Stephen Hawking
Running Press | 2007 | 1375 páginas | rar - pdf | 6,9 Mb
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Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.
CONTENTS
Introduction xiii
EUCLID (C. 325BC–265BC)
His Life and Work 01
Selections from Euclid’s Elements
Book I: Basic Geometry—Definitions, Postulates, Common Notions; and Proposition 47, (leading up to the Pythagorean Theorem) 07
Book V: The Eudoxian Theory of Proportion—Definitions & Propositions 25
Book VII: Elementary Number Theory—Definitions & Propositions 63
Book IX: Proposition 20: The Infinitude of Prime Numbers 101
Book IX: Proposition 36: Even Perfect Numbers 102
Book X: Commensurable and Incommensurable Magnitudes 104
ARCHIMEDES (287BC–212BC)
His Life and Work 119
Selections from The Works of Archimedes
On the Sphere and Cylinder, Books I and II 126/168
Measurement of a Circle 194
The Sand Reckoner 200
The Methods 209
DIOPHANTUS (C. 200–284)
His Life and Work 241
Selections from Diophantus of Alexandria, A Study in the History of Greek Algebra
Book II Problems 8–35 246
Book III Problems 5–21 255
Book V Problems 1–29 265
RENÉ DESCARTES (1596–1650)
His Life and Work 285
The Geometry of Rene Descartes 292
ISAAC NEWTON (1642–1727)
His Life and Work 365
Selections from Principia
On First and Last Ratios of Quantities 374
LEONHARD EULER (1707–1783)
His Life and Work 383
On the sums of series of reciprocals (De summis serierum reciprocarum) 393
The Seven Bridges of Konigsberg 400
Proof that Every Integer is A Sum of Four Squares 407
PIERRE SIMON LAPLACE (1749–1827)
His Life and Work 411
A Philosophical Essay on Probabilities 418
JEAN BAPTISTE JOSEPH FOURIER (1768–1830)
His Life and Work 519
Selection from The Analytical Theory of Heat
Chapter III: Propagation of Heat in an Infinite Rectangular Solid (The Fourier series) 528
CARL FRIEDRICH GAUSS (1777–1855)
His Life and Work 591
Selections from Disquisitiones Arithmeticae (Arithmetic Disquisitions)
Section III Residues of Powers 599
Section IV Congruences of the Second Degree 625
AUGUSTIN-LOUIS CAUCHY (1789–1857)
His Life and Work 663
Selections from Oeuvres complètes d’Augustin Cauchy
Résumé des leçons données à l’École Royale Polytechnique sur le calcul infinitésimal (1823), series 2, vol. 4
Lessons 3–4 on differential calculus 671
Lessons 21–24 on the integral 679
NIKOLAI IVANOVICH LOBACHEVSKY (1792–1856)
His Life and Work 813
Geometrical Researches on the Theory of Parallels 820
JÁNOS BOLYAI (1802–1860)
His Life and Work 743
The Science of Absolute Space 750
ÉVARISTE GALOIS (1811–1832)
His Life and Work 797
On the conditions that an equation be soluble by radicals 807
Of the primitive equations which are soluble by radicals 820
On Groups and Equations and Abelian Integrals 828
GEORGE BOOLE (1815–1864)
His Life and Work 835
An Investigation of the Laws of Thought 842
BERNHARD RIEMANN (1826–1866)
His Life and Work 979
On the Representability of a Function by Means of a Trigonometric Series (Ueber die Darstellbarkeit eine Function durch einer trigonometrische Reihe) 992
On the Hypotheses which lie at the Bases of Geometry (Ueber die Hypothesen, welche der Geometrie zu Grunde liegen) 1031
On the Number of Prime Numbers Less than a Given Quantity (Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse) 1042
KARL WEIERSTRASS (1815–1897)
His Life and Work 1053
Selected Chapters on the Theory of Functions, Lecture Given in Berlin in 1886, with the Inaugural Academic Speech, Berlin 1857
§ 7 Gleichmässige Stetigkeit (Uniform Continuity) 1060
RICHARD DEDEKIND (1831–1916)
His Life and Work 1067
Essays on the Theory of Numbers 1072
GEORG CANTOR (1848–1918)
His Life and Work 1131
Selections from Contributions to the Founding of the Theory of Transfinite Numbers
Articles I and II 1137
HENRI LEBESGUE (1875–1941)
His Life and Work 1207
Selections from Integrale, Longeur, Aire (Intergral, Length, Area) Preliminaries and Integral 1212
KURT GÖDEL (1906–1978)
His Life and Work 1555
On Formally Undecidable Propositions of Principia Mathematica and Related Systems 1263
ALAN TURING (1912–1954)
His Life and Work 1285
On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society 1293
