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RT Book, Whole SR Electronic DC OPAC T1 Computer Algebra Handbook : Foundations · Applications · Systems / edited by Johannes Grabmeier, Erich Kaltofen, Volker Weispfenning A1 Grabmeier, Johannes A1 Kaltofen, Erich A1 Weispfenning, Volker A1 SpringerLink (Online service) YR 2003 FD 2003 SP XX, 637 p K1 Mathematics K1 Computer science -- Mathematics K1 Algebra K1 Algorithms K1 Computer software K1 Mathematics K1 Mathematical Software K1 Algebra K1 Algorithms K1 Symbolic and Algebraic Manipulation PB Springer Berlin Heidelberg : Imprint: Springer PP Berlin, Heidelberg SN 9783642558269 LA English (英語) CL DC23:004 NO Two ideas lie gleaming on the jeweler's velvet. The first is the calculus, the sec ond, the algorithm. The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible; but it has been the algorithm that has made possible the modern world. -David Berlinski, The Advent of the Algorithm First there was the concept of integers, then there were symbols for integers: I, II, III, 1111, fttt (what might be called a sticks and stones representation); I, II, III, IV, V (Roman numerals); 1, 2, 3, 4, 5 (Arabic numerals), etc. Then there were other concepts with symbols for them and algorithms (sometimes) for ma nipulating the new symbols. Then came collections of mathematical knowledge (tables of mathematical computations, theorems of general results). Soon after algorithms came devices that provided assistancefor carryingout computations. Then mathematical knowledge was organized and structured into several related concepts (and symbols): logic, algebra, analysis, topology, algebraic geometry, number theory, combinatorics, etc. This organization and abstraction lead to new algorithms and new fields like universal algebra. But always our symbol systems reflected and influenced our thinking, our concepts, and our algorithms NO 書誌ID=1002996402; LK [E Book]http://dx.doi.org/10.1007/978-3-642-55826-9 OL 30