Customer Reviews

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

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[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.

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.