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Number theory in science and communication : with applications in cryptography, physics, digital information, computing, and self-similarity

Author: M R Schroeder
Publisher: Berlin ; New York : Springer-Verlag, ©1986.
Series: Springer series in information sciences, 7.
Edition/Format:   Print book : English : 2nd enl. edView all editions and formats
Summary:

An introduction for nonmathematicians. The book stresses intuitive understanding rather than abstract theory. Concepts such as continued fractions, the golden ratio, quadratic residues, trapdoor  Read more...

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Additional Physical Format: Online version:
Schroeder, M.R. (Manfred Robert), 1926-
Number theory in science and communication.
Berlin ; New York : Springer-Verlag, ©1986
(OCoLC)626022227
Named Person: Hermann Minkowski
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: M R Schroeder
ISBN: 0387158006 9780387158006 3540158006 9783540158004
OCLC Number: 12341666
Notes: Includes indexes.
Description: xix, 374 pages : illustrations ; 24 cm.
Contents: pt. I.A few fundamentals. Introduction --
The natural numbers --
Primes --
The prime distribution --
pt. II. Some simple applications. Fractions: continued, Egyptian and Farey --
pt. III. Congruences and the like. Linear congruences --
Diophantine equations --
The theorems of Fermat, Wilson and Euler --
pt. IV. Cryptography and divisors. Euler trap doors and public-key encryption --
The divisor functions --
The prime divisor functions --
Certified signatures --
Primitive roots --
Knapsack encryption --
pt. V. Residues and diffraction. Quadratic residues --
pt. VI. Chinese and other fast algorithms. The Chinese remainder theorem and simultaneous congruences --
Fast transformations and Kronecker products --
Quadratic congruences --
pt. VII. Pseudoprimes, Möbius transform, and partitions. Pseudoprimes, poker and remote coin tossing --
The Möbius function and the Möbius transform --
Generating functions and partitions --
pt. VIII. Cyclotomy and polynomials. Cyclotomic polynomials --
Linear systems and polynomials --
Polynomial theory --
pt. IX. Galois fields and more applications. Galois fields --
Spectral properties of Galois sequences --
Random number generators --
Waveforms and radiation patterns --
Number theory, randomness and "art" --
pt. X. Self similarity, fractals and art. Self-similarity, fractals, deterministic chaos and a new state of matter --
Appendix. A.A calculator program for exponentiation and residue reduction --
B.A calculator program for calculating Fibonacci and Lucas numbers --
C.A calculator program for decomposing an integer according to the Fibonacci number system.
Series Title: Springer series in information sciences, 7.
Responsibility: M.R. Schroeder.
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..."A lighthearted and readable volume with a wide range of applications to which the author has been a productive contributor - useful mathematics given outside the formalities of theorem and Read more...

 
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