Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity (Springer Series in Information Sciences) [Paperback]

Manfred Schroeder (Author)

Book Description

ISBN-10: 3540620060 | ISBN-13: 978-3540620068 | Publication Date: May 20, 1997 | Edition: 3rd

Number Theory in Science and Communication is an introduction for non-mathematicians. The book 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 is one of the main themes of the book. This third 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.

Editorial Reviews

Review

From reviews of an 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

From the Back Cover

"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 --This text refers to the Hardcover edition.

Product Details

• Paperback: 400 pages
• Publisher: Springer; 3rd edition (May 20, 1997)
• Language: English
• ISBN-10: 3540620060
• ISBN-13: 978-3540620068
• Product Dimensions: 9.3 x 6.1 x 0.8 inches
• Shipping Weight: 1.5 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,651,006 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

3 of 4 people found the following review helpful:

4.0 out of 5 stars could have included some problems, January 28, 2007

By 

W Boudville (Terra, Sol 3) - See all my reviews
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This review is from: Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity (Springer Series in Information Sciences) (Hardcover)

[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.

0 of 3 people found the following review helpful:

4.0 out of 5 stars Good mix of theory and mathematics, February 27, 2009

By 

Sameer Yami (Silicon Valley, CA, USA) - See all my reviews
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This review is from: Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity (Springer Series in Information Sciences) (Paperback)

This book provides good examples and has a good mix of number theory and the associated mathematics. Very useful for people interested in cryptography and number theory in general.
However, this book is not easy to read and requires some effort to digest the given information.