|The Divine Proportion |
by H. E. Huntley
Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.
|A Mathematical History of the Golden Number |
by Roger Herz-Fischler
This comprehensive study traces the historic development of division in extreme and mean ratio ("the golden number") from its first appearance in Euclid's Elements through the 18th century. Features numerous illustrations.
|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
|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.
|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.
|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.
|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.
|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.
|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.
|Excursions in Number Theory |
by C. Stanley Ogilvy, John T. Anderson
Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. "Splendidly written, well selected and presented collection." — Martin Gardner.
|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.
|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.
|Topics in Number Theory, Volumes I and II |
by William J. LeVeque
Classic 2-part work now available in a single volume. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes problems and solutions. 1956 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.
|Famous Problems of Geometry and How to Solve Them |
by Benjamin Bold
Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.
|Foundations of Geometry |
by C. R. Wylie, Jr.
Geared toward students preparing to teach high school mathematics, this text explores the principles of Euclidean and non-Euclidean geometry and covers both generalities and specifics of the axiomatic method. 1964 edition.
|Fundamental Concepts of Geometry |
by Bruce E. Meserve
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
|Geometry from Euclid to Knots |
by Saul Stahl
This text provides a historical perspective on plane geometry and covers non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, informal topology, and more. Includes 1,000 practice problems. Solutions available. 2003 edition.
|The Geometry of Art and Life |
by Matila Ghyka
This classic study probes the geometric interrelationships between art and life in dissertations by Plato, Pythagoras, and Archimedes and examples of modern architecture and art. 80 plates and 64 figures.
|Geometry: A Comprehensive Course |
by Dan Pedoe
Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.
|Taxicab Geometry: An Adventure in Non-Euclidean Geometry |
by Eugene F. Krause
Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.