Number Theory in Science and Communication, 3e / Edition 3

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Overview

Number Theory in Science and Communication is an introduction for non-mathematicians. The book stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world is one of the main themes of the book. This third edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.

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Product Details

  • ISBN-13: 9783540620068
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 5/28/1997
  • Series: Springer Series in Information Sciences
  • Edition description: REV
  • Edition number: 3
  • Pages: 363
  • Product dimensions: 6.14 (w) x 9.33 (h) x 0.75 (d)

Table of Contents

1 Introduction 1
2 The Natural Numbers 16
3 Primes 25
4 The Prime Distribution 38
5 Fractions: Continued, Egyptian and Farey 62
6 Linear Congruences 95
7 Diophantine Equations 102
8 The Theorems of Fermat, Wilson and Euler 118
9 Euler Trap Doors and Public-Key Encryption 125
10 The Divisor Functions 135
11 The Prime Divisor Functions 142
12 Certified Signatures 154
13 Primitive Roots 156
14 Knapsack Encryption 173
15 Quadratic Residues 177
16 The Chinese Remainder Theorem and Simultaneous Congruences 190
17 Fast Transformation and Kronecker Products 199
18 Quadratic Congruences 203
19 Pseudoprimes, Poker and Remote Coin Tossing 205
20 The Mobius Function and the Mobius Transform 216
21 Generating Functions and Partitions 224
22 Cyclotomic Polynomials 232
23 Linear Systems and Polynomials 247
24 Polynomial Theory 250
25 Galois Fields 256
26 Spectral Properties of Galois Sequences 269
27 Random Number Generators 283
28 Waveforms and Radiation Patterns 289
29 Number Theory, Randomness and "Art" 301
30 Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter 311
Glossary of Symbols 336
References 339
Name Index 351
Subject Index 355
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