Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity

This book illustrates the application of Number Theory to practical problems in physics, digital information processing. computing, cryptography, acoustics, crystallography (quasicrystals), fractals and self-similarity. Its aim is to widen the horizon of readers with a minimum of mathematicasl training to the basic facts of number theory. The otpics treated informally, stressing intuition rather then formal proofs. The book demonstrates that there are a surprising numbe rof applications of a field which is tradiationally considered raterh abstract, and from this realization readers are led to a depp appreciation of tzhe usefulness of finite mathematics and its multi-faeted interactions with the real world. The Second Edition includes much new material on self-similarity, factals, quasicrystals, Cantor sets, Hausdorff dimensions, detemrinicstic chaos, errof-free computation, spread-spectrum communication systems, optimal ambiguity functions for radar and sonar, and Fibonacci numbers. From the reviews "A lighthearted and readable volume with a wide range of applications to which the author has been a püroductive contributor - useful mathematics given outside the formalities of theorem and proof. Philip Morrison - Scientific American NTS***

"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography.

From reviews of earlier editions –

"I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvellous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American)

"A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner