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An Introduction to Symbolic Dynamics and Coding, by Douglas Lind, Brian Marcus
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Symbolic dynamics is a rapidly growing area of dynamical systems. Although it originated as a method to study general dynamical systems, it has found significant uses in coding for data storage and transmission as well as in linear algebra. This book is the first general textbook on symbolic dynamics and its applications to coding. Mathematical prerequisites are relatively modest (mainly linear algebra at the undergraduate level) especially for the first half of the book. Topics are carefully developed and motivated with many examples, and there are over 500 exercises to test the reader's understanding. The last chapter contains a survey of more advanced topics, and a comprehensive bibliography is included. This book will serve as an introduction to symbolic dynamics for advanced undergraduate students in mathematics, engineering, and computer science.
- Sales Rank: #1781767 in Books
- Brand: Brand: Cambridge University Press
- Published on: 1995-11-24
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.14" w x 6.14" l, 1.68 pounds
- Binding: Paperback
- 516 pages
- Used Book in Good Condition
Review
"The book is well organized, and lucidly written. It is completely rigorous and yet easy to read....There is a wealth of examples illustrating the definitions and theorems. They are very instructive in helping to understand the principles involved in the proofs. There are also many exercises ranging from simple verifications to hard problems. The book is to be recommended both as an introductory textbook and as a standard reference in the field." Petr Kurka, Mathematical Reviews
"The presentation combines the necessary rigor with a lucidity that makes this book a pleasure to read. It is not only an excellent text for an introductory course, but should be well suited for self-study." F.W. Stallmann, Computing Reviews
"The book is a model of organization and clarity, consistent in pace and tone, with very few errata....The book aims to be accessible to engineers and even strong undergraduates, and the mathematical prerequisites are correspondingly modest....I was pleased with it as a the main source for a one-semester graduate course, supplemented with more advanced material....the book is a very fine and broadly accessible introduction to symbolic dynamics and coding." Mike Boyle, Siam Review
Most helpful customer reviews
0 of 0 people found the following review helpful.
Fantastic Introductory text
By K
I was introduced to symbolic dynamics through a preliminary study of chaotic dynamical systems, and to satisfy my interest in the subject, took an independent study course on what I lovingly refer to as "Symba" as an undergraduate, using this textbook. Doug Lind and Brian Marcus have done a fantastic job at introducing and motivating the subject, and have placed some very well thought-out exercises after each section. The text gradually advances to some heavier material, so it's fit for undergraduates and graduate students who have a good grasp of abstract algebra (and maybe some graph theory). Though some of the examples are a bit outdated now (e.g. the section dealing with the Road Coloring Problem which has been solved), they remain quite illustrative and interesting.
4 of 4 people found the following review helpful.
Dense but well-written
By Bobby Winters
It is late March as I write this. I have been reading the book since mid-January and have made it to page 77. This is in spite of the fact that I put in about 10 hours a week on it. The bulk of the time is spent learning the language for new concepts. I am pleased with the book in that it does an excellent job of foreshadowing those concepts in the wonderful examples and in the exercises.
I would give the advice to do as many of the exercises as possible while continuing to read ahead. If you do this, you will be prepare for what is to come, but you will be less likely to get bogged down.
I began this book because I wanted to understand entropy. It looks as if I will be well-prepared for that when I get to the topic in a few more weeks. It is only about 20 or so more pages away.
2 of 4 people found the following review helpful.
very dense
By theskeptic
Well, this seems to be the only textbook on the topic of Symbolic Dynamics, but I think it fails as an "introduction". The initial chapter provides very little motivation for the use of Symbolic Dynamics, how it differs or improves on other fields such as Coding Theory and Dynamic Systems, and what kind of problems it would be most suitable for. Frankly, about 20 pages into the book I couldn't even remember why I was reading it.
For better or worse (worse, in my case) the book is written in the style of traditional graduate math books... Definition, Proposition, Definition, Proposition, Definition, Proposition... with very little intervening discussion. Simple, simple concepts are presented in dense, dense notation. Some people appreciate this, I'm sure. Not me.
In summary, I believe this book is written for smarter people than engineering sorts like myself, but as the only text in the area I think a more inclusive approach would have been appropriate.
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