Spanning Trees and Optimization Problems (Discrete Mathematics and Its Applications)

Book Description

The design of approximation algorithms for spanning tree problems has become an exciting and important area of theoretical computer science and also plays a significant role in emerging fields such as biological sequence alignments and evolutionary tree construction. While work in this field remains quite active, the time has come to collect under one cover spanning tree properties, classical results, and recent research developments. Spanning Trees and Optimization Problems offers the first complete treatment of spanning tree algorithms, from their role in classical computer science to their most modern applications. The authors first explain the general properties of spanning trees, then focus on three main categories: minimum spanning trees, shortest-paths trees, and minimum routing cost spanning trees. Along with the theoretical descriptions of the methods, numerous examples and applications illustrate the concepts in practice. The final chapter explores several other interesting spanning trees, including maximum leaf spanning trees, minimum diameter spanning trees, Steiner trees, and evolutionary trees. With logical organization, well chosen topics, and easy to understand pseudocode, the authors provide not only a full, rigorous treatment of theory and applications, but also an excellent handbook for spanning tree algorithms. This book will be a welcome addition to your reference shelf whether your interests lie in graph and approximation algorithms for theoretical work or you use graph techniques to solve practical problems

Customer Reviews:

Good book.......2007-05-07

I think that this is a well-written and very interesting book. It approaches spanning trees in a very concise but complete way. In addition, its size makes it possible to carry the book anywhere, i.e., it's a good handbook. For those, as I, studying/working on spanning trees I would recommend this book. Anyhow, as usual, most of the stuff you find in the book can also be gathered from papers published along the years on this topic. The merit of the authors was to compile this material in a book.

Discrete Dynamical Systems, Bifurcations and Chaos in Economics, Volume 204 (Mathematics in Science and Engineering)

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Discrete Dynamical Systems, Bifurcations and Chaos in Economics, Volume 204 (Mathematics in Science and Engineering)
Wei-Bin Zhang
Manufacturer: Elsevier Science
ProductGroup: Book
Binding: Hardcover

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ASIN: 0444521976

Book Description

This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics.

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Book Description

Discrete dynamical systems are essentially iterated functions. Given the ease with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. The level of the presentation is suitable for advanced undergraduates with a year of calculus behind them. Students in the author's courses using this material have come from numerous disciplines; many have been majors in other disciplines who are taking mathematics courses out of general interest. Concepts from calculus are reviewed as necessary. Mathematica programs that illustrate the dynamics and that will aid the student in doing the exercises are included in an appendix.

Customer Reviews:

An excellent book.......2004-05-27

This is an excellent book for teaching for mathematics students. Besides the standard material it contains a chapter about some numerical methods as dynamical systems. I strongly propose that a third updated edition is made.

Does God Play Dice: The New Mathematics of Chaos

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Great if you are new to the study of chaos
A great intro to non-linear dynamics
Stewart is a reliable guide to chaos
Good tasting without indigestion
The best chaos for layman

Does God Play Dice: The New Mathematics of Chaos
Ian Stewart
Manufacturer: Blackwell Publishers
ProductGroup: Book
Binding: Paperback

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ASIN: 0631232516

Amazon.com

We'd better get used to chaos because it certainly isn't going anywhere. Mathematician Ian Stewart--who is also a very talented writer--shares his insights into the history and nature of the highly complex in Does God Play Dice: The New Mathematics of Chaos. While his delightful phrasings will draw in nearly every reader, those with a strong aversion to figures and formulae should understand that it will be slow going. Chaos math suffuses everything from dreaming to the motion of the planets, and Stewart's words can never match the precision of his numbers. Persistence pays off, though; there are so many "aha" moments of insight herein that it almost qualifies as a religious text. The second edition has been partially revised in the wake of 1990s research, and three exciting new chapters report on prediction and other applications of chaos mathematics. --Rob Lightner

Book Description

"You believe in a God who plays dice, and I in complete law and order." Albert Einstein The science of chaos is forcing scientists to rethink Einstein's fundamental assumptions regarding the way the universe behaves. Chaos theory has already shown that simple systems, obeying precise laws, can nevertheless act in a random manner. Perhaps God plays dice within a cosmic game of complete law and order. Does God Play Dice? reveals a strange universe in which nothing may be as it seems. Familiar geometrical shapes such as circles and ellipses give way to infinitely complex structures known as fractals, the fluttering of a butterfly's wings can change the weather, and the gravitational attraction of a creature in a distant galaxy can change the fate of the solar system.

