Friendly Introduction To Number Theory A Classic Version

Author : Joseph Silverman
Publisher : Unknown
Page : 0 pages
File Size : 48,9 Mb
Release : 2017-02-13
Category : Number theory
ISBN : 0134689461

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Friendly Introduction to Number Theory, a (Classic Version) by Joseph Silverman Pdf

For one-semester undergraduate courses in Elementary Number Theory This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. A Friendly Introduction to Number Theory, 4th Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet-number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.

Author : Joseph H. Silverman
Publisher : Pearson
Page : 472 pages
File Size : 50,5 Mb
Release : 2013-11-01
Category : Electronic
ISBN : 1292027096

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A Friendly Introduction to Number Theory by Joseph H. Silverman Pdf

For one-semester undergraduate courses in Elementary Number Theory. A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet-number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.

Author : K. Ireland,M. Rosen
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 40,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475717792

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A Classical Introduction to Modern Number Theory by K. Ireland,M. Rosen Pdf

This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.

Author : Oystein Ore
Publisher : Courier Corporation
Page : 400 pages
File Size : 55,7 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 : Andrew Granville
Publisher : American Mathematical Society
Page : 587 pages
File Size : 42,8 Mb
Release : 2020-09-23
Category : Mathematics
ISBN : 9781470463700

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Number Theory Revealed: A Masterclass by Andrew Granville Pdf

Number Theory Revealed: A Masterclass acquaints enthusiastic students with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials. About the Author: Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.

Author : Anthony Vazzana,Martin Erickson,David Garth
Publisher : CRC Press
Page : 530 pages
File Size : 48,7 Mb
Release : 2007-10-30
Category : Computers
ISBN : 9781584889380

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Introduction to Number Theory by Anthony Vazzana,Martin Erickson,David Garth Pdf

One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi

Author : Daniel E. Flath
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 44,8 Mb
Release : 2018-09-27
Category : Number theory
ISBN : 9781470446949

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Introduction to Number Theory by Daniel E. Flath Pdf

Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honors-level undergraduates, Flath's Introduction to Number Theory focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with abstract algebra. The text treats a variety of topics from elementary number theory including the distribution of primes, sums of squares, continued factions, the Legendre, Jacobi and Kronecker symbols, the class group and genera. But the focus is on quadratic reciprocity (several proofs are given including one that highlights the p−q symmetry) and binary quadratic forms. The reader will come away with a good understanding of what Gauss intended in the Disquisitiones and Dirichlet in his Vorlesungen. The text also includes a lovely appendix by J. P. Serre titled Δ=b2−4ac. The clarity of the author's vision is matched by the clarity of his exposition. This is a book that reveals the discovery of the quadratic core of algebraic number theory. It should be on the desk of every instructor of introductory number theory as a source of inspiration, motivation, examples, and historical insight.

Author : Victor Shoup
Publisher : Cambridge University Press
Page : 544 pages
File Size : 53,9 Mb
Release : 2005-04-28
Category : Computers
ISBN : 0521851548

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A Computational Introduction to Number Theory and Algebra by Victor Shoup Pdf

This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes.

Author : Richard Friedberg
Publisher : Courier Corporation
Page : 241 pages
File Size : 43,5 Mb
Release : 2012-07-06
Category : Mathematics
ISBN : 9780486152691

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An Adventurer's Guide to Number Theory by Richard Friedberg Pdf

This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.

Author : Martin H. Weissman
Publisher : American Mathematical Soc.
Page : 341 pages
File Size : 52,6 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 : Diane L. Herrmann,Paul J. Sally, Jr.
Publisher : CRC Press
Page : 446 pages
File Size : 48,5 Mb
Release : 2012-10-18
Category : Mathematics
ISBN : 9781466554641

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Number, Shape, & Symmetry by Diane L. Herrmann,Paul J. Sally, Jr. Pdf

Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.

Author : Charles Stanley Ogilvy,John Timothy Anderson
Publisher : Courier Corporation
Page : 196 pages
File Size : 45,8 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 0486257789

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Excursions in Number Theory by Charles Stanley Ogilvy,John Timothy Anderson Pdf

Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.

Author : James Pommersheim,Tim Marks,Erica Flapan
Publisher : Wiley
Page : 0 pages
File Size : 40,8 Mb
Release : 2010-02-15
Category : Mathematics
ISBN : 0470424133

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Number Theory by James Pommersheim,Tim Marks,Erica Flapan Pdf

Number Theory: A Lively Introduction with Proofs, Applications, and Stories, is a new book that provides a rigorous yet accessible introduction to elementary number theory along with relevant applications. Readable discussions motivate new concepts and theorems before their formal definitions and statements are presented. Many theorems are preceded by Numerical Proof Previews, which are numerical examples that will help give students a concrete understanding of both the statements of the theorems and the ideas behind their proofs, before the statement and proof are formalized in more abstract terms. In addition, many applications of number theory are explained in detail throughout the text, including some that have rarely (if ever) appeared in textbooks. A unique feature of the book is that every chapter includes a math myth, a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exercise sets include in-depth Explorations, in which a series of exercises develop a topic that is related to the material in the section.

Author : Ivan Niven,Herbert S. Zuckerman
Publisher : Unknown
Page : 280 pages
File Size : 52,7 Mb
Release : 1968
Category : Number theory
ISBN : LCCN:90013013

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An Introduction to the Theory of Numbers by Ivan Niven,Herbert S. Zuckerman Pdf

Author : William Stein
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 53,7 Mb
Release : 2008-10-28
Category : Mathematics
ISBN : 9780387855257

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Elementary Number Theory: Primes, Congruences, and Secrets by William Stein Pdf

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.