The unreasonable effectiveness of number theory in science and communication (1987 Rayleigh Lecture)

Author

Schroeder, M.R.

Volume

5

Issue

1

fYear

1988

Firstpage

5

Lastpage

12

Abstract

A brief overview is given of the role of integers and integer relationships in the science. The effectiveness of discrete mathematics in physics, music, and communication (and its negation, cryptography) is examined. The discussion covers: numbers and musical scales; concert halls and quadratic residues; wave diffraction and primitive roots; forbidding property of Fermat primes; Euler totients and cryptography; uses of finite fields; error correction codes from Galois fields; correlation and Fourier properties of Galois sequences; Galois sequences and the fourth effect of general relativity; and Chinese remainders feed fast algorithm.<>

Keywords

cryptography; number theory; Chinese remainders feed fast algorithm; Euler totients; Fermat primes; Galois fields; concert halls; cryptography; discrete mathematics; error correction codes; finite fields; forbidding property; general relativity; integers; musical scales; number theory; primitive roots; quadratic residues; wave diffraction; Argon; Books; Cryptography; Gaussian processes; Mathematics; Medals; Physics; Quantum mechanics; Rayleigh scattering; Surface waves;

fLanguage

English

Journal_Title

ASSP Magazine, IEEE

Publisher

ieee

ISSN

0740-7467

Type

jour

DOI

10.1109/53.661

Filename

661