Topics In The Theory Of Numbers

Author : Emil Grosswald
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 47,5 Mb
Release : 2010-02-23
Category : Mathematics
ISBN : 9780817648381

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Topics from the Theory of Numbers by Emil Grosswald Pdf

Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate.

Author : Janos Suranyi,Paul Erdös
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 42,5 Mb
Release : 2003-01-14
Category : Mathematics
ISBN : 0387953205

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Topics in the Theory of Numbers by Janos Suranyi,Paul Erdös Pdf

Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.

Author : Martin H. Weissman
Publisher : American Mathematical Soc.
Page : 341 pages
File Size : 41,8 Mb
Release : 2020-09-15
Category : Education
ISBN : 9781470463717

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An Illustrated Theory of Numbers by Martin H. Weissman Pdf

News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.

Author : Leo Moser
Publisher : The Trillia Group
Page : 95 pages
File Size : 49,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9781931705011

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An Introduction to the Theory of Numbers by Leo Moser Pdf

"This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text."--Publisher's description

Author : Anonim
Publisher : Unknown
Page : 435 pages
File Size : 42,5 Mb
Release : 2007
Category : Number theory
ISBN : 7115156115

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数论导引 by Anonim Pdf

本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。

Author : Joseph B. Dence,Thomas P. Dence
Publisher : Academic Press
Page : 542 pages
File Size : 49,5 Mb
Release : 1999-01-20
Category : Mathematics
ISBN : 0122091302

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Elements of the Theory of Numbers by Joseph B. Dence,Thomas P. Dence Pdf

Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors have created a two-pronged pedagogical approach that integrates analysis and algebra with classical number theory. Making greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses, this pedagogical approach helps to instill in the minds of the students the idea of the unity of mathematics. Elements of the Theory of Numbers is a superb summary of classical material as well as allowing the reader to take a look at the exciting role of analysis and algebra in number theory. * In-depth coverage of classical number theory * Thorough discussion of the theory of groups and rings * Includes application of Taylor polynomials * Contains more advanced material than other texts * Illustrates the results of a theorem with an example * Excellent presentation of the standard computational exercises * Nearly 1000 problems--many are proof-oriented, several others require the writing of computer programs to complete the computations * Clear and well-motivated presentation * Provides historical references noting distinguished number theory luminaries such as Euclid, de Fermat, Hilbert, Brun, and Lehmer, to name a few * Annotated bibliographies appear at the end of all of the chapters

Author : Hugh L. Montgomery
Publisher : Springer
Page : 187 pages
File Size : 48,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540369356

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Topics in Multiplicative Number Theory by Hugh L. Montgomery Pdf

Author : K. C. Chowdhury
Publisher : Unknown
Page : 316 pages
File Size : 53,6 Mb
Release : 2007-07-01
Category : Number theory
ISBN : 8186299653

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A First Course In Theory Of Numbers by K. C. Chowdhury Pdf

Contents: Number System; Congruencies And Its Basic Properties; Algebraic Congruences And Primitive Roots; Arithmetic Functions; Farey Sequence, Continued Fraction, Pell S Equations; Quadratic Residues, Levender S Symbols, Jacobi S Symbols; Homogeneous Quadratic Diophantine Equation; Some Number Theoretic Problems Related To Mathematics Olympiads; Answers; Etc.

Author : Sylvia Forman,Agnes M. Rash
Publisher : Springer
Page : 281 pages
File Size : 46,9 Mb
Release : 2015-01-02
Category : Mathematics
ISBN : 9783319110356

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The Whole Truth About Whole Numbers by Sylvia Forman,Agnes M. Rash Pdf

The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory. The topics covered are many of those included in an introductory Number Theory course for mathematics majors, but the presentation is carefully tailored to meet the needs of elementary education, liberal arts, and other non-mathematical majors. The text covers logic and proofs, as well as major concepts in Number Theory, and contains an abundance of worked examples and exercises to both clearly illustrate concepts and evaluate the students’ mastery of the material.

Author : William J. LeVeque
Publisher : Courier Corporation
Page : 496 pages
File Size : 54,6 Mb
Release : 2012-06-22
Category : Mathematics
ISBN : 9780486152080

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Topics in Number Theory, Volumes I and II by William J. LeVeque Pdf

Classic 2-part work now available in a single volume. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes problems and solutions. 1956 edition.

Author : Oystein Ore
Publisher : Courier Corporation
Page : 400 pages
File Size : 42,6 Mb
Release : 2012-07-06
Category : Mathematics
ISBN : 9780486136431

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Number Theory and Its History by Oystein Ore Pdf

Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

Author : H. E. Rose
Publisher : Oxford University Press
Page : 420 pages
File Size : 40,7 Mb
Release : 1995
Category : Mathematics
ISBN : 0198523769

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A Course in Number Theory by H. E. Rose Pdf

This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.

Author : Valérie Berthé,Michel Rigo
Publisher : Birkhäuser
Page : 578 pages
File Size : 47,9 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783319691527

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Sequences, Groups, and Number Theory by Valérie Berthé,Michel Rigo Pdf

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Author : Carl Friedrich Gauss,William C. Waterhouse
Publisher : Springer
Page : 472 pages
File Size : 41,6 Mb
Release : 2018-02-07
Category : Mathematics
ISBN : 9781493975600

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Disquisitiones Arithmeticae by Carl Friedrich Gauss,William C. Waterhouse Pdf

Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .

Author : Thomas Koshy
Publisher : Elsevier
Page : 801 pages
File Size : 40,8 Mb
Release : 2007-05-08
Category : Mathematics
ISBN : 9780080547091

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Elementary Number Theory with Applications by Thomas Koshy Pdf

This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East