Concise History of Mathematics by
INTRODUCTION
I. THE BEGINNINGS
II. THE ANCIENT ORIENT
III. GREECE
IV. THE ORIENT AFTER THE DECLINE OF GREEK SOCIETY
V. THE BEGINNINGS IN WESTERN EUROPE
VI. THE SEVENTEENTH CENTURY
VII. THE EIGHTEENTH CENTURY
VIII. THE NINETEENTH CENTURY
IX. THE FIRST HALF OF THE TWENTIETH CENTURY
Excursions in the History of Mathematics by
A. Number Theory
1. Highlights in the History of Number Theory: 1700 BC - 2008
2. Fermat: The Founder of Modern Number Theory
3. Fermat's Last Theorem: From Fermat to Wiles.- B. Calculus/Analysis.
4. A History of the Infinitely Small and the Infinitely Large in Calculus, with Remarks for the Teacher
5. A Brief History of the Function Concept
6. More on the History of Functions, Including Remarks on Teaching
7. Highlights in the Practice of Proof: 1600 BC - 2009
8. Paradoxes: What are they Good for?
9. Principle of Continuity: 16th - 19th centuries
10. Proof: A Many-Splendored Thing.- D. Courses Inspired by History
11. Numbers as a Source of Mathematical Ideas
12. History of Complex Numbers, with a Moral for Teachers
13. A History-of-Mathematics Course for Teachers, Based on Great Quotations
14. Famous Problems in Mathematics.- E. Brief Biographies of Selected Mathematicians.
15. The Biographies.- Index.
A History of Mathematics by
Origins.
Egypt.
Mesopotamia.
Ionia and the Pythagoreans.
The Heroic Age.
The Age of Plato and Aristotle.
Euclid of Alexandria.
Archimedes of Syracuse.
Apollonius of Perga.
Greek Trigonometry and Mensuration.
Revival and Decline of Greek Mathematics.
China and India.
The Arabic Hegemony.
Europe in the Middle Ages.
The Renaissance.
Prelude to Modern Mathematics.
The Time of Fermat and Descartes.
A Transitional Period.
Newton and Leibniz.
The Bernoulli Era.
The Age of Euler.
Mathematicians of the French Revolution.
The Time of Gauss and Cauchy.
Geometry.
Analysis.
Algebra.
Poincare and Hilbert.
Aspects of the Twentieth Century.
References.
General Bibliography.
Appendix.
Index.
A History of Mathematics by
Table of Contents
I. MATHEMATICS BEFORE THE SIXTH CENTURY.
Ancient Mathematics.
The Beginnings of Mathematics in Greece.
Archimedes and Apollonius.
Mathematical Methods in Hellenistic Times.
The Final Chapters of Greek Mathematics.
II. MEDIEVAL MATHEMATICS: 500-1400.
Medieval China and India.
The Mathematics of Islam.
Mathematics in Medieval Europe.
Mathematics Around the World.
III. EARLY MODERN MATHEMATICS: 1400-1700.
Algebra in the Renaissance.
Mathematical Methods in the Renaissance.
Geometry, Algebra, and Probability in the Seventeenth Century.
The Beginnings of Calculus.
IV. MODERN MATHEMATICS: 1700-2000.
Analysis in the Eighteenth Century.
Probability, Algebra, and Geometry in the Eighteenth Century.
Algebra in the Nineteenth Century.
Analysis in the Nineteenth Century.
Geometry in the Nineteenth Century.
Aspects of the Twentieth Century.
Answers to Selected Problems.
General References in the History of Mathematics.
Index and Pronunciation Guide.
Mathematics: A Concise History and Philosophy by
1 Mathematics for Civil Servants
2 The Earliest Number Theory
3 The Dawn of Deductive Mathematics
4 The Pythagoreans
5 The Pythagoreans and Perfection
6 The Pythagoreans and Polyhedra
7 The Pythagoreans and Irrationality
8 The Need for the Infinite
9 Mathematics in Athens Before Plato
10 Plato
11 Aristotle
12 In the Time of Eudoxus
13 Ruler and Compass Constructions
14 The Oldest Surviving Math Book
15 Euclid’s Geometry Continued
16 Alexandria and Archimedes
17 The End of Greek Mathematics
18 Early Medieval Number Theory
19 Algebra in the Early Middle Ages
20 Geometry in the Early Middle Ages
21 Khayyam and the Cubic
22 The Later Middle Ages
23 Modern Mathematical Notation
24 The Secret of the Cubic
25 The Secret Revealed
26 A New Calculating Device
27 Mathematics and Astronomy
28 The Seventeenth Century
29 Pascal
30 The Seventeenth Century II
31 Leibniz
32 The Eighteenth Century
33 Lagrange
34 Nineteenth-Century Algebra
35 Nineteenth-Century Analysis
36 Nineteenth-Century Geometry
37 Nineteenth-Century Number Theory
38 Cantor
39 Foundations
40 Twentieth-Century Number Theory
Mathematics and the Historian's Craft by
Introduction: The Birth and Growth of a Community
History or Heritage? An Important Distinction in Mathematics and for Mathematics Education
Ptolemy’s Mathematical Models and their Meaning
Mathematics, Instruments and Navigation, 1600-1800
Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions
The Mathematics and Science of Leonhard Euler (1707-1783)
Mathematics in Canada before 1945: A Preliminary Survey
The Emergence of the American Mathematical Research Community
19th Century Logic Between Philosophy and Mathematics
The Battle for Cantorian Set Theory
Hilbert and his Twenty-Four Problems
Turing and the Origins of AI,
Mathematics and Gender: Some Cross-Cultural Observations
Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century by
Mathematics in the French Revolution.- Poncelet (and Pole and Polar).- Theorems in Projective Geometry.- Poncelet’s Traité.- Duality and the Duality Controversy.- Poncelet, Chasles, and the Early Years of Projective Geometry.- Euclidean Geometry, the Parallel Postulate, and the Work of Lambert and Legendre.- Gauss (Schweikart and Taurinus) and Gauss’s Differential Geometry.- János Bolyai.- Lobachevskii.- Publication and Non-Reception up to 1855.- On Writing the History of Geometry – 1.- Across the Rhine – Möbius’s Algebraic Version of Projective Geometry.- Plücker, Hesse, Higher Plane Curves, and the Resolution of the Duality Paradox.- The Plücker Formulae.- The Mathematical Theory of Plane Curves.- Complex Curves.- Riemann: Geometry and Physics.- Differential Geometry of Surfaces.- Beltrami, Klein, and the Acceptance of Non-Euclidean Geometry.- On Writing the History of Geometry – 2.- Projective Geometry as the Fundamental Geometry.- Hilbert and his Grundlagen der Geometrie.- The Foundations of Projective Geometry in Italy.- Henri Poincaré and the Disc Model of non-Euclidean Geometry.- Is the Geometry of Space Euclidean or Non-Euclidean?.- Summary: Geometry to 1900.- What is Geometry? The Formal Side.- What is Geometry? The Physical Side.- What is Geometry? Is it True? Why is it Important?.- On Writing the History of Geometry – 3
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