Book Description
In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology.
Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties.
The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines.
Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum--or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience.
An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.
Customer Reviews:
An Interesting Book on Spiking Mechanism and Nonlinear Dynamical System.......2007-08-10
The goal of Izhikevich's book is to study "the relationship between electrophysiology, bifurcations, and computational properties of neurons." The book also introduces the fundamental concepts of nonlinear dynamical system such as (1) equilibrium, (2) stability, (3) limit cycle attractor, and (4) bifurcations. Actually, it is a good introductory book on applying nonlinear dynamical system on scientific research. The primary subject of the book is the spiking (excitability and bursting) of neurons. By utilizing graphs or phase portraits to demonstrate the mechanism of the spiking generation of neurons, the author makes the readers understand both the spiking mechanism and the concepts of nonlinear dynamical system with ease.
Book Description
From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2
Customer Reviews:
Christians fundimentalists have the King James Version, Computational geometrists have..........2005-10-17
This book is to computational geometrists what the King James Version of the Bible is to christian fundimenalists. Even though newer translations of the Bible are easier to read, somehow nothing sounds quite so authentically like the voice of God than those Elisibethen cadences, written in an almost archaic language....
...similarly for this book. Many times, the descriptions of algorithms presented in this book are made unnecesarily hard by very arcane langauge.
But this book is authoritative and definitive in a way that no other text on computational geometry is ever likely to achieve. Even though there are any number of books which are newer and easier to read, it seems like this the one book on the shelf of every serious computational geometer I know.
This book is history.......2003-05-12
This book is a classic, in fact the author's PhD thesis created this field, but this book is too old for any meaningful graduate work. There are new bounds and algorithms on almost all topics, which makes this a somewhat undesirable book. Also, this book has failed to keep me interested in it, while I am reading it...
Very useful for code development. Very clear and readable........2001-11-02
The ideas and algorithms presented in this book are clear enough for straight implementation in code. I have long experience in developing comercial and production software for VLSI layout applications, which made extensive use of the algorithms presented in this book.
I also use some chapters of this book as a part of a graduate course in VLSI layout algorithms being tought at the Technion, Israel. The contents of this book is well understood by EE and CS students.
I personally love this book, which introduced me into the area of computational geometry and its applications.
Useful but thick.......2001-06-19
Most of the papers that I've read on computational geometry refer to this text -- and for good reason. There's many good algorithms to be found here.
The book only gets 4 stars because it's hard to read. It took me several tries to pick up the ideas in this text. I think the De Berg text is MUCH easier to read.
The book is also getting a little dated. Some of the topics have come a long way since the 80's.
This book seems to be in most University libraries if you have that option.
Still interesting after so many years ..........2001-03-22
I have just happened to exhume this book from my library, after it spent some years gathering dust above the shelf. In spite of the long time I have not being reading it, it still retains the full meaning it showed me when I was using in calculations relating radar domain definition. May be the textbook wins by far the comparison to the current vague and inflated computer publications, may be it is not a manager-oriented issue but it is for nearly specialistic use, you find in it clearly stated, and straight, answers to the questions you meet, or at least a definite reference where a more detailed explanation can be find. It presents interesting problems, and explains you how to solve them. I think it is the best you can say about a computer science book.
Average customer rating:
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Protein Geometry, Classification, Topology and Symmetry: A Computational Analysis of Structure (Series in Biophysics)
William R. Taylor , and
Andras Aszodi
Manufacturer: Taylor & Francis
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ASIN: 0750309857 |
Book Description
Using a geometric perspective, Protein Geometry, Classification, Topology, and Symmetry reviews and analyzes the structural principals of proteins with the goal of revealing the underlying regularities in their construction. It also reviews computer methods for structure analysis and the automatic comparison and classification of these structures with an analysis of the statistical significance of comparing different shapes. Following an analysis of the current state of protein classification, the authors explore more abstract geometric and topological representations, including the occurrence of knotted topologies. The book concludes with a consideration of the origin of higher-level symmetries in protein structure. The authors focus on simple geometric methods that are deterministic rather than probabilistic and on the more abstract simplifications of protein structure that allow a better understanding of the overall fold of the structure. Most of the methods described in this book have corresponding computer programs. These can be found (as C source code) at the ftp site of the Division of Mathematical Biology at the National Institute for Medical Research. This collection of ideas contains pedagogical material that make it ideal for post-graduate courses as well as new ideas and results essential for researchers investigating protein structures.
