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    Elementary Number Theory (Dover Books on Mathematics) (Paperback) By (author) Underwood Dudley

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    DescriptionIdeal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems--some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.


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  • Full bibliographic data for Elementary Number Theory

    Title
    Elementary Number Theory
    Authors and contributors
    By (author) Underwood Dudley
    Physical properties
    Format: Paperback
    Number of pages: 272
    Width: 139 mm
    Height: 216 mm
    Thickness: 13 mm
    Weight: 286 g
    Language
    English
    ISBN
    ISBN 13: 9780486469317
    ISBN 10: 048646931X
    Classifications

    BIC E4L: MAT
    B&T Book Type: NF
    Nielsen BookScan Product Class 3: S7.9T
    B&T Modifier: Region of Publication: 01
    B&T Modifier: Academic Level: 01
    B&T Merchandise Category: SCI
    B&T General Subject: 710
    BIC subject category V2: PBH
    Ingram Subject Code: MA
    Libri: I-MA
    B&T Modifier: Text Format: 06
    Warengruppen-Systematik des deutschen Buchhandels: 26280
    LC subject heading: ,
    DC21: 512.72
    DC22: 512.72, 512.7/2
    BISAC V2.8: MAT022000
    LC classification: QA241 .D79 2008
    Thema V1.0: PBH
    Edition
    2, Revised
    Edition statement
    2nd Revised edition
    Publisher
    Dover Publications Inc.
    Imprint name
    Dover Publications Inc.
    Publication date
    26 December 2008
    Publication City/Country
    New York
    Author Information
    Underwood Dudley is Professor Emeritus of Mathematics at DePauw University.Underwood Dudley: Cranking Out Classics Any editor involved with publishing in mathematics for any length of time is familiar with the phenomena -- the receipt, usually via snail mail, of generally handwritten, and generally interminable, really, really interminable, theses on some bizarre and unprovable point -- theses hoping, trying against all hope, demanding in fact, to prove the unprovable, to rewrite some fundamental part of mathematics, often in my experience to demonstrate for one final time that, for example, Einstein didn't know what he was talking about -- in short, the work of a mathematical crank! Underwood Dudley (Woody to everyone in the math world), Professor Emeritus, Depauw University, provided an inestimable service to all math editors in the universe by demonstrating that they are not alone in their experience. His unique and wonderful book "Mathematical Cranks" (The Mathematics Association of America, 1992) is a readable feast, especially for those who have been on the receiving end of mathematical crank mail. We're all in Woody's debt for having assembled this collection of failed squared circles, angle trisections, and much, much more. However, chronicling the cranks -- as enjoyable as it may have been to the rest of us -- is hardly a career, Woody has written many other books as well. And any reader who wants to check out a totally uncranky, reader- and student-friendly, time-tested basic text in "Elementary Number Theory" could hardly do better than to look at the Dover edition of Woody's book by that name, which started its career with Freeman in 1969 and which Dover was pleased to reprint in 2008.
    Table of contents
    PrefaceIntegersUnique FactorizationLinear Diophantine EquationsCongruencesLinear CongruencesFermat's and Wilson's TheoremsThe Divisors of an IntegerPerfect NumbersEuler's Theorem and FunctionPrimitive RootsQuadratic CongruencesQuadratic ReciprocityNumbers of Other BasesDuodecimalsDecimalsPythagorean TrianglesInfinite Descent and Fermat's ConjectureSums of Two SquaresSums of Four Squaresx(superscript 2) - Ny(superscript 2) = 1Bounds for pi(x)Formulas for PrimesAdditional problemsProof by InductionComputer ProblemsFactor Table for Integers Less Than 10,000ReferencesAnswers to Selected ExercisesAnswers to Selected Odd-Numbered ProblemsComments on Selected Odd-Numbered ProblemsIndex