God Created The Integers

by Hawking, Stephen

• ISBN13: 9780762419227
• ISBN10: 0762419229
• Format: Hardcover
• Copyright: 2005-10-03
• Publisher: Running Pr Book Pub
• More Book Details
• Purchase Benefits

Summary

From e-commerce to flying in airplanes and spacecraft, mathematics enables almost every aspect of our lives in this post-industrial age. But exactly what are the areas of mathematics that make these things possible? And just what was it that made someone sit up and think, 'I must solve this!'

Author Biography

Stephen Hawking’s ability to make science understandable and compelling to a lay audience was established with the publication of his first book, A Brief History of Time, which has sold nearly 10 million copies in 40 languages. Hawking has authored or participated in the creation of numerous other popular science books, including On the Shoulders of Giants and The Illustrated On the Shoulders of Giants.

Table of Contents

Introduction	xi
Euclid (c. 325BC-265BC) His Life and Work	01	(118)
Selections from Euclid's Elements
Book I: Basic Geometry---Definitions, Postulates, Common Notions and Proposition 47 (Leading up to the Pythagorean Theorem)	07	(18)
Book V: The Eudoxian Theory of Proportion---Definitions & Propositions	25	(38)
Book VII: Elementary Number Theory---Definitions & Propositions	63	(38)
Book IX: Proposition 20: The Infinitude of Prime Numbers	101	(1)
Book IX: Proposition 36: Even Perfect Numbers	102	(2)
Book X: Commensurable and Incommensurable Magnitudes	104	(15)
Archimedes (287BC-212BC) His Life and Work	119	(122)
Selections from The Works of Archimedes
On the Sphere and Cylinder, Book I	126	(42)
On the Sphere and Cylinder, Book II	168	(26)
Measurement of a Circle	194	(6)
The Sand Reckoner	200	(9)
The Methods	209	(32)
Diophantus (Third Century AD) His Life and Work	241	(44)
Selections from Diophantus of Alexandria, A Study in the History of Greek Algebra
Book II Problems 8-35	246	(9)
Book III Problems 5-21	255	(10)
Book V Problems 1-29	265	(20)
Rene Descartes (1596-1650) His Life and Work	285	(80)
The Geometry of Rene Descartes	292	(73)
Isaac Newton (1642-1727) His Life and Work	365	(18)
Selections from Principia
Book I: Of the Motion of Bodies	374	(9)
Pierre Simon De Laplace (1749-1827) His Life and Work	383	(108)
A Philosophical Essay on Probabilities	390	(101)
Jean Baptiste Joseph Fourier (1768-1830) His Life and Work	491	(72)
Selection from The Analytical Theory of Heat
Propagation of Heat in an Infinite Rectangular Solid (The Fourier series)	500	(63)
Carl Friedrich Gauss (1777-1855) His Life and Work	563	(72)
Selections from Disquisitiones Arithmeticae (Arithmetic Disquisitions)
Section III Residues of Powers	571	(26)
Section IV Congruences of the Second Degree	597	(38)
Augustin-Louis Cauchy (1789-1857) His Life and Work	635	(34)
Selection from Oeuvres completes d'Augustin Cauchy
Resume des lecons donnees a l'Ecole Royale Polytechnique sur le calcul infinitesimal (1823), series 2, vol. 4
Lessons 3--4 on differential calculus	643	(8)
Lessons 21--24 on the integral	651	(18)
George Boole (1815-1864) His Life and Work	669	(144)
An Investigation of the Laws of Thought	676	(137)
Georg Friedrich Bernhard Riemann (1826-1866) His Life and Work	813	(74)
On the Representability of a Function by Means of a Trigonometric Series (Ueber die Darstellbarkeit einer Function durch einer trigonometrische Reihe)	826	(39)
On the Hypotheses which lie at the Bases of Geometry (Ueber die Hypothesen welche der Geometrie zu Grundle liegen)	865	(11)
On the Number of Prime Numbers Less than a Given Quantity (Ueber di Anzahl of Primzahlen unter eine gegeben Grosse)	876	(11)
Karl Weierstrass (1815-1897) His Life and Work	887	(14)
A Theory of Functions (Lecture Given in Berlin in 1886, with the Inaugural Academic Speech, Berlin 1857)
§7 Uniform Continuity (Gleichmassige Stetigkeit)	894	(7)
Richard Julius Wilhelm Dedekind (1831-1916) His Life and Work	901	(64)
Essays on the Theory of Numbers	906	(59)
Georg Cantor (1845-1918) His Life and Work	965	(76)
Selections from Contributions to the Founding of the Theory of Transfinite Numbers
Articles I and II	971	(70)
Henri Lebesgue (1875-1941) His Life and Work	1041	(48)
Selections from Integrale, Longeur, Aire (Intergral, Length, Area)	1046	(43)
Kurt Godel (1906-1978) His Life and Work	1089	(30)
On Formally Undecidable Propositions of Principia Mathematica and Related Systems	1097	(22)
Alan Mathison Turing (1912-1954) His Life and Work	1119	(8)
On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society	1127