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
Euler As Physicist by
The Predecessors: Descartes, Newton and Leibniz
Newton and Leibniz on Time, Space and Forces
Newton and Leibniz on the Foundation of the Calculus
Euler’s Program for Mechanics
The Foundation of the Calculus
Euler’s Early Relativistic Theory
Euler’s Wirksamkeit, Helmholtz’s Treatment of Energy Law and Beyond
Euler’s Mechanics and Schrödinger’s Quantum Mechanics
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.
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.
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
Remarkable Mathematicians by
1. From Euler to Legendre
2. From Fourier to Cauchy
3. From Abel to Grassmann
4. From Kummer to Cayley
5. From Hermite to Lie
6. From Cantor to Hilbert
7. From Moore to Takagi
From Hardy to Lefschetz
9. From Birkhoff to Alexander
10. From Banach to von Neumann
Sherlock Holmes in Babylon and Other Tales of Mathematical History by
Part I. Ancient Mathematics
Sherlock Holmes in Babylon
Words and pictures: new light on Plimpton 322
Mathematics 600 BC–600 AD
Diophantus of Alexandria; Hypatia of Alexandria
Hypatia and her mathematics
The evolution of mathematics in ancient China, Liu Hui and the first golden age of Chinese mathematics
Number systems of the North American Indians
The number systems of the Mayas
Before the conquest
Part II. Medieval and renaissance mathematics
The discovery of the series formula for π
Ideas of calculus in Islam and India
Was calculus invented in India?
An early iterative method for the determination of sin 1º
Leonardo of Pisa and his liber quadratorum
The algorists vs. the abacists: an ancient controversy on the use of calculators
Sidelights on the Cardan-Tartaglia controversy
Reading Bombelli's x-purgated algebra
The first work on mathematics printed in the New World
Part III. The Seventeenth Century
An application of geography to mathematics: history of the integral of the secant
Some historical notes on the cycloid
Descartes and problem-solving
Rene Descartes' curve-drawing devices: experiments in the relations between mechanical motion and symbolic language
Certain mathematical achievements of James Gregory
The changing concept of change: the derivative from Fermat to Weierstrauss
The crooked made straight: Roberval and Newton on tangents
On the discovery of the logarithmic series and its development in England up to Cotes
Isaac Newton: man, myth, and mathematics
Reading the master: Newton and the birth of celestial mechanics
Newton as an originator of polar coordinates
Newton's method for resolving affected equations
A contribution of Leibniz to the history of complex numbers
Functions of a curve: Leibniz's original notion of functions and its meaning for the parabola;
Part IV. The Eighteenth Century
Brook Taylor and the mathematical theory of Linear Perspective
Was Newton's calculus a dead end? The continental influence of Maclaurin's treatise of fluxions
Discussion of fluxions: from Berkeley to Woodhouse
The Bernoulli and the harmonic series
Leonhard Euler 1707–1783
The number
Euler's vision of a general partial differential calculus for a generalized kind of function
Euler and the fundamental theorem of algebra
Euler and the differentials
Euler and quadratic reciprocity
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