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: 9741


Elementary Theory of Numbers

Author: William J. LeVeque

Publisher: Courier Corporation

ISBN: 0486150763

Category: Mathematics

Page: 160

View: 4797

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.

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: 4424

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.

Number Theory

Structures, Examples, and Problems

Author: Titu Andreescu,Dorin Andrica

Publisher: Springer Science & Business Media

ISBN: 9780817646455

Category: Mathematics

Page: 384

View: 787

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.

Number Theory

An Introduction to Mathematics

Author: W.A. Coppel

Publisher: Springer Science & Business Media

ISBN: 0387894853

Category: Mathematics

Page: 610

View: 9154

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.

The Theory of Algebraic Numbers

Author: Harry Pollard,Harold G. Diamond

Publisher: Courier Corporation

ISBN: 9780486404547

Category: Mathematics

Page: 162

View: 4300

Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; Fermat conjecture. 1975 edition.

Abstract analytic number theory

Author: Knopfmacher

Publisher: Newnes

ISBN: 0444107797

Category: Computers

Page: 321

View: 591

North-Holland Mathematical Library, Volume 12: Abstract Analytic Number Theory focuses on the approaches, methodologies, and principles of the abstract analytic number theory. The publication first deals with arithmetical semigroups, arithmetical functions, and enumeration problems. Discussions focus on special functions and additive arithmetical semigroups, enumeration and zeta functions in special cases, infinite sums and products, double series and products, integral domains and arithmetical semigroups, and categories satisfying theorems of the Krull-Schmidt type. The text then ponders on semigroups satisfying Axiom A, asymptotic enumeration and "statistical" properties of arithmetical functions, and abstract prime number theorem. Topics include asymptotic properties of prime-divisor functions, maximum and minimum orders of magnitude of certain functions, asymptotic enumeration in certain categories, distribution functions of prime-independent functions, and approximate average values of special arithmetical functions. The manuscript takes a look at arithmetical formations, additive arithmetical semigroups, and Fourier analysis of arithmetical functions, including Fourier theory of almost even functions, additive abstract prime number theorem, asymptotic average values and densities, and average values of arithmetical functions over a class. The book is a vital reference for researchers interested in the abstract analytic number theory.

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: 6406

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.

Analytic Number Theory

Author: Donald J. Newman

Publisher: Springer Science & Business Media

ISBN: 0387983082

Category: Mathematics

Page: 76

View: 4027

This is a concise introduction to analytic number theory. The author includes plenty of clever and interesting examples. He covers an amazing amount of material in just a few pages, despite his leisurely pace and emphasis on readability. The book is suitable for a graduate course in analytic number theory.

A Source Book in Mathematics

Author: David Eugene Smith

Publisher: Courier Corporation

ISBN: 0486158292

Category: Mathematics

Page: 736

View: 8883

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.

Elementary Methods in Number Theory

Author: Melvyn B. Nathanson

Publisher: Springer Science & Business Media

ISBN: 9780387989129

Category: Mathematics

Page: 513

View: 9642

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.

Lectures on the Theory of Algebraic Numbers

Author: E. T. Hecke

Publisher: Springer Science & Business Media

ISBN: 1475740921

Category: Mathematics

Page: 242

View: 1645

. . . 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.

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: 6155

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.


Author: John C. Slater,Nathaniel H. Frank

Publisher: Courier Corporation

ISBN: 0486150402

Category: Science

Page: 256

View: 2146

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.

Elementary Matrix Theory

Author: Howard Whitley Eves

Publisher: Courier Corporation

ISBN: 9780486639468

Category: Mathematics

Page: 325

View: 389

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

An Introduction to Linear Algebra

Author: L. Mirsky

Publisher: Courier Corporation

ISBN: 0486166449

Category: Mathematics

Page: 464

View: 7716

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.

A Select Bibliography of Modern Economic Theory 1870-1929

Author: Harold E. Batson

Publisher: Routledge

ISBN: 1136507035

Category: Business & Economics

Page: 240

View: 9067

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.

Elementary Number Theory and Its Applications

Author: Kenneth H. Rosen

Publisher: Addison Wesley


Category: Nombres, Théorie des

Page: 638

View: 8441

The fourth edition of Kenneth Rosen's widely used and successful text, Elementary Number Theory and Its Applications, preserves the strengths of the previous editions, while enhancing the book's flexibility and depth of content coverage.The blending of classical theory with modern applications is a hallmark feature of the text. The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

Music in the World of Islam

A Socio-Cultural Study

Author: Amnon Shiloah

Publisher: Wayne State University Press

ISBN: 9780814329702

Category: Literary Criticism

Page: 272

View: 8752

Provides basic musicological information about a vast variety of Middle Eastern musical genres within an ethnomusical context.