Book:William Dunham/Journey Through Genius

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William Dunham: Journey Through Genius: The Great Theorems of Mathematics

Published $\text {1990}$, Wiley Science Editions

ISBN 978-0-140-14739-1.


Subject Matter

  • History of Mathematics


Contents

PREFACE
ACKNOWLEDGMENTS
chapter $1$ Hippocrates' Quadrature of the Lune (ca. 440 b.c.)
The Appearance of Demonstrative Mathematics
Some Remarks on Quadrature
Great Theorem
Epilogue
chapter $2$ Euclid's Proof of the Pythagorean Theorem (ca. 300 b.c.)
The Elements of Euclid
Book I: Preliminaries
Book I: The Early Propositions
Book I: Parallelism and Related Topics
Great Theorem
Epilogue
chapter $3$ Euclid and the Infinitude of Primes (ca. 300 b.c.)
The Elements, Books II-VI
Number Theory in Euclid
Great Theorem
The Final Books of the Elements
Epilogue
chapter $4$ Archimedes' Determination of Circular Area (ca. 225 b.c.)
The Life of Archimedes
Great Theorem
Archimedes' Masterpiece: On the Sphere and tbe Cylinder
Epilogue
chapter $5$ Heron's Formula for Triangular Area (ca. a.d. 75)
Classical Mathematics after Archimedes
Great Theorem
Epilogue
chapter $6$ Cardano and the Solution of the Cubic (1545)
A Horatio Algebra Story
Great Theorem
Funher Topics on Solving Equations
Epilogue
chapter $7$ A Gem from Isaac Newton (Late 1660s)
Mathematics of the Heroic Century
A Mind Unleashed
Newton's Binomial Theorem
Great Theorem
Epilogue
chapter $8$ The Bemoullis and the Harmonic Series (1689)
The Contributions of Leibniz
The Brothers Bernoulli
Great Theorem
The Challenge of the Brachistochrone
Epilogue
chapter $9$ The Extraordinary Sums of Leonhard Euler (1734)
The Master of All Mathematical Trades
Great Theorem
Epilogue
chapter $10$ A Sampler of Euler's Number Theory (1736)
The Legacy of Fermat
Great Theorem
Epilogue
chapter $11$ The Non-Denumerability of the Continuum (1874)
Mathematics of the Nineteenth Century
Cantor and the Challenge of the Infinite
Great Theorem
Epilogue
chapter $12$ Cantor and the Transfinite Realm (1891)
The Nature of Infinite Cardinals
Great Theorem
Epilogue
AFTERWORD
CHAPTER NOTES
REFERENCES
INDEX