Journey through genius : the great theorems of mathematics / William Dunham.
Editor: New York : Penguin Books, 1991, c1990Descripción: xiii, 300 p, : il. ; 20 cmISBN: 9780140147391 (pbk.)Otro título: Great theorems of mathematicsOtra clasificación: 00A05 (01A05)PREFACE V ACKNOWLEDGMENTS ix chapter 1 Hippocrates' Quadrature of the Lune (ca. 440 b.c.) [1] The Appearance of Demonstrative Mathematics [1] Some Remarks on Quadrature [11] Great Theorem [17] Epilogue [20] chapter 2 Euclid’s Proof of the Pythagorean Theorem (ca. 300 b.c.) [27] The Elements of Euclid [27] Book I: Preliminaries [32] Book I: The Early Propositions [37] Book I: Parallelism and Related Topics [44] Great Theorem [48] Epilogue [53] 3 Euclid and the Infinitude of Primes (a. 300 b.c.) [61] The Elements, Books II—VI [61] Number Theory in Euclid [68] Great Theorem [73] The Final Books of the Elements 75 Epilogue [81] chapter 4 Archimedes' Determination of Circular Area (ca. 225 b.c.) [84] The Life of Archimedes [84] Great Theorem [89] Archimedes’ Masterpiece: On the Sphere and the Cylinder 99 Epilogue [106] chapter 5 Heron’s Formula for Triangular Area (ca. a.d. 75) [113] Classical Mathematics after Archimedes [113] Great Theorem [118] Epilogue [127] chapter 6 Cardano and the Solution of the Cubic (1545) [133] A Horatio Algebra Story 133 Great Theorem [142] Further Topics on Solving Equations [147] Epilogue [151] chapter 7 A Gem from Isaac Newton (Late 1660s) [155] Mathematics of the Heroic Century [155] A Mind Unleashed [160] Newton’s Binomial Theorem [165] Great Theorem [174] Epilogue [177] chapter 8 The Bernoullis and the Harmonic Series (1689) [184] The Contributions of Leibniz [184] The Brothers Bernoulli [191] Great Theorem [196] The Challenge of the Brachistochrone 199 Epilogue [202] chapter 9 The Extraordinary Sums of Leonhard Euler (1734) [207] The Master of All Mathematical Trades [207] Great Theorem [212] Epilogue [218] chapter 10 A Sampler of Euler’s Number Theory (1736) [223] The Legacy of Fermat 223 Great Theorem 229 Epilogue [235] chapter 11 The Non-Denumerability of the Continuum (1874) [245] Mathematics of the Nineteenth Century [245] Cantor and the Challenge of the Infinite [251] Great Theorem [259] Epilogue [265] chapter 12 Cantor and the Transfinite Realm (1891) [267] The Nature of Infinite Cardinals [267] Great Theorem [274] Epilogue [281] AFTERWORD [285] CHAPTER NOTES [287] REFERENCES [291] INDEX [295]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | 00A05 D917 (Browse shelf) | Available | A-8714 |
Publicado previamente por John Wiley & Sons, 1990.
Incluye referencias bibliográficas (p. 291-293) e índice.
PREFACE V --
ACKNOWLEDGMENTS ix --
chapter 1 Hippocrates' Quadrature of the Lune (ca. 440 b.c.) [1] --
The Appearance of Demonstrative Mathematics [1] --
Some Remarks on Quadrature [11] --
Great Theorem [17] --
Epilogue [20] --
chapter 2 Euclid’s Proof of the Pythagorean Theorem (ca. 300 b.c.) [27] --
The Elements of Euclid [27] --
Book I: Preliminaries [32] --
Book I: The Early Propositions [37] --
Book I: Parallelism and Related Topics [44] --
Great Theorem [48] --
Epilogue [53] --
3 Euclid and the Infinitude of Primes (a. 300 b.c.) [61] --
The Elements, Books II—VI [61] --
Number Theory in Euclid [68] --
Great Theorem [73] --
The Final Books of the Elements 75 Epilogue [81] --
chapter 4 Archimedes' Determination of Circular Area (ca. 225 b.c.) [84] --
The Life of Archimedes [84] --
Great Theorem [89] --
Archimedes’ Masterpiece: On the Sphere and the Cylinder 99 Epilogue [106] --
chapter 5 Heron’s Formula for Triangular Area (ca. a.d. 75) [113] --
Classical Mathematics after Archimedes [113] --
Great Theorem [118] --
Epilogue [127] --
chapter 6 Cardano and the Solution of the Cubic (1545) [133] --
A Horatio Algebra Story 133 Great Theorem [142] --
Further Topics on Solving Equations [147] --
Epilogue [151] --
chapter 7 A Gem from Isaac Newton (Late 1660s) [155] --
Mathematics of the Heroic Century [155] --
A Mind Unleashed [160] --
Newton’s Binomial Theorem [165] --
Great Theorem [174] --
Epilogue [177] --
chapter 8 The Bernoullis and the Harmonic Series (1689) [184] --
The Contributions of Leibniz [184] --
The Brothers Bernoulli [191] --
Great Theorem [196] --
The Challenge of the Brachistochrone 199 Epilogue [202] --
chapter 9 The Extraordinary Sums of Leonhard Euler (1734) [207] --
The Master of All Mathematical Trades [207] --
Great Theorem [212] --
Epilogue [218] --
chapter 10 A Sampler of Euler’s Number Theory (1736) [223] --
The Legacy of Fermat 223 Great Theorem 229 Epilogue [235] --
chapter 11 The Non-Denumerability of the Continuum (1874) [245] --
Mathematics of the Nineteenth Century [245] --
Cantor and the Challenge of the Infinite [251] --
Great Theorem [259] --
Epilogue [265] --
chapter 12 Cantor and the Transfinite Realm (1891) [267] --
The Nature of Infinite Cardinals [267] --
Great Theorem [274] --
Epilogue [281] --
AFTERWORD [285] --
CHAPTER NOTES [287] --
REFERENCES [291] --
INDEX [295] --
MR, 92k:00008
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