Critical Appraisal of Physical Science As a Human Enterprise by
Introduction
Quantitative imperative vs the imperative of presuppositions
Understanding scientific progress: From Duhem to Lakatos
Kinetic theory: Maxwell’s Presuppositions
Periodic table of the chemical elements: From Mendeleev to Moseley
Foundations of modern atomic theory: Thomson, Rutherford, and Bohr
Determination of the elementary electrical charge: Millikan and Ehrenhaft
Paradox of the photoelectric effect: Einstein and Millikan
Bending of light in the 1919 eclipse experiments: Einstein and Eddington
Lewis’s covalent bond: From transfer of electrons to sharing of electrons
Quantum mechanics: From Bohr to Bohm
Wave-particle duality: De Broglie, Einstein and Schrödinger
Searching for quarks: Perl’s philosophy of speculative experiments
Conclusion: Inductive method as a chimera
Great Physicists: the life and times of leading physicists from Galileo to Hawking by
I. Mechanics
Historical Synopsis
How the Heavens Go Galileo Galilei
A Man Obsessed Isaac Newton
II Thermodynamics
Historical Synopsis
A Tale of Two Revolutions Sadi Carnot
On the Dark Side Robert Mayer
A Holy Undertaking James Joule
Unities and a Unifier Hermann Helmholtz
The Scientist as Virtuoso William Thomson
The Road to Entropy Rudolf Clausius
The Greatest Simplicity Willard Gibbs
The Last Law Walther Nernst
III. Electromagnetism
Historical Synopsis
A Force of Nature Michael Faraday
The Scientist as Magician James ClerkMaxwell
IV. Statistical Mechanics
Historical Synopsis
Molecules and Entropy Ludwig Boltzmann
V. Relativity
Historical Synopsis
Adventure in Thought Albert Einstein
VI. Quantum Mechanics
Historical Synopsis
Reluctant Revolutionary Max Planck
Science by Conversation Niels Bohr
The Scientist as Critic Wolfgang Pauli
Matrix Mechanics Werner Heisenberg
Wave Mechanics Erwin Schrodinger and Louis de Broglie
VII. Nuclear Physics
Historical Synopsis
Opening Doors Marie Curie
On the Crest of a Wave Ernest Rutherford
Physics and Friendships Lise Meitner
Complete Physicist Enrico Fermi
VIII. Particle Physics
Historical Synopsis
What Do You Care? Richard Feynman
Telling the Tale of the Quarks Murray Gell-Mann
IX. Astronomy, Astrophysics, and Cosmology
Historical Synopsis
Beyond the Galaxy Edwin Hubble
Ideal Scholar Subrahmanyan Chandrasekhar
Affliction, Fame, and Fortune Stephen Hawking
Chronology of the Main Events
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 Its History by
The Theorem of Pythagoras
Greek Geometry
Greek Number Theory
Infinity in Greek Mathematics
Number Theory in Asia
Polynomial Equations
Analytic Geometry
Projective Geometry
Calculus
Infinite Series
The Number Theory Revival
Elliptic Functions
Mechanics
Complex Numbers in Algebra
Complex Numbers and Curves
Complex Numbers and Functions
Differential Geometry
Non-Euclidean Geometry
Group Theory
Hypercomplex Numbers
Algebraic Number Theory
Topology
Simple Groups
Sets, Logic, and Computation
Combinatorics
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
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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