This revised and updated edition includes three chapters on the prediction and control of chaotic systems. New information regarding the solar system and an account of complexity theory is also incorporated. It is a lucid and witty book which makes the complex mathematics of chaos accessible and entertaining.

Customer Reviews:

Great if you are new to the study of chaos.......2007-06-25

This is a good book for those who are either starting to learn about chaos and nonlinear dynamics or those who would just like an overall view of what the subject is about without getting bogged down into heavy-duty math. This book has two distinct themes. One is to explain the mathematical concept of chaos, and why it is both natural and inevitable. The other is to ask the rather long question "Does the mathematical model of chaos exist in the real world, and does it help us understand some of the things that we see?".

This book covers a variety of subjects that might at first seem unrelated - mathematical history, various chaotic models, weather patterns, applications - but by the end of the book everything comes together to give you a good overall view of the field. This second edition is mainly different from the first in the added three chapters on applications. These chapters cover prediction in chaotic systems, the control of chaotic systems, and then there is a speculative chapter that attempts to explain how the concept of chaos might lead to a new answer to Einstein's famous question which is also the title of this book.

This book requires more imagination and an ability to visualize than a talent for mathematics, and it makes a good introduction to more technical books on the subject such as "Nonlinear Dynamics and Chaos" by Strogatz. Of course, that book requires much more in the way of mathematical maturity. This book looks more at the forest, the Strogatz book looks more at the trees.

A great intro to non-linear dynamics.......2006-03-26

I read and thoroughly enjoyed the first edition and purchased the second for the three new chapters. This book is a fun romp through the subject matter, just mathematical enough to get the gist wthout getting bogged down. I read this book for the overview of the subject and am now going through the Strogatz textbook for the details.
One thing to be aware of is that the original books published by Blackwell are preferable to the Penguin reprints. The Penguin books have *much* smaller text and figures.

Stewart is a reliable guide to chaos.......2006-02-02

Although chaos was a hype some years ago, it still is relevant to many branches of the physical and mathematical sciences. For non-mathematicians, like myself, it is quite difficult to get some good, solid, reliable information about what chaos theory is all about. Ian Stewart is that source of reliable information, and if you want to know what chaos is about, read this book first.

Stewart's approach is down-to-earth, leaving all the mystical ideas about the interconnectedness of the universe, behind. However, that does not mean that his writing is dull in any way. On the contrary, one can feel Stewart's enthousiasm for the mathematical weirdness of chaotic systems on every page. And the informal language and many puns make it a delight to read this book.

Stewart describes how chaotic behavior was discovered in the late 1800s but was forgotten for nearly a century. He describes how mathematical chaos relates to chaotic features of the empirical world such as the butterfly effect (quite a difficult subject, but Stewart does a magnificant job here). And he points to some of the ramification of chaos for our thinking about the universe (determinism and all that stuff).

All in all - a book that will make you think about the world in a different way.

Good tasting without indigestion.......2003-12-22

(1st edition '89) Stewart's book gives the reader as strong a flavor for the constructs of chaos as possible without formulas everywhere. The author makes great use of figures to depict ideas and even gives readers home-projects to test for themselves. Further reading is given (with difficulty levels indicated) for the brave-hearted. Unfortunately, the book is lacking as a reference due to it's vague table of contents and sparse index. But as compared to Mark Ward's "Beyond Chaos", Stewart gives the reader a deeper understanding of the subject matter. Overall good read.

The best chaos for layman.......2002-06-05

This mesmerizing historical overview of nonlinear science, full of seedy ideas and fascinating expositions (from heartbeat to weather forecast) is well worth reading. One of those "aha !" books that will broaden your understanding of the universe (and the rest), it is very "visual" and..well, a friend of mine said she considered it a "mental thriller" since it touches on the great old questions of determinism and predictability. As for "mathematics" in the title- don't be put off. The book is virtually mathless.

