Introduction vii
I Foundations 1
1 This Tomb Holds Diophantus 3
2 The Irrational and the Transcendental 13
3 Centuries of Progress 35
II Computable Numbers 55
4 The Education of Alan Turing 57
5 Machines at Work 79
6 Addition and Multiplication 97
7 Also Known as Subroutines 111
8 Everything Is a Number 127
9 The Universal Machine 143
10 Computers and Computability 163
11 Of Machines and Men 189
III Das Entscheidungsproblem 199
12 Logic and Computability 201
13 Computable Functions 231
14 The Major Proof 259
15 The Lambda Calculus 281
16 Conceiving the Continuum 299
IV And Beyond 323
17 Is Everything a Turing Machine? 325
18 The Long Sleep of Diophantus 351
Selected Bibliography 361
Index 366
English mathematician Alan Turing (1912–1954) is the author of the 1936 paper "On Computable Numbers, with an Application to the Entscheidungsproblem" that introduced the imaginary computer called the Turing Machine for understanding the nature and limitations of computing. His famous 1950 article "Computing Machinery and Intelligence" introduced the Turing Test for gauging artificial intelligence.
American writer Charles Petzold (1953–) is the author of the acclaimed 1999 book Code: The Hidden Language of Computer Hardware and Software, a unique exploration into the digital technologies of computers. He is also the author of hundreds of articles about computer programming, as well as several books on writing programs that run under Microsoft Windows. His Web site is www.charlespetzold.com.
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