Book Description
This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added.
Customer Reviews:
Excellent Background.......2007-06-13
This book is extremely well written, easy to understand, and actually is the standard text for Computational Geometry classes, as far as I know. The only thing I didn't like about it was that there seemed to be a few errors in some of the pseudocode. But, it's to be expected when publishing a textbook, and I think it'll probably be cleared up in future editions.
Overall, great book. I'd recommend it to anyone taking graphics or a computational geometry class.
good source of many methods.......2006-02-24
The authors amass an impressive array of algorithms related to finding geometrical properties. Where these algorithms are performed on a computer. The book itself does not advocate any particular programming language. The algorithms are given in pseudocode, and you are expected to manually convert these to code in your choice of language. Given the calibre of the discussion in the text, which suggests that the readers are quite experienced, then this manual step should be easy to most.
There are numerous contexts in which the text might prove useful. Ranging from graphics to GIS to robotics. Thus, there is an entire chapter on the planning of robotic motion. The robot can in general translate and rotate.
Each chapter comes with an exercise set. Which helps make the book suitable as a graduate or even undergraduate text.
Important book but substandard layout and typesetting.......2005-12-27
This is one of the really few computational geometry books available. It fills a niche and does it decently. However it could be better:
1. The chapter layout is not very good. There are many "revisiting this" and "we saw in chapter so-and-so".
2. The mathematical proofs are often written in a single paragraph full of "English" interspersed with mathematical notation, instead of the tried and true way of numbered equations and one-per explanations. This makes for disconcerting reading.
3. The book in general could have done with more math and code, and less "English", not to mention more and better diagrams -- they tend to be sparsely detailed (ie. a picture is worth only a hundred words). The arrangement of diagrams also needs to be better: some are in the margins, some are in the middle, again not easy and intuitive to follow.
Hopefully a future edition will address this issues.
Good Introduction but look elsewhere for detailed reference.......2003-01-31
Pro:
(1) Each chapter begins with a practical example. For example, the chapter computing intersections of lines starts with a discussion of a map-making application that goes into enough detail to see how the algorithms they present would be useful. This is a considerable step up from the common practice in algorithms literature of motivation by way of vaguely mentioning some related field (i.e. "These string matching algorithms are useful in computational biology"). This book does a much better job of motivating the material it presents, but if you're primarily interested in the abstract problem, these sections can be skipped.
(2) Each chapter is relatively self-contained. Feel free to skip ahead to subjects that interest you.
(3) Surprisingly readable. Unlike most technical material, one can read an entire chapter in a single sitting without missing much. Generally, each chapter will develop a single algorithm for a single kind of problem.
(4) It's very up to date. This second edition is less than two years old, it includes some new results in the field.
Con:
(1) Algorithms are only given in pseudocode. The emphasis is on describing algorithms and data structures clearly and completely. If you're looking for a "cookbook" with code to copy and paste into an application, perhaps O'Rourke's "Computational Geometry in C" would be a better choice.
(2) There are many important advanced results that are not discussed in the main text. An obvious example is the first chapter, which describes a well-known convex hull algorithm that takes O(n log n) time but algorithms that are faster for most inputs are mentioned only in the "Notes and Comments" at the end of the chapter. Someone interested in lots of gory details would be well-served to combine this book with Boissonnat and Yvinec's more detailed and mathematical "Algorithmic Geometry".
Extremely well written.......2002-10-26
Algorithm books are often quite hard to understand, but this is not the case with this book. The information is very compact so it is a slow read but due to the high quality of the text this is only an advantage. You are never left wondering what the authors might have meant with a certain statement.
The book focuses solely on theory, so it presents no real source code (only pseudo-code) which I think is good thing since that would otherwise have polluted the clarity of the explanations.
