The Theory of Numbers

A Text and Source Book of Problems

Author: Andrew Adler,John E. Coury

Publisher: Jones & Bartlett Pub

ISBN: 9780867204728

Category: Mathematics

Page: 401

View: 9789

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Elementary Theory of Numbers

Author: William J. LeVeque

Publisher: Courier Corporation

ISBN: 0486150763

Category: Mathematics

Page: 160

View: 1911

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.
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Recreations in the Theory of Numbers

The Queen of Mathematics Entertains

Author: Albert H. Beiler

Publisher: Courier Corporation

ISBN: 0486210960

Category: Games

Page: 349

View: 1737

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.
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Number Theory

An Introduction to Mathematics

Author: W.A. Coppel

Publisher: Springer Science & Business Media

ISBN: 0387894853

Category: Mathematics

Page: 610

View: 4227

Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.
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Introduction to Number Theory, 2nd Edition

Author: Anthony Vazzana,David Garth

Publisher: CRC Press

ISBN: 1498717500

Category: Mathematics

Page: 414

View: 9448

Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbert’s tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Euler’s theorem in RSA encryption, and quadratic residues in the construction of tournaments. Ideal for a one- or two-semester undergraduate-level course, this Second Edition: Features a more flexible structure that offers a greater range of options for course design Adds new sections on the representations of integers and the Chinese remainder theorem Expands exercise sets to encompass a wider variety of problems, many of which relate number theory to fields outside of mathematics (e.g., music) Provides calculations for computational experimentation using SageMath, a free open-source mathematics software system, as well as Mathematica® and MapleTM, online via a robust, author-maintained website Includes a solutions manual with qualifying course adoption By tackling both fundamental and advanced subjects—and using worked examples, numerous exercises, and popular software packages to ensure a practical understanding—Introduction to Number Theory, Second Edition instills a solid foundation of number theory knowledge.
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Number Theory

Structures, Examples, and Problems

Author: Titu Andreescu,Dorin Andrica

Publisher: Springer Science & Business Media

ISBN: 9780817646455

Category: Mathematics

Page: 384

View: 2489

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.
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Topics in Number Theory

Author: William Judson LeVeque

Publisher: Courier Corporation

ISBN: 9780486425399

Category: Mathematics

Page: 496

View: 6009

Classic two-part work now available in a single volume assumes no prior theoretical knowledge on reader's part and develops the subject fully. Volume I is a suitable first course text for advanced undergraduate and beginning graduate students. Volume II requires a much higher level of mathematical maturity, including a working knowledge of the theory of analytic functions. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes numerous problems and hints for their solutions. 1956 edition. Supplementary Reading. List of Symbols. Index.
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The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae

Author: Catherine Goldstein,Norbert Schappacher,Joachim Schwermer

Publisher: Springer Science & Business Media

ISBN: 3540347208

Category: Mathematics

Page: 578

View: 5716

Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.
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Equations and Inequalities

Elementary Problems and Theorems in Algebra and Number Theory

Author: Jiri Herman,Radan Kucera,Jaromir Simsa

Publisher: Springer Science & Business Media

ISBN: 1461212707

Category: Mathematics

Page: 344

View: 9695

A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.
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Numbers and Geometry

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 9780387982892

Category: Mathematics

Page: 343

View: 8700

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 calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He covers the main ideas of Euclid, but with 2000 years of extra insights attached. Presupposing only high school algebra, it can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics due to its attractive and unusual treatment of fundamental topics. A set of well-written exercises at the end of each section allows new ideas to be instantly tested and reinforced.
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Lectures on the Theory of Algebraic Numbers

Author: E. T. Hecke

Publisher: Springer Science & Business Media

ISBN: 1475740921

Category: Mathematics

Page: 242

View: 6992

. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.
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Elementary number theory

Author: David M. Burton

Publisher: WCB/McGraw-Hill

ISBN: N.A

Category: Mathematics

Page: 450

View: 6948

"Elementary Number Theory," Sixth Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton's engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.
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Elementary Matrix Theory

Author: Howard Whitley Eves

Publisher: Courier Corporation

ISBN: 9780486639468

Category: Mathematics

Page: 325

View: 3447

This text for undergraduates "employs a concrete elementary approach, avoiding abstraction until the final chapter."--Back cover.
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Elementary Methods in Number Theory

Author: Melvyn B. Nathanson,Springer-Verlag

Publisher: Springer Science & Business Media

ISBN: 9780387989129

Category: Mathematics

Page: 513

View: 336

Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods. Part II is about multiplicative number theory, and includes two of the most famous results in mathematics: the Erdös-Selberg elementary proof of the prime number theorem, and Dirichlets theorem on primes in arithmetic progressions. Part III is an introduction to three classical topics in additive number theory: Warings problems for polynomials, Liouvilles method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions. Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of the two other graduate texts: Additive Number Theory: The Classical Bases and Additive Number Theory: Inverse Problems and the Geometry of Sumsets.
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Electromagnetism

Author: John C. Slater,Nathaniel H. Frank

Publisher: Courier Corporation

ISBN: 0486150402

Category: Science

Page: 256

View: 4860

A basic introduction to electromagnetism, supplying the fundamentals of electrostatics and magnetostatics, in addition to a thorough investigation of electromagnetic theory. Numerous problems and references. Calculus and differential equations required. 1947 edition.
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A Course in Number Theory and Cryptography

Author: Neal Koblitz

Publisher: Springer Science & Business Media

ISBN: 9780387942933

Category: Mathematics

Page: 235

View: 4455

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 background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.
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An Introduction to Linear Algebra

Author: L. Mirsky

Publisher: Courier Corporation

ISBN: 0486166449

Category: Mathematics

Page: 464

View: 310

Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.
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A Select Bibliography of Modern Economic Theory 1870-1929

Author: Harold E. Batson

Publisher: Routledge

ISBN: 1136507035

Category: Business & Economics

Page: 240

View: 1940

A bibliography of this kind has long been needed. The book is clearly and accurately printed and well arranged." Times Literary Supplement. The scope of the bibliography is economic theory between 1870-1929, the heyday of the neo-classical revolution. The first part of the work is a series of select bibliographies of the different branches of theory. The second part covers a series of bibliographies of the works of key authors. * Bibliography covers American & English publications and German, French and Italian sources. * Subjects covered include: International Trade, Risk, Supply & Demand, Competition & Monopoly, Taxation and Public Expenditure.
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