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Development of Mathematics.

Author: E T Bell
Publisher: Dover Publications, 2012.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This time-honored study by one of the 20th century's foremost scholars and interpreters of the history and meaning of mathematics surveys the role of mathematics in civilization. It describes clearly the main principles, methods, and theories of mathematics that have survived from 4000 B.C. to 1945. 1945 edition.
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Genre/Form: Electronic books
History
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: E T Bell
ISBN: 1306363292 9781306363297
OCLC Number: 868966212
Description: 1 online resource
Contents: DOVER BOOKS ON MATHEMATICS; Title Page; Copyright Page; To Any Prospective Reader; Table of Contents; CHAPTER 1 --
General Prospectus; Necessity for proof; emergence of mathematics; Necessity for abstractness; History and proof; Five streams; The time-scale; Seven periods; Some general characteristics; Motivation in mathematics; Residues of epochs; CHAPTER 2 --
The Age of Empiricism; Arithmetic to 600 B.C.; Algebra without symbolism; Toward geometry and analysis; The greatest Egyptian pyramid; The contribution of Babylon and Egypt; CHAPTER 3 --
Firmly Established; Mathematics and computation. Ex Oriente luxTwo supreme achievements; Chronology of Greek mathematics; Number from Pythagoras to Diophantus; The postulational method; Flight from intellectual prudery; Through geometry to metaphysics; Plane, solid, and linear loci; A wrong turning?; CHAPTER 4 --
The European Depression; European mathematics from Boethius to Aquinas; Submathematical analysis; CHAPTER 5 --
Detour through India, Arabia, and Spain; Partial emergence of algebra; The emergence of trigonometry; Mathematics at the crossroads; CHAPTER 6 --
Four Centuries of Transition; Opposing currents; A terminus in algebra. A beginning in algebra and trigonometryThe development of symbolism; CHAPTER 7 --
The Beginning of Modern Mathematics; Five major advances; 'Anticipations'; Descartes, Fermat, and analytic geometry; Newton, Leibniz, and the calculus; Newton's version of the calculus; Leibniz' version; Rigor; anticipations; Emergence of the mathematical theory of probability; The origin of modern arithmetic; Emergence of synthetic projective geometry; Origin of modern applied mathematics; CHAPTER 8 --
Extensions of Number; Four critical periods; The Pythagorean adventure; Extension by inversion and formalism. From manipulation to interpretationThe Euclidean program; Pythagoras to 1900; CHAPTER 9 --
Toward Mathematical Structure; Abstraction and the recent period; Prospect; From supernaturalism to naturalism; Congruence from 1801 to 1887; A period of transition; The liberation of algebra; From vectors to tensors; Toward structure; CHAPTER 10 --
Arithmetic Generalized; Generalized divisibility; Further developments; The general gain to 1910; The contribution from algebraic equations; Changing outlooks, 1870-1920; Mathematics and society; CHAPTER 11 --
Emergence of Structural Analysis. Three phases in linear algebraThe abstract method; Toward structure in algebra; Toward abstraction in analysis and geometry; A terminus in arithmetic; Newer directions; Retrospect and prospect; CHAPTER 12 --
Cardinal and Ordinal to 1902; Equivalence and similarity; Arithmetized analysis; Existence and constructibility; CHAPTER 13 --
From Intuition to Absolute Rigor; Two decirive turning points; Five stages; The golden age of 'nothing'; Taylor's contribution; Attack by an amateur; The triumph of formalism; Lagrange's remedy; Gains to 1800; Ridiculous interlude; Intuition transformed.

Abstract:

This time-honored study by one of the 20th century's foremost scholars and interpreters of the history and meaning of mathematics surveys the role of mathematics in civilization. It describes clearly the main principles, methods, and theories of mathematics that have survived from 4000 B.C. to 1945. 1945 edition.

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