Many of the topics it covers has been a help to me as a programmer. Can be recommended for anyone interested in computation geometry - but it requires some computer science maturity so I don't recommend it unless you have a bachelor's degree in C.S. or something similar.
Jacob Marner, M.Sc.
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Handbook of Computational Geometry
Manufacturer: North Holland
ProductGroup: Book
Binding: Hardcover
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ASIN: 0444825371 |
Book Description
Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.
Book Description
Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric theorem proving. In preparing a new edition of
Ideals, Varieties and
Algorithms the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple , Mathematica and REDUCE.
Customer Reviews:
Symbolic computation.......2003-08-29
This book explains and illustrates the algorithms used by symbolic math packages such as Mathematica, Maple, CoCoA, MatLab, MuPAD,... to solve problems involving polynomials in many variables, and along the way teaches the elements of real algebraic geometry-- most mathematics texts concentrate on the complex-variable version. It is not just for undergraduates; electrical engineers, for instance, should see it. Lots of pictures!
Easiest introduction to Algebraic Geometry.......2003-04-23
This is the easiest introduction to algebraic geometry and commutative algebra, the authors had done a great job in writing a book that assume very little from the readers. To learn some algebraic geometry, you can either start with this book, or you can spend a year to read a lot of background materials in algebra and then go to a Graduate Text like Harris' book. Of course, if you want to be an expert in algebra, you eventually need a lot of background, what this book can help you is to offer you a quick start, much quicker than you would ever imagine.
Straightforward and lucidly written.......2002-04-09
Having just finished using this text in the course of an undergraduate seminar, I can attest to the fact that the authors' style is outstanding - they are able to synthesize an enormous amount of material in this volume and present it in a manner that is highly accessible to almost all students of mathematics. The presentation of important theorems (for example, Hilbert's Nullstellensatz and Basis Theorem) along with just the right amount of copncrete examples makes for a book of superb quality. All-around, I highly recommend this volume to anyone who has an interest in learning about Algebraic Geometry.
Good book.......2001-05-27
I don't have the second edition of this book but did read the first, and the authors do a fine job of introducing the reader to the computational side of algebraic geometry. I will forego a chapter by chapter review therefore, but no doubt the second edition (which I do not own) is as well-written as the first. I would recommend it to anyone interested in the many applications of algebraic geometry and to those who need to understand how to compute things in algebraic geometry. The good thing about this book is that it gives a concrete flavor to a highly abstract subject. Algebraic geometry, through its applications to coding theory, cryptography, and computer graphics, is fast becoming the subject to learn. It is no longer just an esoteric, high-brow subject but one that is taking on major importance in the information age. Even without applications though it is a fascinating subject, and readers will get a taste of this in this book.
The best book on the topic.......2001-01-26
I learned the basics of Groebner bases from this book and its the best introductory book on this topic. Authors have explained all concepts with the help of examples which makes it readable for people from other fields also. It also talks about applications of Groebner bases to other fields. The book gives lot of exercises which help in understanding the contents more. I recommend that if you wish to learn Algebraic Geometry and Groebner bases then this is the book to start with.
Average customer rating:
- good book
- Not a self contained book!
- Not for beginners
- Good introduction to level set methods
- This is The Introduction to Level-Set Method
|
Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (Cambridge ... on Applied and Computational Mathematics)
J. A. Sethian
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback
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Level Set Methods and Dynamic Implicit Surfaces
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Geometric Level Set Methods in Imaging, Vision, and Graphics
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Numerical Geometry of Images: Theory, Algorithms, and Applications
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Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
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Handbook of Mathematical Models in Computer Vision
ASIN: 0521645573 |
Book Description
In this new edition of the successful book Level Set Methods, Professor Sethian incorporates the most recent advances in Fast Marching Methods, many of which appear here for the first time. Continuing the expository style of the first edition, this introductory volume presents cutting edge algorithms in these groundbreaking techniques and provides the reader with a wealth of application areas for further study. Fresh applications to computer-aided design and optimal control are explored and studies of computer vision, fluid mechanics, geometry, and semiconductor manufacture have been revised and updated. The text includes over thirty new chapters. It will be an invaluable reference for researchers and students.
