Item description for Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity (Springer Series in Information Sciences) by M.R. Schroeder...
"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 fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.
From reviews ofearlier 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
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Est. Packaging Dimensions: Length: 9.5" Width: 6.3" Height: 0.9" Weight: 1.6 lbs.
Release Date Dec 19, 2005
ISBN 3540265961 ISBN13 9783540265962
Reviews - What do customers think about Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity (Springer Series in Information Sciences)?
could have included some problems Jan 29, 2007
[A review of the 4th Edition 2006.]
It is possible when teaching number theory to drown the reader in theorems, lemmas and corrolaries. So much so that she can get lost in the thickets and fail to appreciate the broad motivating ideas. Schroeder refrains from such a presentation. He is certainly rigorous enough, when needed. But the book is a graceful exposition. Explaining key concepts and proving enough along the way to satisfy most readers.
So Euler, Fermat, Gauss and other luminaries make their appearance at numerous points. Along with the classic and still unproven Goldbach Conjecture. Many readers will probably turn to the sections on modern applications, notably in cryptography. The explanation of the public key algorithm is elegant.
Other applications include making random numbers. Something quite subtle and difficult to do well. And vitally necessary for cryptography.
The last chapter on fractals and self similar transformations is accompanied by a few pretty pictures of fractals and Julia sets in the plane. Though by now most readers must be familiar with fractal art.
The only drawback of the book is the lack of problems. Pity, as it reduces the book's suitability as an undergrad text.
Number theory for cryptoheads Feb 19, 1999
This is a great book for helping would-be cryptographers to convince other would-be cryptographers that they understand the number theory behind some of today's popular crypto algorithms. While not primarily a cryptography book, it does cover residues, Galois fields, primitive roots, indexes, and the Chinese Remainder Theorem. The book seems to expect the reader to have some minimal exposure to calculus, liner algebra, and statistics, as well as some modern physics. I highly recommend this book! Don't think, just buy it.
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