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Zbl 1084.11002
Schroeder, Manfred R.
Number theory in science and communication. With applications in cryptography, physics, digital information, computing, and self-similarity. 4th ed. (English)
[B] Springer Series in Information Sciences 7. Berlin: Springer. xxvi, 367~p. EUR~59.95/net; sFr~106.00; \sterling~46.00; \$~79.95 (2006). ISBN 3-540-26596-1/hbk

This is the fourth edition of the classical title {\it 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".\par 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 provided at the end of the book.
[Juan Tena Ayuso (Valladolid)]

MSC 2000:: *11-01 Textbooks (number theory)
68-01 Textbooks (computer science)
94-01 Textbooks (information and communication)
11Axx Elementary number theory
11A41 Elementary prime number theory
11T22 Cyclotomy
11T71 Algebraic coding theory
11Y05 Factorization

Keywords: primes and pseudoprimes; continued fractions; congruences; cryptography; fast transforms; Galois fields; random number generators; self-similarity; fractals

Citations: Zbl 0997.11501; Zbl 0613.10001; Zbl 0542.10001

Cited in: Zbl 1152.11001

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