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The Theory of Numbers

The Theory of Numbers Author Andrew Adler
ISBN-10 0867204729
Release 1995
Pages 401
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The Theory of Numbers has been writing in one form or another for most of life. You can find so many inspiration from The Theory of Numbers also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Theory of Numbers book for free.

1001 Problems in Classical Number Theory

1001 Problems in Classical Number Theory Author Armel Mercier
ISBN-10 0821886185
Pages 336
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1001 Problems in Classical Number Theory has been writing in one form or another for most of life. You can find so many inspiration from 1001 Problems in Classical Number Theory also informative, and entertaining. Click DOWNLOAD or Read Online button to get full 1001 Problems in Classical Number Theory book for free.

Recreations in the Theory of Numbers

Recreations in the Theory of Numbers Author Albert H. Beiler
ISBN-10 9780486210964
Release 1964
Pages 349
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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

Elementary Theory of Numbers Author William J. LeVeque
ISBN-10 9780486150765
Release 2014-01-15
Pages 160
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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.

Problem Solving and Selected Topics in Number Theory

Problem Solving and Selected Topics in Number Theory Author Michael Th. Rassias
ISBN-10 9781441904959
Release 2010-11-16
Pages 324
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The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

Elementary Number Theory Primes Congruences and Secrets

Elementary Number Theory  Primes  Congruences  and Secrets Author William Stein
ISBN-10 9780387855257
Release 2008-10-28
Pages 168
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This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.

Number Theory

Number Theory Author Titu Andreescu
ISBN-10 0817646450
Release 2009-06-12
Pages 384
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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.

Ergodic Theory

Ergodic Theory Author Manfred Einsiedler
ISBN-10 0857290215
Release 2010-09-11
Pages 481
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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.

Discrete Mathematics and Its Applications

Discrete Mathematics and Its Applications Author Kenneth Rosen
ISBN-10 9780077418939
Release 1995
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Discrete Mathematics and Its Applications has been writing in one form or another for most of life. You can find so many inspiration from Discrete Mathematics and Its Applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Discrete Mathematics and Its Applications book for free.

Elements of Algebra

Elements of Algebra Author John Stillwell
ISBN-10 9781475739763
Release 2013-04-18
Pages 184
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Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.

Number Theory

Number Theory Author André Weil
ISBN-10 9780817645717
Release 2009-05-21
Pages 377
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This book presents a historical overview of number theory. It examines texts that span some thirty-six centuries of arithmetical work, from an Old Babylonian tablet to Legendre’s Essai sur la Théorie des Nombres, written in 1798. Coverage employs a historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. The book also takes the reader into the workshops of four major authors of modern number theory: Fermat, Euler, Lagrange and Legendre and presents a detailed and critical examination of their work.

Introduction to the Theory of Numbers

Introduction to the Theory of Numbers Author Harold N. Shapiro
ISBN-10 9780486466699
Release 1983
Pages 459
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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.

The Knot Book

The Knot Book Author Colin Conrad Adams
ISBN-10 9780821836781
Release 2004
Pages 306
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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.

Probability Theory

Probability Theory Author Y. A. Rozanov
ISBN-10 9780486321141
Release 2013-05-27
Pages 148
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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.

A Problem Book in Real Analysis

A Problem Book in Real Analysis Author Asuman G. Aksoy
ISBN-10 9781441912961
Release 2010-03-10
Pages 254
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Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.


ISBN-10 8126518111
Release 2008-08-01
Pages 545
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· 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

Discrete Mathematics

Discrete Mathematics Author László Lovász
ISBN-10 9780387217772
Release 2006-05-11
Pages 284
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Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.