Mathematics: An Illustrated History of Numbers

Description

Introduction Prehistory to the Middle Ages 1 Learning to Count 2 Positional Notation 3 The Abacus 4 Pythagoras Theorem 5 The Rhind Papyrus 6 Zero 7 The Math of Music 8 The Golden Ratio 9 Platonic Solids 10 Logic 11 Geometry 12 Magic Squares 13 Prime Numbers 14 Pi 15 Measuring the Earth 16 The Powers of Ten 17 The Modern Calendar 18 Diophantine Equations 19 Hindu-Arabic Number System 20 Algorithms 21 Cryptography 22 Algebra 23 Fibonacci Sequence The Renaissance and the Age of Enlightenment 24 Perspective Geometry 25 Non-Linear Equations 26 Pendulum Law 27 x and y 28 Ellipses 29 Logarithms 30 Napier's Bones 31 Slide Rule 32 Complex Numbers 33 Cartesian Coordinates 34 Laws of Fall 35 Calculators 36 Pascal's Triangle 37 Chance 38 Principle of Induction 39 Calculus 40 Math of Gravity 41 Binary Numbers New Numbers, New Theories 42 e 43 Graph Theory 44 Three-Body Problem 45 Euler's Identity 46 Bayes' Theorem 47 Maskelyne and the Personal Equation 48 Malthusianism 49 Fundamental Theorem of Algebra 50 Perturbation Theory 51 Central Limit Theorem 52 Fourier Analysis 53 The Mechanical Computer 54 Bessel Function 55 Group Theory 56 Non-Euclidean Geometry 57 The Average Person 58 The Poisson Distribution 59 Quaternions 60 Transcendental Numbers 61 Finding Neptune 62 Fechner-Weber Law 63 Boolean Algebra 64 Maxwell-Boltzmann 65 Defining Irrationals 66 Infinity 67 Set Theory 68 Peano Axioms 69 Simple Lie Groups 70 Statistical Techniques Modern Mathematics 71 Topology 72 A New Geometry 73 Hilbert's 23 Problems 74 Mass Energy 75 Markov Chains 76 Population Genetics 77 Foundations of Mathematics 78 General Relativity 79 The Mathematics of Quantum Physics 80 Gbdel's Theorem 81 Turing Machine 82 Fields Medals 83 Zuse and the Electronic Computer 84 Game Theory 85 Information Theory 86 Geodesics 87 Chaos Theory 88 String Theory 89 Catastrophe Theory 90 Four-Color Theorem 91 Public Key Encryption 92 Fractals 93 The Fourth Dimension and Beyond 94 Classification of all Simple Finite Groups 95 Self-Organized Criticality 96 Fermat's Last Theorem 97 Proof by Computer 98 Millennium Problems 99 Poincare Conjecture 100 The Search for Mersenne Primes 101 Mathematics: a guide Imponderables The Great Mathematicians Bibliography and Other Resources Index Acknowledgements