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