Number theory in science and communication. With applications in cryptography, physics, digital information, computing, and self-similarity
type: Item
instance of: scholarly article
title: Number theory in science and communication. With applications in cryptography, physics, digital information, computing, and self-similarity
zbMATH Open document ID: 1084.11002
published in: Springer Series in Information Sciences
publication date: 2006-02-28T00:00:00Z
review text: This is the fourth edition of the classical title \textit{Number Theory in Science and Communication} (for a review of the previous editions see Zbl 0997.11501, Zbl 0613.10001 and Zbl 0542.10001) written by a physicist ``inclined toward mathematics''. Obviously his idea of Number Theory is opposed to the famous of G. H. Hardy (``\dots there is one science [number theory] whose very remoteness from ordinary human activities should keep it gentle and clean'', A Mathematician's Apology). As the title makes clear the author considers Number Theory related to ``ordinary human activities'' and the aim of the book is to show some of such interrelations in domains like Information Transmission, Concert Hall Acoustics and many others. The book has 30 chapters divided into ten parts whose titles allow an image of the contents of the book: Part I. A Few Fundamentals (Natural Numbers, Primes); Part II. Some Simple Applications (Fractions: Continued, Egyptians and Farey); Part III. Congruences and the Like; Part IV. Cryptography and Divisors (Public-Key Cryptography, Primitive Roots); Part V. Residues and Diffraction; Part VI. Chinese and other Fast Algorithms; Part VII. Pseudoprimes, Möbius Transform and Partitions); Part VIII. Cyclotomy and Polynomials; Part IX. Galois Fields and More Applications (Spectral Properties of Galois Sequences, Random Number Generators, Waveforms and Radiation Patterns, Number Theory, Randomness and ``Art''); Part X. Self-Similarity, Fractals and Art. In this fourth edition new materials have been added on Fibonacci Numbers, Divisibility Tests for 7, 13, 17 and 19, Two Square Theorem, new Factoring Methods (the Lenstra's Factoring with Elliptic Curves) and Primality Tests. The book intends to be self-contained and the definitions and materials of Number Theory are introduced and studied when they are needed, always with a view to showing their relationship and applications in the ``real world''. References to the contents of each chapter are provide…
Mathematics Subject Classification ID: 11-01
Mathematics Subject Classification ID: 68-01
Mathematics Subject Classification ID: 94-01
Mathematics Subject Classification ID: 11Axx
Mathematics Subject Classification ID: 11A41
Mathematics Subject Classification ID: 11T22
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 11Y05
zbMATH DE Number: 5009166
zbMATH Keywords: primes and pseudoprimes
zbMATH Keywords: continued fractions
zbMATH Keywords: congruences
zbMATH Keywords: cryptography
zbMATH Keywords: fast transforms
zbMATH Keywords: Galois fields
zbMATH Keywords: random number generators
zbMATH Keywords: self-similarity
zbMATH Keywords: fractals
author: Manfred R. Schroeder
reviewed by: Juan Tena Ayuso
MaRDI profile type: Publication
full work available at URL: b137861
OpenAlex ID: W4317522997
DOI: 10.1007/B137861
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description: scientific article; zbMATH DE number 5009166