Product Description
Algorithms for Computer Algebra is the firstcomprehensive textbook to be published on the topic of computationalsymbolic mathematics. The book first develops the foundationalmaterial from modern algebra that is required for subsequent topics.It then presents a thorough development of modern computationalalgorithms for such problems as multivariate polynomial arithmetic andgreatest common divisor calculations, factorization of multivariatepolynomials, symbolic solution of linear and polynomial systems ofequations, and analytic integration of elementary functions. Numerousexamples are integrated into the text as an aid to understanding themathematical development. The algorithms developed for each topic arepresented in a Pascal-like computer language. An extensive set ofexercises is presented at the end of each chapter.
Algorithms for Computer Algebra is suitable for use as atextbook for a course on algebraic algorithms at the third-year,fourth-year, or graduate level. Although the mathematical developmentuses concepts from modern algebra, the book is self-contained in thesense that a one-term undergraduate course introducing students torings and fields is the only prerequisite assumed. The book alsoserves well as a supplementary textbook for a traditional modernalgebra course, by presenting concrete applications to motivate theunderstanding of the theory of rings and fields.
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Customer Reviews (2)

an excellent treatment
We used this book in an advanced undergraduate/early graduate class in computer algebra.The book provides a concise and rigorous, but very readable introduction to computational algebra theory, with algorithms written in pseudo code.

Assuming proficiency in programming, as further pre-requisite I would suggest an undergraduate course in abstract algebra (or equivalent mathematical maturity) for maximum benefit.

An excellent collection of algorithms, proofs, and advanced introductory material, written in a (comparatively) breezy style.

Clear and understandable, but some bugs
I found this book very useful as a reference while writing a smallcomputer algebra system.It's a definate must-have for all the hordes ofpeople out there who are rewriting subsets of Maple, Mathematica, etc.Theexplanation of the theory is relatively clear and helpful so that anot-so-theory-inclined person (such as myself) can understand the material. The cost of such clarity is a loss of some conciseness so someone wholives and breathes abstract algebra may desire a more esoteric book (likeWinkler's). The biggest flaw of the book are the poorly debuggedalgorithms.Almost every algorithm presented in the book has some sort ofminor flaw with serious reprecussions on correctness.This results in muchfrustration if you're actually trying to implement the algorithms. ... Read more

Product Description
The use of software packages to solve mathematical problems is becoming increasingly popular. This comprehensive book illustrates how Mathcad can be used to solve many mathematical tasks. It also provides the mathematical background for the Mathcad package. Practical Use of Mathcad contains many solutions to basic mathematical tasks for engineering and natural science. It can be used both as a reference and tutorial manual for lecturers and students, and as a practical manual for engineers mathematicians and computer scientists. The latest version of Mathcad V. 8 Professional for Windows 95/98 is used throughout. ... Read more

Customer Reviews (3)

OLD - OLD
I can't believe a book advertising MATHCAD 8 is still out there with windows 95/98.
The latest MATHCAD is "11". - that is 3 versions ago. And I have read Springer books, they are okay but they are translation from German.

I am suprised with the review -- this is an OLD book and it certainly shouldn't be selling for a NEW price. I had to be critical. I have 8 and just purchased 11.

Not user friendly
Perhaps something went wrong in the translation because the book is hard to use. Example:To find subscript in the index you have to know if you want an array subscript or a literal subscript.The user guide is better if you can find one so don't waste your money.

Practical use of Mathcad...
A very good reference book. I find it easier to get information than the user guide. The first part covers the basic of the program while the second part (what I like) classifies into each type of mathematical problems withexamples. If you know what type of the problem you encoutered, just lookthrough the required chapter you'll find related theory and example.Covered version 7&8. ... Read more

Product Description

Until recently, all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming.

Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down.

Customer Reviews (4)

ok, but...
It's a good book, but the mathematics is poorly treated, not enough rigorous as would be expected.

very good text
This is the text I would first recommend to anyone involved in geometrical programming who would like to learn geometrical algebra.

An excellent introduction to the subject.
The book Geometric Algebra For Computer Science, by Dorst, Fontijne, and Mann has one of the best introductions to the subject that I have seen.

It contains particularly good introductions to the dot and wedge products and how they can be applied and what they can be used to model.After one gets comfortable with these ideas they introduce the subject axiomatically.Much of the pre-axiomatic introductory material is based on the use of the scalar product, defined as a determinant.You'll have to be patient to see where and why that comes from, but this choice allows the authors to defer some of the mathematical learning overhead until one is ready for the ideas a bit better.

Having started study of the subject with papers of Hestenes, Cambridge, and Baylis papers, I found the alternate notation for the generalized dot product (L and backwards L for contraction) distracting at first but adjusting to it does not end up being that hard.

This book has three sections, the first covering the basics, the second covering the conformal applications for graphics, and the last covering implementation.As one reads geometric algebra books it is natural to wonder about this, and the pros, cons and efficiencies of various implementation techniques are discussed.

