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: 2291


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: 2325

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: 1445

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: 4244

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.

Introduction to Number Theory

Author: Anthony Vazzana,David Garth

Publisher: CRC Press

ISBN: 1498717500

Category: Mathematics

Page: 414

View: 6828

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.

Elementary Methods in Number Theory

Author: Melvyn B. Nathanson,Springer-Verlag

Publisher: Springer Science & Business Media

ISBN: 9780387989129

Category: Mathematics

Page: 513

View: 4956

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.

Topics in Number Theory

Author: William Judson LeVeque

Publisher: Courier Corporation

ISBN: 9780486425399

Category: Mathematics

Page: 496

View: 8680

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.


Author: John C. Slater,Nathaniel H. Frank

Publisher: Courier Corporation

ISBN: 0486150402

Category: Science

Page: 256

View: 3212

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.

The Theory of Groups

Author: Aleksandr Gennadievich Kurosh

Publisher: American Mathematical Soc.

ISBN: 0821834770

Category: Mathematics

Page: 308

View: 1838

This book is translated from the second Russian edition and with added notes by K.A. Hirsch. ""Teoriya Grupp"" by Kurosh was widely acclaimed, in its first edition, as the first modern text on the general theory of groups, with the major emphasis on infinite groups. The decade that followed brought about a remarkable growth and maturity in the theory of groups, so that this second edition, in English translation, represents a complete rewriting of the first edition.The book can be used as a beginning text, the only requirement being some mathematical maturity and a knowledge of the elements of transfinite numbers. Many new sections were added to this second edition, and many old ones were completely revised: the theory of abelian groups was significantly revised; many significant additions were made to the section on the theory of free groups and free products; an entire chapter is devoted to group extensions; and the deep changes in the theory of solvable and nilpotent groups - one of the large and rich branches of the theory of groups - are covered in this work. Each volume concludes with Editor's Notes and a Bibliography.

Introducing Translation Studies

Theories and Applications

Author: Jeremy Munday

Publisher: Routledge

ISBN: 1135198195

Category: Language Arts & Disciplines

Page: 256

View: 7426

This textbook provides an accessible overview of the key contributions to translation theory. Each chapter explores a new theory and approaches are tested by applying them to texts from a range of languages, with English translations provided.

An Introduction to Linear Algebra

Author: L. Mirsky

Publisher: Courier Corporation

ISBN: 0486166449

Category: Mathematics

Page: 464

View: 6107

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: 2495

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.

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: 8055

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

Key Terms in Systemic Functional Linguistics

Author: Christian Matthiessen,Marvin Lam,Kazuhiro Teruya

Publisher: Bloomsbury Publishing

ISBN: 144116829X

Category: Language Arts & Disciplines

Page: 320

View: 1642

The field of Systemic Functional Linguistics is a social semiotic approach to language pioneered by M. A. K. Halliday, which has assumed a central importance in linguistics in recent years, anchored by a growing body of work. This book details the key terms, the key thinkers and the key texts in this field in an approachable, easy to understand and accessible manner. It is authored by leading names in the field and is aimed at undergraduates and postgraduates studying linguistics and language studies.

Number Theory for Computing

Author: Song Y. Yan

Publisher: Springer Science & Business Media

ISBN: 9783540430728

Category: Computers

Page: 435

View: 2855

This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.

Workbook in Introductory Economics

Author: Colin Harbury

Publisher: Elsevier

ISBN: 1483138712

Category: Business & Economics

Page: 172

View: 9163

Workbook in Introductory Economics, Third Edition, is designed to help readers learn and use economics, to aid in testing their level of understanding, and to improve their skills in answering multiple-choice and data-response questions. This workbook, unlike many others, is not written to ""accompany"" a particular text, but to be suitable for use with the standard ones on the market. The book begins with discussion of the subject of economics. This is followed by separate chapters on concepts such as supply and demand; production and distribution; national income; money, banking, and prices; international trade; and economic policy. Each chapter is divided into four main sections—textual summaries of the ground covered, questions and problems in economic analysis, questions and exercises on the U.K. economy, and essays. The book also includes a Reading Guide, which lists the major British standard general textbooks at an introductory level as well as one or two of the best-known American and a small number in special fields.

A Comprehensive Course in Number Theory

Author: Alan Baker

Publisher: Cambridge University Press

ISBN: 1139560824

Category: Mathematics

Page: N.A

View: 4727

Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.

From Frege to Gödel

a source book in mathematical logic, 1879-1932

Author: Jean Van Heijenoort

Publisher: Harvard University Press

ISBN: 9780674324497


Page: 664

View: 4409


Linear Integral Equations

Author: Rainer Kress

Publisher: Springer Science & Business Media

ISBN: 1461495938

Category: Mathematics

Page: 412

View: 490

This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)