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.

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.

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.

Introduction to the Theory of Numbers

Author: Harold N. Shapiro
Publisher: Courier Corporation
ISBN: 9780486466699
Release Date: 1983
Genre: Mathematics

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 for undergraduate courses. The first five chapters focus on the basic material of number theory, employing special problems, some of which are of historical interest. Succeeding chapters explore evolutions from the notion of congruence, examine a variety of applications related to counting problems, and develop the roots of number theory. Two "do-it-yourself" chapters offer readers the chance to carry out small-scale mathematical investigations that involve material covered in previous chapters.

Set Theory and the Continuum Hypothesis

Author: Paul J. Cohen
Publisher: Courier Corporation
ISBN: 9780486469218
Release Date: 2008-12-09
Genre: Mathematics

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

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.


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

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.

Visual Complex Analysis

Author: Tristan Needham
Publisher: Oxford University Press
ISBN: 0198534469
Release Date: 1998
Genre: Mathematics

Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

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.

A Source Book in Mathematics

Author: David Eugene Smith
Publisher: Courier Corporation
ISBN: 9780486158297
Release Date: 2012-05-07
Genre: Mathematics

The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.

History of the Theory of Numbers

Author: Leonard Eugene Dickson
Publisher: Courier Corporation
ISBN: 9780486154602
Release Date: 2013-10-17
Genre: Mathematics

Written by a distinguished University of Chicago professor, this 2nd volume in the series History of the Theory of Numbers presents material related to Diophantine Analysis. 1919 edition.