Number theory and its history / Oystein Ore.

Author
Ore, Øystein, 1899-1968 [Browse]
Format
Book
Language
English
Published/​Created
  • New York : Dover, 1988.
  • ©1948
Description
x, 370 pages : illustrations ; 22 cm.

Availability

Copies in the Library

Location Call Number Status Location Service Notes
Firestone Library - Stacks QA241 .O7 1988 Browse related items Request

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    Summary note
    This book, written by a prominent mathematician and Sterling Professor of Mathematics at Yale, differs from most books on number theory in two important ways: first, it presents the principal ideas and methods of number theory within a historical and cultural framework, making the subject more tangible and easily grasped. Second, the material requires substantially less mathematical background than many comparable texts. Technical complications and mathematical requirements have been kept to a minimum in order to make the book as accessible as possible to readers with limited mathematical knowledge. For the majority of the book, a basic knowledge of algebra will suffice. In developing the importance and meaning of number theory in the history of mathematics, Professor Ore documents the contributions of a host of history's greatest mathematicians: Diophantos, Euclid, Fibonacci, Euler, Fermat, Mersenne, Gauss, and many more, showing how these thinkers evolved the major outlines of number theory. Topics covered include counting and recording of numbers, the properties of numbers, prime numbers, the Aliquot parts, indeterminate problems, theory of linear indeterminate problems, Diophantine problems, congruences, analysis of congruences. Wilson's Theorem, Euler's theorem, theory of decimal expansions, the converse of Fermat's theorem, and the classical construction problems. Based on a course the author gave for a number of years at Yale, this book covers the essentials of number theory with a clarity and avoidance of abstruse mathematics that make it an ideal resource for undergraduates or for amateur mathematicians (who have historically contributed much to number theory). It has even been recommended for self-study by gifted high school students. -- from back cover.
    Notes
    Includes indexes.
    Bibliographic references
    Bibliography: p. 359d.
    Original version
    Reprint, with supplement. Originally published: New York : McGraw-Hill, 1948.
    Contents
    • Counting and recording of numbers : Numbers and counting ; Basic number groups ; The number systems ; Large numbers ; Finger numbers ; Recordings of numbers ; Writing of numbers ; Calculations ; Positional numeral systems ; Hindu-Arabic numerals
    • Properties of numbers. division : Number theory and numerology ; Multiples and divisors ; Division and remainders ; Number systems ; Binary number systems
    • Euclid's algorism : Greatest common divisor. Euclid's algorism ; The division lemma ; Least common multiple ; Greatest common divisor and least common multiple for several numbers
    • Prime numbers : Prime numbers and the prime factorization theorem ; Determination of prime factors ; Factor tables ; Fermat's factorization method ; Euler's factorization method ; The sieve of Eratosthenes ; Mersenne and Fermat primes ; The distribution of primes
    • The Aliquot parts : The divisors of a number ; Perfect numbers ; Amicable numbers ; Greatest common divisor and least common multiple ; Euler's function
    • Indeterminate problems : Problems and puzzles ; Indeterminate problems ; Problems with two unknowns ; Problems with several unknowns
    • Theory of linear indeterminate problems : Theory of linear indeterminate equations with two unknowns ; Linear indeterminate equations in several unknowns ; Classification of systems of numbers
    • Diophantine problems : The Pythagorean triangle ; The Plimpton library tablet ; Diophantos of Alexandria ; Al-Karkhi and Leonardo Pisano ; From Diophantos to Fermat ; The method of infinite descent ; Fermat's last theorem
    • Congruences : The disquisitiones arithmeticae ; The properties of congruences ; Residue systems ; Operations with congruences ; Casting out nines
    • Analysis of congruences : Algebraic congruences ; Linear congruences ; Simultaneous congruences and the Chinese remainder theorem ; Further study of algebraic congruences
    • Wilson's theorem and its consequences : Wilson's theorem ; Gauss's generalization of Wilson's theorem ; Representations of numbers as the sum of two squares
    • Euler's theorem and its consequences : Euler's theorem ; Fermat's theorem ; Exponents of numbers ; Primitive roots for primes ; Primitive roots for powers of primes ; Universal exponents ; Indices ; Number theory and the splicing of telephone cables
    • Theory of decimal expansions : Decimal fractions ; The properties of decimal fractions
    • The converse of Fermat's theorem : The converse of Fermat's theorem ; Numbers with the Fermat property
    • The classical construction problems : The classical construction problems ; The construction of regular polygons ; Examples of constructible polygons.
    ISBN
    • 0486656209 ((pbk.))
    • 9780486656205 ((pbk.))
    Tech. report no.
    88000372
    LCCN
    88000372
    OCLC
    17413345
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