Mathematical Thought from Ancient to Modern Times

ISBN-10: 0195061357

ISBN-13: 9780195061352

Edition: 1972 (Reprint)

Authors: Morris Kline

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Description:

This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Originally published in 1972, it is now available as a three volume paperback edition. Volume 1 looks at the discipline's 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 nineteenth 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 Gdel on recent mathematical study.
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Book details

List price: $24.95
Copyright year: 1972
Publisher: Oxford University Press, Incorporated
Publication date: 3/1/1990
Binding: Paperback
Pages: 432
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.100

Mathematics in Mesopotamia
Where Did Mathematics Begin?
Political History in Mesopotamia
The Number Symbols
Arithmetic Operations
Babylonian Algebra
Babylonian Geometry
The Uses of Mathematics in Babylonia
Evaluation of Babylonian Mathematics
Egyptian Mathematics
Background
The Arithmetic
Algebra and Geometry
Egyptian Uses of Mathematics
Summary
The Creation of Classical Greek Mathematics
Background
The General Sources
The Major Schools of the Classical Period
The Ionian School
The Pythagoreans
The Eleatic School
The Sophist School
The Platonic School
The School of Eudoxus
Aristotle and His School
Euclid and Apollonius
Introduction
The Background of Euclid's Elements
The Definitions and Axioms of the Elements
Books I to IV of the Elements
Book V: The Theory of Proportion
Book VI: Similar Figures
Books VII, VIII, and IX: The Theory of Numbers
Book X: The Classification of Incommensurables
Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion
The Merits and Defects of the Elements
Other Mathematical Works by Euclid
The Mathematical Work of Apollonius
The Alexandrian Greek Period: Geometry and Trigonometry
The Founding of Alexandria
The Character of Alexandrian Greek Mathematics
Areas and Volumes in the Work of Archimedes
Areas and Volumes in the Work of Heron
Some Exceptional Curves
The Creation of Trigonometry
Late Alexandrian Activity in Geometry
The Alexandrian Period: The Reemergence of Arithmetic and Algebra
The Symbols and Operations of Greek Arithmetic
Arithmetic and Algebra as an Independent Development
The Greek Rationalization of Nature
The Inspiration for Greek Mathematics
The Beginnings of a Rational View of Nature
The Development of the Belief in Mathematical Design
Greek Mathematical Astronomy
Geography
Mechanics
Optics
Astrology
The Demise of the Greek World
A Review of the Greek Achievements
The Limitations of Greek Mathematics
The Problems Bequeathed by the Greeks
The Demise of the Greek Civilization
The Mathematics of the Hindus and Arabs
Early Hindu Mathematics
Hindu Arithmetic and Algebra of the Period A.D. 200-1200
Hindu Geometry and Trigonometry of the Period A.D. 200-1200
The Arabs
Arabic Arithmetic and Algebra
Arabic Geometry and Trigonometry
Mathematics circa 1300
The Medieval Period in Europe
The Beginnings of a European Civilization
The Materials Available for Learning
The Role of Mathematics in Early Medieval Europe
The Stagnation in Mathematics
The First Revival of the Greek Works
The Revival of Rationalism and Interest in Nature
Progress in Mathematics Proper
Progress in Physical Science
Summary
The Renaissance
Revolutionary Influences in Europe
The New Intellectual Outlook
The Spread of Learning
Humanistic Activity in Mathematics
The Clamor for the Reform of Science
The Rise of Empiricism
Mathematical Contributions in the Renaissance
Perspective
Geometry Proper
Algebra
Trigonometry
The Major Scientific Progress in the Renaissance
Remarks on the Renaissance
Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries
Introduction
The Status of the Number System and Arithmetic
Symbolism
The Solution of Third and Fourth Degree Equations
The Theory of Equations
The Binomial Theorem and Allied Topics
The Theory of Numbers
The Relationship of Algebra to Geometry
The Beginnings of Projective Geometry
The Rebirth of Geometry
The Problems Raised by the Work on Perspective
The Work of Desargues
The Work of Pascal and La Hire
The Emergence of New Principles
Coordinate Geometry
The Motivation for Coordinate Geometry
The Coordinate Geometry of Fermat
Rene Descartes
Descartes's Work in Coordinate Geometry
Seventeenth-Century Extensions of Coordinate Geometry
The Importance of Coordinate Geometry
The Mathematization of Science
Introduction
Descartes's Concept of Science
Galileo's Approach to Science
The Function Concept
The Creation of the Calculus
The Motivation for the Calculus
Early Seventeenth-Century Work on the Calculus
The Work of Newton
The Work of Leibniz
A Comparison of the Work of Newton and Leibniz
The Controversy over Priority
Some Immediate Additions to the Calculus
The Soundness of the Calculus
List of Abbreviations
Index
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