Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicat... read more
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.
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.
The Theory of Algebraic Numbers by Harry Pollard, Harold G. Diamond Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; more. 1975 edition.
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.
Number Theory and Its History by Oystein Ore A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Fascinating, accessible coverage of prime numbers, Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, and more.
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.
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.
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, and more. 1964 edition.
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.
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.
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, and much more.
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.
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.
Sieve Methods by Heine Halberstam, Hans Egon Richert This text by a noted pair of experts is regarded as the definitive work on sieve methods. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 edition.
Three Pearls of Number Theory by A. Y. Khinchin These 3 puzzles require proof of a basic law governing the world of numbers. Features van der Waerden's theorem, the Landau-Schnirelmann hypothesis and Mann's theorem, and a solution to Waring's problem. Solutions included.
Abstract Algebra and Solution by Radicals by John E. Maxfield, Margaret W. Maxfield Accessible advanced undergraduate-level text starts with groups, rings, fields, and polynomials and advances to Galois theory, radicals and roots of unity, and solution by radicals. Numerous examples, illustrations, exercises, appendixes. 1971 edition.
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.
Uniform Distribution of Sequences by L. Kuipers, H. Niederreiter The theory of uniform distribution began with Weyl's celebrated paper of 1916 and this book summarizes its development through the mid-1970s, with comprehensive coverage of methods and principles. 1974 edition.
The Method of Trigonometrical Sums in the Theory of Numbers by I. M. Vinogradov This text investigates Waring's problem, approximation by fractional parts of the values of a polynomial, estimates for Weyl sums, distribution of fractional parts of polynomial values, Goldbach's problem, more. 1954 edition.
Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
Reprint of the W. B. Saunders Co., Philadelphia, PA, 1971 edition.
George E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text Number Theory (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field — number theory. Perhaps his greatest discovery, however, was not solely one in the intellectual realm but in the physical world as well.
In 1975, on a visit to Trinity College in Cambridge to study the papers of the late mathematician George N. Watson, Andrews found what turned out to be one of the actual Holy Grails of number theory, the document that became known as the "Lost Notebook" of the great Indian mathematician Srinivasa Ramanujan. It happened that the previously unknown notebook thus discovered included an immense amount of Ramanujan's original work bearing on one of Andrews' main mathematical preoccupations — mock theta functions. Collaborating with colleague Bruce C. Berndt of the University of Illinois at Urbana-Champaign, Andrews has since published the first two of a planned three-volume sequence based on Ramanujan's Lost Notebook, and will see the project completed with the appearance of the third volume in the next few years.
In the Author's Own Words: "It seems to me that there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally surprise me. I do not think of mathematics as invented but rather discovered." — George E. Andrews
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