Beyond Numeracy

JOHN ALLEN PAULOS

Introduction xi
A Mathematical Accent 3
Algebra-Some Basic Principles 7
Analytic Geometry 10
Arabic Numerals IS
Areas and Volumes 18
Binary Numbers and Codes , 24
Calculus 27
Chaos Theory 32
Coincidences 38
Combinatorics, Graphs, and Maps 42
Complexity of Programs 47
Computation and Rote 52
Correlation, Intervals, and Testing 56
Differential Equations 59
E 62
Mathematics in Ethics 66
Exponential Growth 71
Fermat's Last Theorem 75
Mathematical Folklore 78
Fractals 82
Functions 97
Game Theory
Godel and His Theorem 95
Golden Rectangle, Fibonacci Sequences 98
Groups and Abstract Algebra 102
Human Consciousness, Its Fractal Nature 107
Humor and Mathematics 112
Imaginary and Negative Numbers 115
Impossibilities-T'hree Old, Three New 118
Mathematical Induction 121
Infinite Sets 124
Limits 129
Linear Programming 133
Matrices and Vectors 136
Mean, Median, and Mode 141
M6bius Strips and Orientability 144
Monte Carlo Method of Simulation 147
The Multiplication Principle 150
Music, Art, and Digitalization 154
Non-Euclidean Geometry 1S8
Notation i63
Oulipo-Mathematics in Literature i66
Partial Orderings and Comparisons 168
Pascal's Triangle 171
Philosophy of Mathematics 17S
Pi 178
Platonic Solids 181
Prime Numbers 184
Probability 197
The Pythagorean Theorem 192
QED, Proofs, and Theorems 195
The Quadratic and Other Formulas 198
Quantifiers in Logic 202
Rational and Irrational Numbers 205
Recursion-From Definitions to Life 209
Russell's Paradox 214
Scientific Notation 218
Series-Convergence and Divergence 221
Sorting and Retrieving 225
Statistics-Two Theorems 227
Substitutability and More on Rote 231
Symmetry and Invariance 234
Tautologies and Truth Tables 237
Time, Space, and Immensity 241
Topology 246
Trigonometry 251
Turing's Test, Expert Systems 257
Variables and Pronouns 26o
Voting Systems 262
Zeno and Motion 266
Chronological Listing of the "Top Forty" 271
Suggested Readings 277
Index 281

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Beyond Numeracy

JOHN ALLEN PAULOS

CONTENTS