: Peter Michael Higgins
: Number Story From Counting to Cryptography
: Copernicus
: 9781848000018
: 1
: CHF 17.60
:
: Naturwissenschaft
: English
: 323
: Wasserzeichen/DRM
: PC/MAC/eReader/Tablet
: PDF

Peter Higgins distills centuries of work into one delightful narrative that celebrates the mystery of numbers and explains how different kinds of numbers arose and why they are useful. Full of historical snippets and interesting examples, the book ranges from simple number puzzles and magic tricks, to showing how ideas about numbers relate to real-world problems. This fascinating book will inspire and entertain readers across a range of abilities. Easy material is blended with more challenging ideas. As our understanding of numbers continues to evolve, this book invites us to rediscover the mystery and beauty of numbers.



Peter Higgins is a Professor of Mathematics at Essex University and inventor of Circular Sudoku. His previous books on mathematics include Mathematics for the Curious, Mathematics for the Imagination, and Nets, Puzzles and Postmen: An Exploration of Mathematical Connections.
Preface9
The First Numbers12
How Should We Think About Numbers?16
The Structure of Numbers19
Discovering Numbers28
Counting and Its Consequences34
Some Number Tricks42
What Was the Domino?45
Casting Out Nines46
Divisibility Tests50
Magical Arrays60
Other Magic Number Arrays68
Some Tricky Numbers72
Catalan Numbers76
Fibonacci Numbers78
Stirling and Bell Numbers83
Hailstone Numbers86
The Primes88
Lucky Numbers95
Some Useful Numbers96
Percentages, Ratios, and Odds96
Scientific Notation99
Meaning of Means101
On the Trail of New Numbers112
Pluses and Minuses115
Fractions and Rationals116
Glimpses of Infinity128
The Hilbert Hotel131
Cantor’s Comparisons133
Structure of the Number Line139
Infinity Plus One144
Applications of Number: Chance148
Some Examples152
Some Collectable Problems on Chance159
The Complex History of the Imaginary176
Algebra and its History179
Solution of the Cubic185
From Imaginary to Complex196
The Imaginary World Is Entered200
The Polar System206
Gaussian Integers209
Glimpses of Further Consequences211
The Number Line under the Microscope220
Return to Egypt223
Coin Problems, Sums, and Differences227
Fibonacci and Fractions232
Cantor’s Middle Third Set236
Application of Number: Codes and Public Key Cryptography240
Examples from History241
Unbreakable Codes249
New Codes for a New World of Coding253
Simultaneous Key Creation255
Opening the Trapdoor: Public Key Encryption262
Alice and Bob Vanquish Eve with Modular Arithmetic266
For Connoisseurs274
Chapter 1274
Chapter 3279
Chapter 4282
Chapter 5292
Chapter 6294
Chapter 7300
Chapter 8307
Chapter 9311
Chapter 10314
Chapter 11320
Chapter 12323
Further Reading326
Index330