Book:William Dunham/Journey Through Genius

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 7S
 * Epilogue


 * CHAPTER 4 Archimedes' Determination of Circular Area (ca. 225 D.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) 1SS
 * Mathematics of the Heroic Century 1SS
 * A Mind Unleashed
 * Newton's Binomial Theorem 16S
 * 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