Customer Reviews:
good book.......2006-03-15
Neither an introduction nor a recipe book for level sets. Contains dense information and requires supplemental material.
Not a self contained book!.......2003-10-12
I bought this book with the intent of understanding the level set method AND be able to implement it in code. The book fails on the later. He gives you some basic formulas/algorithms to start with, but they are not good enough for most problems. You need to get the references (and the references of those references) to obtain the actual algorithms people use to implement the level set method.
The first six chapters are good for giving you a nice qualitative understanding of the method and the issues of implementing the method. And the rest of the book claims to show you the more advanced techniques, but whenever the nitty gritty details are needed, he refers you to the references.
My advice: just get his references. If you are at a university, then you probably have free access to the online journals that contain his (and others) research articles. In fact, this book is basically a copy-paste of those articles! Literally!
Not for beginners.......2003-04-23
I am afraid that this book is not for beginners who want to have a clear mind of the level set method. You will have to go to the library quite often to dig out all the references the author mentioned. I would say this book is for experienced researchers only.
Good introduction to level set methods.......2001-06-07
I use these methods in the context of image analysis, for image segmentation essentially. The book is an inescapable introduction by one of the main inventors of these methods. It is easy to read and relatively complete. Be sure to get the second edition. The only slight problems are the remaining typos. There are quite a few, for a second edition, and they might throw off a beginner. You will need to read some introduction text on finite differences methods at least. The chapter in Numerical Recipes is enough.
This is The Introduction to Level-Set Method.......2000-04-27
This is a very good introduction to the very exciting technique, level-set method. The method is basically for front-tracking or interface motion. But its application turned out to be so wide that it is now applied to problems which does not seem relevant to front-tracking, such as computaional grid generation. This book explaines the basics of this powerful tool very clearly, and it is in fact easy to read. Although it was written by a mathematician, it is not very mathematical like some texts on finite-element method written by mathematicians (which are often formidable to engineers). I recommend this book to anyone in engineering. You might find a new application of this technique.
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Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of Riemannian Moduli Space (Porter Lectures)
Shmuel Weinberger
Manufacturer: Princeton University Press
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Three-Dimensional Geometry and Topology
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Fearless Symmetry: Exposing the Hidden Patterns of Numbers
ASIN: 0691118892 |
Book Description
This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow.
The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it.
Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.
Book Description
This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. For the 4th edition, the concept of the book has been completely re-arranged. The new emphasis is on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing.
Customer Reviews:
Excellent reference book.......2007-09-19
I highly recommend the Handbook of Mathematics. It is an excellent resource for every engineering student and professional engineer.
Great, but tough to use.......2007-04-25
This handbook contains more material than I find in any other single source that I happen to have. But I don't use it as frequently as I use the analogous CRC handbook, or MathWorld and Wikipedia on the Web, or the ancient NBS handbook. Why not? Because one uses a handbook, not as a textbook, but as a source for things one should know, but don't (or perhaps once knew but have forgotten). So one wants to find the thing one is looking for, refresh or extend one's memory, and then put the handbook aside and go back to the problem one is trying to solve. I have trouble locating what I'm looking for in Bronshtein and Semendayev, and when I find it, I often find that I have to look up things elsewhere in the volume to get all of whatever it is I was looking for. So I try my other sources first, and if they don't answer my question, I pick up this book, resignedly, and expect to spend hours rather than minutes getting whatever it is I want to know. There is nothing wrong with that; indeed, this book often supplies me with answers to questions I can't find answered elsewhere.
In case the reader of this review attributes my difficulties with this book to a lack of mathematical background, I'll remark that my academic training, very many years ago, was in math, so I find that I can follow the discussion in this book of any particular thing I look up; it's just a slow process for me. I'm not surprised that it's a favorite in Germany (and in Europe more generally); Europeans in their mathematical training are expected to deal with tough subjects by dogged persistence, and probably feel more comfortable with this style than I do, given my US background. So, overall, it's a book I couldn't do without, but hate having to spend time in.