Introduction to Discrete Dynamical Systems and Chaos (Wiley-Interscience Series in Discrete Mathematics and Optimization)

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Horrible
Applause for Martelli's Chaos !
Applause for Martelli's Chaos !
Text for Mathematicians and Scientists.

Introduction to Discrete Dynamical Systems and Chaos (Wiley-Interscience Series in Discrete Mathematics and Optimization)
Mario Martelli
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471319759

Book Description

A timely, accessible introduction to the mathematics of chaos.

The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized.

Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks.

An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author's 1993 book, but boasting at least 60ew, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.

An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Customer Reviews:

Horrible.......2003-03-21

It is soo hard to understand the theorems in this book it's ridiculous. You will only like this book if you already know the material well...e.i. it's useless for you if you want to learn something. My whole class is having trouble with this book. I'm writing this review cuz i'm so angry at this book.

Applause for Martelli's Chaos !.......2000-10-18

This text is about chaos and discrete dynamical systems, but the organization, presentation and discourse of these topics in this wonderful edition are anything but chaotic. The writing and context of the ideas laid out bristles with personality and clear focus for presenting the student with adequate examples and detail. This book serves as a superb introduction to the area, and is rich with a wide variety of situations and problems that will motivate the novice and still challenge those with background. I signed on to teach an introductory course on Chaos at New Mexico Highlands University (I'm am one of three math faculty at this institution). I spent considerable time searching for a text that adequately addressed chaos and dynamical systems, that was challenging and yet personable and reader friendly. We have a wide disparity of math students at NMHU, particularly with regard to background, ability and vocational aspirations. It was important to use a text, I felt, that did not sacrifice detail, but at the same time did not pre-suppose overly technical sophistication. Most of the texts that I sampled, were quite terse, demanding or pedagogically constipated. When I came across MArtelli's text I was struck by the absence of these defects and then by the simple structure and sequence of topics that patiently build and reinforce concepts. The author's enthusiasm for the material comes through clearly and reaction from students I test-sampled echoed this feeling. In fact, both students have decided to enroll in my spring course - I believe their postiive response to this text was more than a contributing factor. In exchange for their time, I promised I would relay encouragement for all who are considering similar course offerings and a companion text that supports and reinforces the excitement of this area of mathematics. This book is a great resource. Bravo, Mario !!

Applause for Martelli's Chaos !.......2000-10-18

Text for Mathematicians and Scientists........2000-10-15

The Introduction to Discrete Dynamical Systems and Chaos is an excellent text for those who just start sturying descrete dynamical systems and for those who already have some knowledge in the field. The book can be used as a textbook or as a guide for individual studies. In the first case the instructors will find a set of carefully chosen problems at the end of each chapter and several interesting projects for the students. While the first part of the book can be understood by a person without extensive mathematical background, the second part deals with topics such as nonlinear dynamical systems and chaotic behavior using Banach contraction principle, fractal dimension, etc.

To illustrate the use of dynamical systems the book also describes few very common models: blood-sell population, predator-prey, Lorenz Model, and neural networks.

Book Description

The main goal of this graduate-level text is to provide a language for understanding, unifying , and implementing a wide variety of algorithms for dgital signal processing -- in particular, to provide ruls and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines. It thus bridges the gap between digital signal processing algorithms and their implementation on a variety of computing platforms. The mathematical concept of tensor product is a recurring theme throughout the book: tensor product factors have a direct interpretation on on many vector and parallel computers and tensor product idetities can be matched to machine implementation. These formulations also highlight the data flow, which is is especially important on supercomputers, where data flow may be the factor limiting the efficiency of a computation. Because of its importance in many appications, much of the discussion centers on algorithms related to the finite Fourier transform and to multiplicative FFT algorithms; other topics covered include convolution algorithms and prime-factor algorithms. This second edition has been revised and brought up to date throughout.

Discrete Dynamical Systems: Theory and Applications

Average customer rating:

Excellent textbook on chaos!

