Higgins Number Story

From Counting to Cryptography
2008
ISBN: 978-1-84800-001-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 323 Seiten

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.

Autoren/Hrsg.

Higgins, Peter Michael

Inhaltsverzeichnis

1;Preface;9
2;The First Numbers;12
2.1;How Should We Think About Numbers?;16
2.2;The Structure of Numbers;19
3;Discovering Numbers;28
3.1;Counting and Its Consequences;34
4;Some Number Tricks;42
4.1;What Was the Domino?;45
4.2;Casting Out Nines;46
4.3;Divisibility Tests;50
4.4;Magical Arrays;60
4.5;Other Magic Number Arrays;68
5;Some Tricky Numbers;72
5.1;Catalan Numbers;76
5.2;Fibonacci Numbers;78
5.3;Stirling and Bell Numbers;83
5.4;Hailstone Numbers;86
5.5;The Primes;88
5.6;Lucky Numbers;95
6;Some Useful Numbers;96
6.1;Percentages, Ratios, and Odds;96
6.2;Scientific Notation;99
6.3;Meaning of Means;101
7;On the Trail of New Numbers;112
7.1;Pluses and Minuses;115
7.2;Fractions and Rationals;116
8;Glimpses of Infinity;128
8.1;The Hilbert Hotel;131
8.2;Cantor’s Comparisons;133
8.3;Structure of the Number Line;139
8.4;Infinity Plus One;144
9;Applications of Number: Chance;148
9.1;Some Examples;152
9.2;Some Collectable Problems on Chance;159
10;The Complex History of the Imaginary;176
10.1;Algebra and its History;179
10.2;Solution of the Cubic;185
11;From Imaginary to Complex;196
11.1;The Imaginary World Is Entered;200
11.2;The Polar System;206
11.3;Gaussian Integers;209
11.4;Glimpses of Further Consequences;211
12;The Number Line under the Microscope;220
12.1;Return to Egypt;223
12.2;Coin Problems, Sums, and Differences;227
12.3;Fibonacci and Fractions;232
12.4;Cantor’s Middle Third Set;236
13;Application of Number: Codes and Public Key Cryptography;240
13.1;Examples from History;241
13.2;Unbreakable Codes;249
13.3;New Codes for a New World of Coding;253
13.4;Simultaneous Key Creation;255
13.5;Opening the Trapdoor: Public Key Encryption;262
13.6;Alice and Bob Vanquish Eve with Modular Arithmetic;266
14;For Connoisseurs;274
14.1;Chapter 1;274
14.2;Chapter 3;279
14.3;Chapter 4;282
14.4;Chapter 5;292
14.5;Chapter 6;294
14.6;Chapter 7;300
14.7;Chapter 8;307
14.8;Chapter 9;311
14.9;Chapter 10;314
14.10;Chapter 11;320
14.11;Chapter 12;323
15;Further Reading;326
16;Index;330