Loaded with Content.......2005-02-25
This book is exactly what the title says it is; a handbook of mathematical techniques and formulas for scientists and engineers. It is more a handbook than a book on mathematics and assumes a prior knowledge on the subjects covered. Readers of this english version of the Bronshtein should take note that it is a "raw" translation of the german version and so some discussion may not do justice to the theory. This in no way takes away from the fact it is an exceptional book and you'd be hard pressed to find any other book with more mathematical content.
There are several Bronshteins.......2004-10-25
Bronstein's "Taschenbuch der Mathematik" is a longtime favorite among german science and engineering students. English language readers should be aware however, that there are numerous different editions of this book. Not only were the german editions constantly enlarged and reworked, but there were also two publishers of the same book, one in East Germany (Teubner Verlag), one in West Germany (Harri Deutsch Verlag). Today both of these publishers sell a "Taschenbuch der Mathematik" based on the original Bronstein, yet they are completely different books. The english edition by Springer Verlag advertised above is based on the current Harri Deutsch edition. An english translation of the Teubner edition is now available as the "Oxford Users' Guide to Mathematics" from Oxford University Press. It is mostly considered to be the better 'Bronstein' (even though Teubner and OUP have dropped his name because the new edition was completely rewritten by E. Zeidler).
Clasic.......2004-03-22
For me it was a remarkable fact, how few of the people in western countries have heard about this handbook. In the east this is probably the most popular mathematical handbook ever. I dont know any eastern european scientist in a field of mathematics, engineering and physics who don't have it. The main reason is it's extensivity and usefulness. In Croatian print it has about 1000 pages in very small format covering all possible parts of applied mathematics up to special functions/markov chains/complex integration/vector algebra. It's "allways in backpack book" and my hot recomandation to any technical scientist.
Book Description
While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: · Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory · Thorough revisions of all remaining chapters · Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software · Two indices: An Index of Defined Terms and an Index of Cited Authors · Greatly expanded bibliographies
Customer Reviews:
Very comprehensive overview of computational geometry.......2001-03-26
This book, written by many well-known experts in the field, is a fine compendium of articles on the most active areas of computational geometry. Each article is supplemented with a glossary of terms needed for understanding the relevant concepts and frequently contains a list of open problems. An overview of the convex hull of a collection of random points in Euclidean n-space is given in one of the articles on discrete aspects of stochastic geometry, where also a very interesting discussion of generalizations of the Buffon needle problem is given.
There are a few articles overviewing Voronoi diagrams, such as the one on Voronoi diagrams and triangulations. The applications of Voronoi diagrams are many, and include tumour cell diagnosis, biometry, galaxy distributions, and pattern recognition. This article is a little short considering the importance of the subject.
The article on shortest paths and networks is somewhat disappointing since there is no in-depth discussion on network routing algorithms.
The article on computational topology highlights some of the results in this very important area. Many problems in topology have been tackled recently using computers, particularly the work of the mathematician A.T. Fomenko. Computational topology is a relatively young field, having been in existence only since the early 1990's. The applications are enormous, ranging from meshing, morphing, feature extraction, data compression, and in many scientific areas such as computational medicine, chemistry, and astrophysics. It can also be used in computer security via graphical passwords. It is an immense help in visualizing complicated topological objects, such as Lens spaces, horned spheres, and thickened knots. The article does not touch on the use of Mayer-Vietoris sequences to design efficient divide-and-conquer schemes for computing the homology of higher-dimensional complexes. The interplay between topology and finding better algorithms in computational geometry is one that will flourish no doubt in years to come.
The last section of the book covers applications with the most interesting article being the one on sphere packing and coding theory. The algorithms in sphere packing have direct applicability to error correctiong codes over the field GF(q). The author of this article does touch briefly on general algebraic-geometric codes, which is good considering their importance in applications.
The last article appropriately discusses available software for computational geometry. Although the list of Web sites is quite extensive, there are many more available since this book was first printed.
A very fine addition to the literature on computational geometry and should be on everyone's shelf who is interested in this important area.
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