Mathematical Thought From Ancient to Modern Times, 1
This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. 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 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 Gode
1 online resource (691 pages)
9780199770465, 0199770468
1052587153
Cover Page
Title Page
Copyright Page
Dedication
Preface to the Three-Volume: Paperback Edition of Mathematical Thought
Preface
Contents
Publisher's Note
1. Mathematics in Mesopotamia
1. Where Did Mathematics Begin?
2. Political History in Mesopotamia
3. The Number Symbols
4. Arithmetic Operations
5. Babylonian Algebra
6. Babylonian Geometry
7. The Uses of Mathematics in Babylonia
8. Evaluation of Babylonian Mathematics
2. Egyptian Mathematics
1. Background
2. The Arithmetic
3. Algebra and Geometry
4. Egyptian Uses of Mathematics. 5. Summary
3. The Creation of Classical Greek Mathematics
1. Background
2. The General Sources
3. The Major Schools of the Classical Period
4. The Ionian School
5. The Pythagoreans
6. The Eleatic School
7. The Sophist School
8. The Platonic School
9. The School of Eudoxus
10. Aristotle and His School
4. Euclid and Apollonius
1. Introduction
2. The Background of Euclid's Elements
3. The Definitions and Axioms of the Elements
4. Books I to IV of the Elements
5. Book V: The Theory of Proportion
6. Book VI: Similar Figures. 7. Books VII, VIII, and IX: TheTheory of Numbers
8. Book X: The Classification of Incommensurables
9. Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion
10. The Merits and Defects of the Elements
11. Other Mathematical Works by Euclid
12. The Mathematical Work of Apollonius
5. The Alexandrian Greek Period: Geometry and Trigonometry
1. The Founding of Alexandria
2. The Character of Alexandrian Greek Mathematics
3. Areas and Volumes in the Work of Archimedes
4. Areas and Volumes in the Work of Heron
5. Some Exceptional Curves. 6. The Creation of Trigonometry
7. Late Alexandrian Activity in Geometry
6. The Alexandrian Period: The Reemergence of Arithmetic and Algebra
1. The Symbols and Operations of Greek Arithmetic
2. Arithmetic and Algebra as an Independent Development
7. The Greek Rationalization of Nature
1. The Inspiration for Greek Mathematics
2. The Beginnings of a Rational View of Nature
3. The Development of the Belief in Mathematical Design
4. Greek Mathematical Astronomy
5. Geography
6. Mechanics
7. Optics
8. Astrology
8. The Demise of the Greek World. 1. A Review of the Greek Achievements
2. The Limitations of Greek Mathematics
3. The Problems Bequeathed by the Greeks
4. The Demise of the Greek Civilization
9. The Mathematics of the Hindus and Arabs
1. Early Hindu Mathematics
2. Hindu Arithmetic and Algebra of the Period A.D. 200-1200
3. Hindu Geometry and Trigonometry of the Period A.D. 200-1200
4. The Arabs
5. Arabic Arithmetic and Algebra
6. Arabic Geometry and Trigonometry
7. Mathematics circa 1300
10. The Medieval Period in Europe
1. The Beginnings of a European Civilization
2. The Materials Available for Learning