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Number Story - From Counting to Cryptography
of: Peter Michael Higgins
Copernicus, 2008
ISBN: 9781848000018 , 323 Pages
Format: PDF, Read online
Copy protection: DRM
Preface
9
The First Numbers
12
How Should We Think About Numbers?
16
The Structure of Numbers
19
Discovering Numbers
28
Counting and Its Consequences
34
Some Number Tricks
42
What Was the Domino?
45
Casting Out Nines
46
Divisibility Tests
50
Magical Arrays
60
Other Magic Number Arrays
68
Some Tricky Numbers
72
Catalan Numbers
76
Fibonacci Numbers
78
Stirling and Bell Numbers
83
Hailstone Numbers
86
The Primes
88
Lucky Numbers
95
Some Useful Numbers
96
Percentages, Ratios, and Odds
96
Scientific Notation
99
Meaning of Means
101
On the Trail of New Numbers
112
Pluses and Minuses
115
Fractions and Rationals
116
Glimpses of Infinity
128
The Hilbert Hotel
131
Cantor’s Comparisons
133
Structure of the Number Line
139
Infinity Plus One
144
Applications of Number: Chance
148
Some Examples
152
Some Collectable Problems on Chance
159
The Complex History of the Imaginary
176
Algebra and its History
179
Solution of the Cubic
185
From Imaginary to Complex
196
The Imaginary World Is Entered
200
The Polar System
206
Gaussian Integers
209
Glimpses of Further Consequences
211
The Number Line under the Microscope
220
Return to Egypt
223
Coin Problems, Sums, and Differences
227
Fibonacci and Fractions
232
Cantor’s Middle Third Set
236
Application of Number: Codes and Public Key Cryptography
240
Examples from History
241
Unbreakable Codes
249
New Codes for a New World of Coding
253
Simultaneous Key Creation
255
Opening the Trapdoor: Public Key Encryption
262
Alice and Bob Vanquish Eve with Modular Arithmetic
266
For Connoisseurs
274
Chapter 1
274
Chapter 3
279
Chapter 4
282
Chapter 5
292
Chapter 6
294
Chapter 7
300
Chapter 8
307
Chapter 9
311
Chapter 10
314
Chapter 11
320
Chapter 12
323
Further Reading
326
Index
330
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