Mathematical Thought From Ancient to Modern Times, Volume 1, Volume 1

Couverture
Oxford University Press, 1 mars 1990 - 432 pages
This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.
 

Pages sélectionnées

Table des matières

Mathematics in Mesopotamia
Egyptian Mathematics
The Creation of Classical Greek Mathematics
Euclid and Apollonius
The Work of Desargues
4-3
The Work of Pascal and La Hire
4-4
The Emergence of New Principles
4-5
Progress inMathematics Proper
4-7
The Status of the Number System and Arithmetic
4-250
Symbolism
4-262
The Solution of Third and Fourth Degree Equations
4-267
The Theory of Equations
4-276
The Binomial Theorem and Allied Topics
4-280
The Theory of Numbers
4-282
The Relationship of Algebra to Geometry
4-288
The Beginnings of Projective Geometry
4-298

The Merits and Defects of the Elements
4-10
Coordinate Geometry
4-15
The Reemergence of Arithmetic
4-78
The Demise of the Greek World
4-135
The Mathematics of the Hindus and Arabs
4-152
The Medieval Period in Europe
4-177
Progress in Physical Science
4-193
Summary
4-196
The Renaissance 1 Revolutionary Inuences in Europe
4-199
The New Intellectual Outlook
4-202
The Spread of Learning
4-205
Humanistic Activity in Mathematics
4-206
The Clamor for the Reform of Science
4-210
The Rise of Empiricism
4-215
Mathematical Contributions in the Renaissance 1 Perspective
4-221
Geometry Proper
4-225
Algebra
4-228
Trigonometry
4-230
The Major Scientific Progress in the Renaissance 6 Remarks on the Renaissance
4-244
and Algebra
4-249
The Rebirth of Geometry
14-1
The Problems Raised by the Work on Perspective
14-2
René Descartes
14-3
Descartess Work in Coordinate Geometry
14-4
SeventeenthCentury Extensions
14-5
The Importance of Coordinate Geometry Coordinate
14-21
The Mathematization of Science 1 Introduction
14-54
Descartess Concept of Science
14-55
Galileos Approach to Science
14-57
The Function Concept
14-69
The Creation of the Calculus 1 The Motivation for the Calculus
14-78
Early SeventeenthCentury Work on the Calculus
14-80
The Work of Newton
14-98
The Work of Leibniz
14-118
A Comparison of the Work of Newton and Leibniz
14-130
The Controversy over Priority
14-132
Some Immediate Additions to the Calculus
14-133
The Soundness of the Calculus 383
14-136
List of Abbreviations Index
24

Autres éditions - Tout afficher

Expressions et termes fréquents

À propos de l'auteur (1990)

Morris Kline is Professor of Mathematics, Emeritus, at the Courant Institute of Mathematical Sciences, New York University, where he directed the Division of Electromagnetic Research for twenty years.

Informations bibliographiques