There are other web resources available associated with this book that are quite good. The best of these is GAViewer, a graphical geometric calculator that was the product of some of the research that generated this book. Performing the GAViewer tutorial exercises is a great way to build some intuition to go along with the math, putting the geometric back in the algebra.

There are specific GAViewer exercises that you can do independent of the book, and there is also an excellent interactive tutorial available.Browse the book website, or Search for '2003 Game Developer Lecture, Interactive GA tutorial. UvA GA Website: Tutorials'.Even if one decided not to learn GA, using this to play with the graphical cross product manipulation, with the ability to rotate viewpoints, is quite neat and worthwhile.

A reader from Los Alamos, NM
Geometric Algebra (GA) is a unifying mathematical language that should be taught instead of or at least in combination with traditional vector analysis. Most other books on GA are aimed at Physicists. This book is a better match for Engineers and Programmers.The authors are all active researchers in applications of GA. They have done a comprehensive and up to date job of collecting, organizing and presenting the material for both beginners and those who follow the development of GA on the web. The examples and problems use GAViewer, an easy to learn programming language with an Open GL view window that can be downloaded for free from the book website. Using GAViewer with the book is very good way to learn GA, especially the 5D Conformal model of 3D space. The authors hold nothing back. Between the book, the code and the website everything is there to make learning GA fun and useful. I highly recommend this book. ... Read more

Product Description
This book still remains the best introduction to computer algebra, catering to both the interested beginner and the experienced pure mathematician and computer scientist. This updated Second Edition provides a comprehensive review, and contains excellent references to fundamental papers and worked examples. In addition to being a general text on the subject, the book includes an appendix describing the use of one particular algebra system-REDUCE. ... Read more

Product Description
Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students, this text's comprehensiveness and reliability also make it an essential reference for professionals. Errors have been corrected and new sections on greatest common divisors and symbolic integration have been added to this updated edition. First Edition Hb (1999): 0-521-64176-4 ... Read more

Customer Reviews (5)

Very nice
This is a very nicely written text, comprehensive in what it aims to cover.The illustrations are plentiful and very helpful.The material is mostly self-contained and presented in a novel way (Fermat, Euler, Hilbert each have their own groups of sections!).

This is the best treatment I've seen for lattice basis reduction (a topic treated in many other texts) as well as for polynomial factoring over fields (Cantor Zassenhaus) and other topics.I've read parts of this book that were irrelevant for my research simply because the book is a joy to read.Highly recommended to anyone with an interest and some degree of mathematical maturity.

The only drawback is that my edition has a number of typos, some serious (however the authors do provide an online corrigenda).

State-of-the-art in CAS
I am a C programmer and this book was fundamental to introduce myself in the field of computer algebra systems (CAS). It's very well structured and at the state-of-the-art in that discipline. The only remarks is about the strong presence of author's mother-tongue influences in some English phrases.

Good overview
A good and complete review, a very good bibliography. Wonderfull graphics. A subtle sense of humor.

Mod. Computer Algebra
A lucidly written book.Has well balanced background and problems.However, it needs to have more tricky problems that really makes one think deeper though there are some. The book proves a very good assest to the Library.

MCA - very adequate book on computer algebra topics
Covering a lot of topics on "Computer Algebra" this book is a fine workout. Many mathematical proofs are provided and most subjects are explained and outlined very accurately. Only sometimes things can not aseasily be seen as the author clames. The homepage of Mr. von zur Gathenprovides a postscript file with corrections and additions and even more onecontaining solutions to many of the given exercises. ... Read more

Product Description
Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polynomial factorization.

It is well-suited for self-study and can be used as the basis for a graduate course. ... Read more

Customer Reviews (1)

well-written guide for building a basic CAS
Excellent book covering the basics of building your own computer algebra system, together with its partner text: "Computer Algebra and Symbolic Computation: Elementary Algorithms".The author presents the mathematical fundamentals, practical challenges, formulaic solutions, suggested implementations, and examples in a few programming languages appropriate for someone building their own CAS from scratch in very clear prose.The author makes extensive further reading recommendations for each topic.

At each stage of the development, the author presents the motivation for each feature of the CAS along with formal basics of the math behind the techniques.The author presents the basic practical challenges faced by the computer and algorithms in working with the math.Together, these make the text appropriate for both those with math experience moving into programming, and programmers moving towards math.The author lists step-by-step techniques from a mathematician's point of view for solving the problems, and then continues to give algorithm listings in an easily-read "Math Pseudo Language", complete with flow charts explaining the more complex algorithms.A formal computational complexity analysis of the algorithms is not included.

