[Book Cover]

Contextual History of Mathematics, A, 1/e

Ronald S. Calinger, The Catholic University of America

Published July, 1999 by Prentice Hall Engineering/Science/Mathematics

Copyright 1999, 751 pp.
Cloth
ISBN 0-02-318285-7


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Summary

For the standard math education history of math course. Taking students on a mathematical journey beginning with pre-civilization's origins of number and culture and spanning through the 1750's , this enlightening and absorbing survey presents both established and new interpretations with careful consideration given to the remappings, redivisions, and renarrations presented by each new body of historians. Analyzing the ancient beginnings and subsequent branches of growth in this rich, diverse, and rapidly expanding field, this text provides a foundation for understanding the core of mathematics with discussions that progress from the theoretical mathematics in ancient Mesopotamia and Egypt to the emergence of higher analysis mathematics in the late seventeenth and early eighteenth centuries.

Features


Opens with a reflective narrative on the nature and roots of mathematics and a look at some of our more important historiographical issues.
Considers mathematics before civilization with examinations of the Neolithic Revolution and writing and metrology in ancient Sumer.
Traces the science from proto- to theoretical mathematics, offering insightful studies into:

  • The mathematical achievements in Ancient Mesopotamia.
  • The beginnings of theoretical mathematics in pre-Socratic Greece.
  • Early Roman civilization and mathematics.
  • Numeration and major literary sources in traditional China.
  • The nature and sources of ancient and medieval Indian mathematics.
Provides a broad survey of mathematics progression in the Islamic world, Latin West, and Maya America from the Middle Ages to 1500.
  • Studies mathematics in the Medieval Islamic world after 1055.
  • Explores the style and applications of late medieval mathematical thought.
  • Covers practical mathematics in high renaissance and reformation Europe.
  • Examines physico-mathematics and computational arithmetic in Western Europe from 1570 to 1630.
Concludes with a discussion on the scientific revolution, delving into such areas as the age of absolutism, the culture of science, inventions of differential and fluxional calculus, and algebra, number theory, and probability.


Table of Contents
    Preface.
    Prologue.
I. BEFORE THE ADVENT OF CIVILIZATION.
    1. Origins of Number and Culture.
II. ANTIQUITY: FROM PROTOMATHEMATICS TO THEORETICAL MATHEMATICS.
    2. The Dawning of Mathematics in the Ancient Near East.
    3. Beginnings of Theoretical Mathematics in Pre-Socratic Greece.
    4. Theoretical Mathematics Established in Fourth-Century Greece.
    5. Ancient Mathematical Zenith in the Hellenistic Third Century B.C., I: The Alexandrian Museum and Euclid.
    6. Ancient Mathematical Zenith in the Hellenistic Third Century B.C., II: Archimedes to Diocles.
    7. Mathematics in Roman and Later Antiquity, Centering in Alexandria.
    8. Mathematics in Traditional China from the Late Shang Dynasty to the Mid-Seventeenth Century.
    9. Indian Mathematics: From Harappan to Keralan Times.
III. THE ISLAMIC WORLD, LATIN WEST, AND MAYA AMERICA FROM THE MIDDLE AGES TO ca. 1500.
    10. Mathematics in the Service of Religion.
    11. The Era of Arabic Primacy and a Persian Flourish.
    12. Recovery and Expansion in Old Europe, 1000 - 1500.
THE TRANSITION TO MODERN MATHEMATICS IN EUROPE.
    13. The First Phase of the Scientific Revolution, ca. 1450 - 1600: Algebra and Geometry.
    14. Transformation ca. 1600 - 1660: I.
    15. Transformation ca. 1600 - 1660: II: To the Edge of Modernity.
    16. The Apex of the Scientific Revolution I: Setting and Laureates.
    17. The Apex of the Scientific Revolution II: Calculus to Probability.
    Endnotes.
    Suggested Further Readings.
    Name Index.
    Subject Index.
    Photo Credits.


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