Number Theory in Science and Communication

"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It 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...

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"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It 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 are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography.

From reviews of earlier editions –

"I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvellous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American)

"A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner

Front Matter
Pages I-XXIV
A Few Fundamentals
Front Matter
Pages 1-1
Introduction
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Front Matter
Pages I-XXIV
A Few Fundamentals
Front Matter
Pages 1-1
Introduction
Manfred Schroeder
Pages 3-20
The Natural Numbers
Manfred Schroeder
Pages 21-29
Primes
Manfred Schroeder
Pages 31-43
The Prime Distribution
Manfred Schroeder
Pages 45-69
Some Simple Applications
Front Matter
Pages 71-71
Fractions: Continued, Egyptian and Farey
Manfred Schroeder
Pages 73-107
Congruences and the Like
Front Matter
Pages 109-109
Linear Congruences
Manfred Schroeder
Pages 111-117
Diophantine Equations
Manfred Schroeder
Pages 119-137
The Theorems of Fermat Wilson and Euler
Manfred Schroeder
Pages 139-145
Permutations Cycles and Derangements
Manfred Schroeder
Pages 147-158
Cryptography and Divisors
Front Matter
Pages 159-159
Euler Trap Doors and Public-Key Encryption
Manfred Schroeder
Pages 161-170
The Divisor Functions
Manfred Schroeder
Pages 171-177
The Prime Divisor Functions
Manfred Schroeder
Pages 179-191
Certified Signatures
Manfred Schroeder
Pages 193-194
Primitive Roots
Manfred Schroeder
Pages 195-211
Knapsack Encryption
Manfred Schroeder
Pages 213-216
Residues and Diffraction
Front Matter
Pages 217-217
Quadratic Residues
Manfred Schroeder
Pages 219-232
Chinese and Other Fast Algorithms
Front Matter
Pages 233-233
The Chinese Remainder Theorem and Simultaneous Congruences
Manfred Schroeder
Pages 235-243
Fast Transformation and Kronecker Products
Manfred Schroeder
Pages 245-249
Quadratic Congruences
Manfred Schroeder
Pages 251-252
Pseudoprimes, Möbius Transform, and Partitions
Front Matter
Pages 253-253
Pseudoprimes Poker and Remote Coin Tossing
Manfred Schroeder
Pages 255-266
The Möbius Function and the Möbius Transform
Manfred Schroeder
Pages 267-274
Generating Functions and Partitions
Manfred Schroeder
Pages 275-282
From Error Correcting Codes to Covering Sets
Manfred Schroeder
Pages 283-285
Cyclotomy and Polynomials
Front Matter
Pages 287-287
Cyclotomic Polynomials
Manfred Schroeder
Pages 289-304
Linear Systems and Polynomials
Manfred Schroeder
Pages 305-307
Polynomial Theory
Manfred Schroeder
Pages 309-314
Galois Fields and More Applications
Front Matter
Pages 315-315
Galois Fields
Manfred Schroeder
Pages 317-329
Spectral Properties of Galois Sequences
Manfred Schroeder
Pages 331-345
Random Number Generators
Manfred Schroeder
Pages 347-353
Waveforms and Radiation Patterns
Manfred Schroeder
Pages 355-366
Number Theory Randomness and “Art”
Manfred Schroeder
Pages 367-375
Self-Similarity, Fractals and Art
Front Matter
Pages 377-377
Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter
Manfred Schroeder
Pages 379-403
Back Matter
Pages 405-418
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