 Essays on the Theory of Numbers
by Richard Dedekind
Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.
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| |  Algebraic Number Theory
by Edwin Weiss
Ideal either for classroom use or as exercises for mathematically-minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
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 Riemann’s Zeta Function
by H. M. Edwards
Superb study of the landmark 1859 publication entitled "On the Number of Primes Less Than a Given Magnitude" traces the developments in mathematical theory that it inspired. Topics include Riemann's main formula, the Riemann-Siegel formula, more.
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| |  Number Theory and Its History
by Oystein Ore
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
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 Elementary Theory of Numbers
by William J. LeVeque
Superb introduction to Euclidean algorithm and its consequences, congruences, continued fractions, powers of an integer modulo m, Gaussian integers, Diophantine equations, more. Problems, with answers. Bibliography.
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| |  Fundamentals of Number Theory
by William J. LeVeque
Basic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition.
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 Continued Fractions
by A. Ya. Khinchin
Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Properties of the apparatus, representation of numbers by continued fractions, more. 1964 edition.
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| |  Game Theory: A Nontechnical Introduction
by Morton D. Davis
This fascinating, newly revised edition offers an overview of game theory, plus lucid coverage of two-person zero-sum game with equilibrium points; general, two-person zero-sum game; utility theory; and other topics.
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| |  Sundials: Their Theory and Construction
by Albert Waugh
A rigorous appraisal of sundial science includes mathematical treatment and pertinent astronomical background, plus a nontechnical treatment so simple that several of the dials can be built by children. 106 illustrations.
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 Fads and Fallacies in the Name of Science
by Martin Gardner
Fair, witty appraisal of cranks, quacks, and quackeries of science and pseudoscience: hollow earth, Velikovsky, orgone energy, Dianetics, flying saucers, Bridey Murphy, food and medical fads, more.
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 Number Systems and the Foundations of Analysis
by Elliott Mendelson
Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.
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| |  Diophantine Approximations
by Ivan Niven
This self-contained treatment covers approximation of irrationals by rationals, product of linear forms, multiples of an irrational number, approximation of complex numbers, and product of complex linear forms. 1963 edition.
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 Elementary Number Theory: Second Edition
by Underwood Dudley
Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition.
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