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Recommendations... 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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| |  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.
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 Number Theory
by George E. Andrews
Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more
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| |  Elementary Number Theory: An Algebraic Approach
by Ethan D. Bolker
This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and more.
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Products in Number Theory | | |  | Advanced Number Theory
by Harvey Cohn
Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, and theories have evolved during last two centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.
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|  | An Adventurer's Guide to Number Theory
by Richard Friedberg
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.
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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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| |  | 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.
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|  | A Course in Algebraic Number Theory
by Robert B. Ash
Graduate-level course covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 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: An Algebraic Approach
by Ethan D. Bolker
This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and more.
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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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|  | 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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|  | 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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|  | Fibonacci Numbers
by Nikolai Nikolaevich Vorob'ev
An engaging treatment of an 800-year-old problem explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. Its entertaining style will appeal to recreational readers and students alike.
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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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| | | |  | The Number System
by H. A. Thurston
This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.
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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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| | Number Theory
by George E. Andrews
Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more
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| | 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.
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