Number Theory in Science and Communication

Beschreibung

"Beauty is the first test: there is no permanent place in the world for ugly mathematics. " - G. H. Hardy Number theory has been considered since time immemorial to be the very paradigm of pure (some would say useless) mathematics. In fact, the Chinese characters for mathematics are Number Science. "Mathematics is the queen of sciences - and number theory is the queen of mathematics," according to Carl Friedrich Gauss, the lifelong Wunderkind, who himself enjoyed the epithet "Princeps Mathematicorum. " What could be more beautiful than a deep, satisfying relation between whole numbers. (One is almost tempted to call them wholesome numbers') In fact, it is hard to come up with a more appropriate designation than their learned name: the integers - meaning the "untouched ones". How high they rank, in the realms of pure thought and aesthetics, above their lesser brethren: the real and complex number- whose first names virtually exude unsavory involvement with the complex realities of everyday life! Yet, as we shall see in this book, the theory of integers can provide totally unexpected answers to real-world problems. In fact, discrete mathematics is taking on an ever more important role. If nothing else, the advent of the digital computer and digital communication has seen to that. But even earlier, in physics the emergence of quantum mechanics and discrete elementary particles put a premium on the methods and, indeed, the spirit of discrete mathematics.
Number Theory in Science and Communication is an introduction for nonmathematicians. The book stresses intuitive understanding rather than abstract theory. Important concepts such as continued fractions, the golden ratio, quadratic residues and chinese remainders, trapdoor functions, pseudoprimes and primitive elements are highlighted. Their application to problems in the real world is one of the main themes of the book. The second edition is augmented by recent advances in error-free computing, fractals, self-similarity, deterministic chaos and quasicrystals.

Autor*in

Manfred R. Schroeder

Themen in »Number Theory in Science and Communication«

Astrophysics Biology Digital Signal Processing Electrical Engineering Geophysics Medicine Physics and Mathematics communication system cryptography number theory sets

Stimmen zu »Number Theory in Science and Communication«

..."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 proof"... #Scientific American#1
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