Discrete Dynamical Systems: Theory and Applications
James T. Sandefur
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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Book Description

Discrete dynamics is the study of change. In particular, it shows how to translate real world situations into the language of mathematics. With the increase in computational ability and the recent interest in chaos, discrete dynamics has emerged as an important area of mathematical study.
This text is the first to provide an elementary introduction to the world of dynamical systems. The aim of the text is to explain both the wide variety of techniques used to study dynamical systems and their many applications in areas ranging from population growth to problems in genetics. This
investigation leads to the fruitful concepts of stability, strange attractors, chaos, and fractals. Very little previous mathematical knowledge is assumed and students with an elementary exposure to calculus and linear algebra will be able to follow the text easily. A large number of worked
examples and exercises are provided to assist instruction. Throughout, students are encouraged to experiment with models of dynamical systems on computers and explore this fascinating area of mathematics on their own.

Customer Reviews:

Excellent textbook on chaos!.......2000-12-27

Although this text lacks the brightly-colored fractals of many other works, the coverage it gives to the mathematics end of things more than makes up for it. It deals very well with the concepts of statistics and dynamic equations that are necessary for the understanding of chaos, presuming very little in the way of mathematical knowledge on the part of the reader. All definitions are clearly delineated, and the answers to the exercises are provided in the back.

Average customer rating:

A well-written, comprehensive introduction to the field
disappointing

Cellular Automata: A Discrete Universe
Andrew Ilachinski
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9810246234

Customer Reviews:

A well-written, comprehensive introduction to the field.......2002-08-27

Cellular Automata: A Discrete Universe is a fascinating overview of the wide variety of discrete systems researchers have developed in the past quarter-century, and how these might be used to model a range of natural phenomena, including (in the book's most speculative section) the universe itself. Illustrations are supplied in all the right places--serving to enlighten, rather than overwhelm, the reader. The list of references is superb, making the book not only a great introduction and an important reference, but also a valuable guide to the field of complexity.

disappointing.......2001-09-24

This book is clearly a labor of love and contains a great wealth of material. However, it sorely lacks focus, the presentation is unclear and the results are often out of date. Here is a selection of more particular criticisms. Many rules remain undefined and the reader has to guess their details. The writer seems to be unfamiliar with the last five years worth of research, so particularly the chapter on probabilistic CA is not worth much. Far too many parts of the book are outlines of original papers (or books) with details omitted. Many claims in the said papers are accepted without scrutiny. (Two examples: (1) There is absolutely no evidence that any cellular automaton studied by Packard and Wolfram has a shape that is close to circular. (2) It has been discovered as far back as 1989 that the famous FHP lattice gas does NOT approach the two-dimensional Navier-Stokes equation, due to the fact that viscosity increases to infinity with increasing size of a finite system.) World Scientific editors need to do a much better job.

Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions

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Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions
Ralph Abraham , Laura Gardini , and Christian Mira
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387943005

Book Description

Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semi-cascades (discrete, irreversible, dynamical systems). Flows and semi-cascades are the classical systems iuntroduced by Poincare a centry ago, and are the subject of the extensively illustrated book: "Dynamics: The Geometry of Behavior," Addison-Wesley 1992 authored by Ralph Abraham and Shaw. Semi- cascades, also know as iterated function systems, are a recent innovation, and have been well-studied only in one dimension (the simplest case) since about 1950. The two-dimensional case is the current frontier of research. And from the computer graphcis of the leading researcher come astonishing views of the new landscape, such as the Julia and Mandelbrot sets in the beautiful books by Heinz-Otto Peigen and his co-workers. Now, the new theory of critical curves developed by Mira and his students and Toulouse provide a unique opportunity to explain the basic concepts of the theory of chaos and bifurcations for discete dynamical systems in two-dimensions. The materials in the book and on the accompanying disc are not solely developed only with the researcher and professional in mind, but also with consideration for the student. The book is replete with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-color animations that are tied directly into the subject matter of the book, itself. In addition, much of this material has also been class-tested by the authors. The cross-platform CD also contains a software program called ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided which give the reader the option of working directly with the code from which the graphcs in the book were

CONVERGENCE, OSCILLATIONS, AND CHAOS IN A DISCRETE MODEL OF COMBAT

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CONVERGENCE, OSCILLATIONS, AND CHAOS IN A DISCRETE MODEL OF COMBAT
H. Sedaghat
Manufacturer: Society for Industrial and Applied MAthematics
ProductGroup: Book
Binding: Paperback
ASIN: B000VL22CW

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