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From: jbuck@epimass.UUCP
Newsgroups: sci.math,sci.crypt
Subject: M. R. Schroeder's "Number Theory in Science and Communications"
Message-ID: <902@epimass.UUCP>
Date: Tue, 17-Feb-87 03:56:38 EST
Article-I.D.: epimass.902
Posted: Tue Feb 17 03:56:38 1987
Date-Received: Wed, 18-Feb-87 03:21:30 EST
Organization: Entropic Processing, Inc., Cupertino, CA
Lines: 29
Xref: watmath sci.math:567 sci.crypt:227

Matt "Phlame" Weiner recently tore into Morris Kline for saying,
among other things, that number theory had no applications.  Of
course sci.crypt readers are under no such delusions.

In this book Schroeder demonstrates the use of number-theoretic
concepts in acoustics, error-correcting codes, fast algorithms for
digital signal processing, fractals, radar, strange attractors, and
of course, cryptography.  His explanation of public-key cryptography
is particularly good.

The book is filled with interesting anecdotes.  For example, when
Heisenburg discovered "matrix" mechanics in 1925, he didn't know
what a matrix was, and didn't know what to make of it.  David Hilbert
suggested that he try to find a differential equation with the same
eigenvalues, if that would make him happier.  He didn't.  If he had,
he would have discovered the Schroedinger wave equation.

I do have one strong beef with him:  he blurs the distinction between
his own work and that of others, and doesn't give much credit to
contemporary researchers.  How can you spend a chapter explaining RSA
without mentioning the names R, S, and A (even in a reference?)  It
would have been very tricky to discuss fractals as much as he does
and say Mandelbrot's name fewer times.  I've seen him do this quite a
bit in other papers as well.  It helps to be dead; Gauss, Fermat, and
Euler get far more reverent treatment.  But in spite of this problem,
it's a very useful book.
-- 
- Joe Buck 	{hplabs,ihnp4,sun,ames}!oliveb!epimass!jbuck
  Entropic Processing, Inc., Cupertino, California