A Text and Source Book of Problems

Author: Andrew Adler,John E. Coury

Publisher: Jones & Bartlett Pub

ISBN: 9780867204728

Category: Mathematics

Page: 401

View: 6497

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The Queen of Mathematics Entertains

Author: Albert H. Beiler

Publisher: Courier Corporation

ISBN: 0486210960

Category: Games

Page: 349

View: 4139

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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An Introduction to Mathematics

Author: W.A. Coppel

Publisher: Springer Science & Business Media

ISBN: 0387894853

Category: Mathematics

Page: 610

View: 6707

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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Author: Anthony Vazzana,David Garth

Publisher: CRC Press

ISBN: 1498717500

Category: Mathematics

Page: 414

View: 5495

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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Structures, Examples, and Problems

Author: Titu Andreescu,Dorin Andrica

Publisher: Springer Science & Business Media

ISBN: 9780817646455

Category: Mathematics

Page: 384

View: 4798

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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Author: William Judson LeVeque

Publisher: Courier Corporation

ISBN: 9780486425399

Category: Mathematics

Page: 496

View: 9532

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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Author: Catherine Goldstein,Norbert Schappacher,Joachim Schwermer

Publisher: Springer Science & Business Media

ISBN: 3540347208

Category: Mathematics

Page: 578

View: 5728

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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Elementary Problems and Theorems in Algebra and Number Theory

Author: Jiri Herman,Radan Kučera,Radan Kucera,Jaromír Šimša,Jaromir Simsa

Publisher: Springer Science & Business Media

ISBN: 9780387989426

Category: Mathematics

Page: 344

View: 7830

This translation of a successfeul Czech book includes more than 1000 problems, which can be used to prepare for the International Mathematical Olympiads or the Putnam exam. Each topic contains brief theoretical discussions that are immediately followed by carefully worked out examples of increasing degrees of difficulty, and by exercises which range from routine to rather challenging problems.
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Author: E. T. Hecke

Publisher: Springer Science & Business Media

ISBN: 1475740921

Category: Mathematics

Page: 242

View: 2875

. . . 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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Author: David M. Burton

Publisher: WCB/McGraw-Hill


Category: Mathematics

Page: 450

View: 4761

"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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Author: Howard Whitley Eves

Publisher: Courier Corporation

ISBN: 9780486639468

Category: Mathematics

Page: 325

View: 6992

This text for undergraduates "employs a concrete elementary approach, avoiding abstraction until the final chapter."--Back cover.
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Author: Melvyn B. Nathanson,Springer-Verlag

Publisher: Springer Science & Business Media

ISBN: 9780387989129

Category: Mathematics

Page: 513

View: 4331

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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Author: John C. Slater,Nathaniel H. Frank

Publisher: Courier Corporation

ISBN: 0486150402

Category: Science

Page: 256

View: 3946

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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Author: Neal Koblitz

Publisher: Springer Science & Business Media

ISBN: 9780387942933

Category: Mathematics

Page: 235

View: 8348

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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Author: L. Mirsky

Publisher: Courier Corporation

ISBN: 0486166449

Category: Mathematics

Page: 464

View: 7388

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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Author: Harold E. Batson

Publisher: Routledge

ISBN: 1136507035

Category: Business & Economics

Page: 240

View: 5371

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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A Socio-Cultural Study

Author: Amnon Shiloah

Publisher: Wayne State University Press

ISBN: 9780814329702

Category: Literary Criticism

Page: 272

View: 4113

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

Publisher: John Wiley & Sons

ISBN: 1118031318

Category: Mathematics

Page: 672

View: 7644

The first comprehensive survey of mathematics' most fascinatingnumber sequences Fibonacci and Lucas numbers have intrigued amateur and professionalmathematicians for centuries. This volume represents the firstattempt to compile a definitive history and authoritative analysisof these famous integer sequences, complete with a wealth ofexciting applications, enlightening examples, and fun exercisesthat offer numerous opportunities for exploration andexperimentation. The author has assembled a myriad of fascinating properties of bothFibonacci and Lucas numbers-as developed by a wide range ofsources-and catalogued their applications in a multitude of widelyvaried disciplines such as art, stock market investing,engineering, and neurophysiology. Most of the engaging anddelightful material here is easily accessible to college and evenhigh school students, though advanced material is included tochallenge more sophisticated Fibonacci enthusiasts. A historicalsurvey of the development of Fibonacci and Lucas numbers,biographical sketches of intriguing personalities involved indeveloping the subject, and illustrative examples round out thisthorough and amusing survey. Most chapters conclude with numericand theoretical exercises that do not rely on long and tediousproofs of theorems. Highlights include: * Balanced blend of theory and real-world applications * Excellent reference material for student reports andprojects * User-friendly, informal, and entertaining writing style * Historical interjections and short biographies that add a richerperspective to the topic * Reference sections providing important symbols, problemsolutions, and fundamental properties from the theory of numbersand matrices Fibonacci and Lucas Numbers with Applications providesmathematicians with a wealth of reference material in oneconvenient volume and presents an in-depth and entertainingresource for enthusiasts at every level and from any background.
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Author: David Hilbert,Bernd Sturmfels

Publisher: Cambridge University Press

ISBN: 9780521449038

Category: Mathematics

Page: 191

View: 6103

In the summer of 1897, David Hilbert (1862-1943) gave an introductory course in Invariant Theory at the University of Gottingen. This book is an English translation of the handwritten notes taken from this course by Hilbert's student Sophus Marxen. At that time his research in the subject had been completed, and his famous finiteness theorem had been proved and published in two papers that changed the course of invariant theory dramatically and that laid the foundation for modern commutative algebra. Thus, these lectures take into account both the old approach of his predecessors and his new ideas. This bridge from nineteenth to twentieth century mathematics makes these lecture notes a special and fascinating account of invariant theory. Hilbert's course was given at a level accessible to graduate students in mathematics, requiring only a familiarity with linear algebra and the basics of ring and group theory. The text will be useful as a self-contained introduction to invariant theory. But it will also be invaluable as a historical source for anyone interested in the foundations of twentieth-century mathematics.
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