The Development of MathematicsDover Publications, 1945 - 637 Seiten "This important book . . . presents a broad account of the part played by mathematics in the evolution of civilization, describing clearly the main principles, methods, and theories of mathematics that have survived from about 4000 BC to 1940." - "Booklist " In this time-honored study, one of the 20th century's foremost scholars and interpreters of the history and meaning of mathematics masterfully outlines the development of its leading ideas, and clearly explains the mathematics involved in each. According to the author, a professor of mathematics at the California Institute of Technology from 1926 until his death in 1960, it is "not a history of the traditional kind, but a narrative of the decisive epochs in the development of mathematics." It is a narrative filled with compelling insights of special interest to every mathematician, engineer, and scientist. Main trends in mathematics from approximately 4000 BC to the 20th century are presented through analyses of typical major episodes in each. The author first examines the evolution of mathematical ideas in the ancient civilizations of Egypt and Babylonia; later developments in India, Arabia, and Spain; and other achievements worldwide through the 16th century. Professor Bell then traces the beginnings of modern mathematics in the 17th century, and the emergence of the importance of extensions of number, mathematical structure, the generalization of arithmetic, and structural analysis.Compelling accounts of major breakthroughs in the 19th and 20th centuries follow, emphasizing rational arithmetic after Fermat, contributions from geometry, and topics as diverse as generalised variables, abstractions, differential equations, invariance, uncertainties, and probabilities. Throughout, Professor Bell subordinates details of mere antiquarian interest - involving concepts and ideas that did not succeed or bear fruit - in favour of the fullest possible exposition of those elements still alive in mathematics. AUTHOR: Eric Temple Bell (1883-1960) was born in Scotland, studied mathematics at universities in the United States, and taught at the University of Washington and the California Institute of Technology. He wrote several books on the history of mathematics, including another Dover title, The Magic of Numbers. He also wrote many science-fiction novels under the pseudonym John Taine. |
Inhalt
TO ANY PROSPECTIVE READER | 3 |
The European Depression | 85 |
Detour through India Arabia and Spain | 93 |
Urheberrecht | |
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Abel abstract abstract algebra algebraic equations algebraic integers algebraic numbers algebraists analysis analytic appear applications Archimedes arithmetic Babylonians calculus calculus of variations Cantor Cauchy century B.C. classical coefficients complex numbers concept congruence continued fractions continuous coordinates corresponding curve Dedekind defined definition Descartes differential equations differential geometry Diophantus elementary elliptic functions equivalent Euclid Euler example Fermat finite number French Galois Galois theory Gauss German given Greek Greek mathematics groups Hilbert infinite infinity integral interest intuition invariants invented Kronecker Lagrange Lagrange's Leibniz linear mathe mathematical logic mathematical physics mathematicians matics mechanics method modern mathematics Moslems natural numbers Newton nineteenth century non-Euclidean geometry noted number system original plane postulates problem projective geometry proof proved Pythagorean quadratic quaternions real numbers reasoning Riemann scientific seems significance solution solved space surface symbolism theorem theory of algebraic theory of functions theory of numbers tion topology transformation twentieth century Weierstrass