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Tracing the roots of mathematics, this fascinating survey covers the ancient beginnings and subsequent branches of growth in this rich, diverse, and rapidly expanding scientific field, with discussions that progress from the theoretical mathematics in ancient Mesopotamia and Egypt to the emergence of higher analysis mathematics in the late seventeenth century. Well-documented, it presents both established and promising emerging theses, with careful consideration throughout to the remappings, redivisions, and renarrations presented by each new body of historians.
Reflects 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, and tracks the science from proto- to theoretical mathematics. Provides a broad survey of mathematics progression in the Islamic world, Latin West, and Maya America from the Middle Ages to 1500, and contain discussions on such topics as the age of absolutism, the culture of science, inventions of differential and fluxional calculus, as well as algebra, number theory, and probability.
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.
Tracing the roots of mathematics, this fascinating survey covers the ancient beginnings and subsequent branches of growth in this rich, diverse, and rapidly expanding scientific field, with discussions that progress from the theoretical mathematics in ancient Mesopotamia and Egypt to the emergence of higher analysis mathematics in the late seventeenth century. Well-documented, it presents both established and promising emerging theses, with careful consideration throughout to the remappings, redivisions, and renarrations presented by each new body of historians.
Reflects 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, and tracks the science from proto- to theoretical mathematics. Provides a broad survey of mathematics progression in the Islamic world, Latin West, and Maya America from the Middle Ages to 1500, and contain discussions on such topics as the age of absolutism, the culture of science, inventions of differential and fluxional calculus, as well as 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.