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

Probability Theory

Author: Y. A. Rozanov
Publisher: Courier Corporation
ISBN: 9780486321141
Release Date: 2013-05-27
Genre: Mathematics

This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, and more. Includes 150 problems, many with answers.

Introduction to Elliptic Curves and Modular Forms

Author: N. Koblitz
Publisher: Springer Science & Business Media
ISBN: 9781468402551
Release Date: 2012-12-06
Genre: Mathematics

This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses, thereby solidifying their under standing of some basic tools used throughout mathematics. Graduate stu dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under graduates could use the book for independent study projects, senior theses, and seminar work.

Elliptic Curves

Author: Lawrence C. Washington
Publisher: CRC Press
ISBN: 1420071475
Release Date: 2008-04-03
Genre: Mathematics

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves. New to the Second Edition Chapters on isogenies and hyperelliptic curves A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues A more complete treatment of the Weil and Tate–Lichtenbaum pairings Doud’s analytic method for computing torsion on elliptic curves over Q An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.

Algebraic Theory of Numbers

Author: Pierre Samuel
ISBN: 0486466663
Release Date: 2008
Genre: Mathematics

Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics — algebraic geometry, in particular. This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Galois theory, Noetherian rings and modules, and rings of fractions. It covers the basics, starting with the divisibility theory in principal ideal domains and ending with the unit theorem, finiteness of the class number, and the more elementary theorems of Hilbert ramification theory. Numerous examples, applications, and exercises appear throughout the text.


Author: Ivan Niven
Publisher: John Wiley & Sons
ISBN: 8126518111
Release Date: 2008-08-01
Genre: Number theory

· Divisibility· Congruences· Quadratic Reciprocity and Quadratic Forms· Some Functions of Number Theory· Some Diophantine Equations· Farey Fractions and Irrational Numbers· Simple Continued Fractions· Primes and Multiplicative Number Theory· Algebraic Numbers· The Partition Function · The Density of Sequences of Integers

Unsolved Problems in Number Theory

Author: Richard Guy
Publisher: Springer Science & Business Media
ISBN: 9781489935854
Release Date: 2013-11-11
Genre: Mathematics

Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.

The Knot Book

Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
ISBN: 9780821836781
Release Date: 2004
Genre: Mathematics

Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. The Knot Book is an introduction to this rich theory, starting from our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research. The Knot Book is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics. This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in The Knot Book.