The author's examples are provided in Mathematica, MuPad, and Maple, but not in C-like languages.The examples, however, are function/structure-based, and are thus clear enough as to be immediately extensible to the reader's language of choice.For an engineer, the examples amount to a practical recipe. The book also contains a CD with the examples & the text of the book as a .pdf.However, this .pdf is only directly accessible to Windows users.Mac users will need to use Windows to run the included Windows app which can access the .pdf and then save it into another .pdf file to use on their Mac.(I've never seen anything like this before!The .pdf files on the CD show up as "Zero KB Symbolic links" on the Mac which don't resolve unless opened in Windows!In the end, I was able to get the .pdf onto my iPhone so I can easily carry the e-book with me when traveling.)

The author provides insight into both the mathematical and computational limitations of the algorithms, the problems caused by the limitations, and frequently gives examples for recognizing the limitations or working around them.

Finally, the author provides extensive references for further reading for details on particular topics.

In all cases, the author's mastery of English prose makes the information easily accessible, which is not at all the case with some other CAS books I've wasted money on...Speaking of price, considering the extreme niche market and the exquisiteness of the text, the combined price of the two books was worth it.

To help the potential customer (as a preview of the contents is not available), this book is the one of the two books (which can be effectively read in any order), and covers the basics of CAS's, the included Math Pseudo Language (MPL), detailed rational number manipulations, automatic simplification of expressions, single and multi-variable polynomial decompositions, resultants, and factorization.

It's possible I may one day find a more extensive text with more advanced techniques, but the two texts provide a foundation for building my own CAS. ... Read more

Product Description
This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems. This book supercedes the SIAM publication Solving Linear Systems on Vector and Shared Memory Computers, which appeared in 1990. The new book includes a considerable amount of new material in addition to incorporating a substantial revision of existing text. ... Read more

Product Description
Numerical Modeling in Science and Engineering Myron B. Allen, George F. Pinder, and Ismael Herrera Emphasizing applications, this treatment combines three traditionally distinct disciplines—continuum mechanics, differential equations, and numerical analysis—to provide a unified treatment of numerical modeling of physical systems. Covers basic equations of macroscopic systems, numerical methods, steady state systems, dissipative systems, nondissipative systems, and high order, nonlinear, and coupled systems. 1988 (0 471-80635-8) 418 pp. Mathematical Modeling and Digital Simulation for Engineers and Scientists Second Edition Jon M. Smith Totally updated, this Second Edition reflects the many developments in simulation and computer modeling theory and practice that have occurred over the past decade. It includes a new section on the use of modern numerical methods for generating chaos and simulating random processes, a section on simulator verification, and provides applications of these methods for personal computers. Readers will find a wealth of practical fault detection and isolation techniques for simulator verification, fast functions evaluation techniques, and nested parenthetical forms and Chebyshev economization techniques. 1987 (0 471-08599-5) 430 pp. Numerical Analysis 1987 David F. Griffiths and George Alistair Watson An invaluable guide to the direction of current research in many areas of numerical analysis, this volume will be of great interest to anyone involved in software design, curve and surface fitting, the numerical solution of ordinary, partial, and integro-differential equations, and the real-world application of numerical techniques. 1988 (0 470-21012-5) 300 pp. ... Read more

Customer Reviews (2)

Fantastic book for beginner.
Great book. I strongly recommend it before reading an advanced book on Computer Algebra.

A book with lots of examples, but...
This book covers mainly the elementary topics in the algorithms of computer algebra. The book has a lot of examples which make it much easier to read. However, comparing to existing algorithmic algebra texts, thisbook is not really covering many topics. For example, Grobner Basis is notin the book. ... Read more

Product Description
Image algebra is a comprehensive, unifying theory of image transformations, image analysis, and image understanding. In 1996, the bestselling first edition of the Handbook of Computer Vision Algorithms in Image Algebra introduced engineers, scientists, and students to this powerful tool, its basic concepts, and its use in the concise representation of computer vision algorithms.Updated to reflect recent developments and advances, the second edition continues to provide an outstanding introduction to image algebra. It describes more than 80 fundamental computer vision techniques and introduces the portable iaC++ library, which supports image algebra programming in the C++ language. Revisions to the first edition include a new chapter on geometric manipulation and spatial transformation, several additional algorithms, and the addition of exercises to each chapter.The authors-both instrumental in the groundbreaking development of image algebra-introduce each technique with a brief discussion of its purpose and methodology, then provide its precise mathematical formulation. In addition to furnishing the simple yet powerful utility of image algebra, the Handbook of Computer Vision Algorithms in Image Algebra supplies the core of knowledge all computer vision practitioners need. It offers a more practical, less esoteric presentation than those found in research publications that will soon earn it a prime location on your reference shelf. ... Read more

Product Description
Computer Algebra and Symbolic Computation: Elementary Algorithms provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages.

The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and construct expressions, we can implement many elementary operations from algebra, trigonometry, calculus, and differential equations.

With a minimum of prerequisites, this book is accessible and useful to students of mathematics, computer science, and other technical fields. The book contains a CD with the full, searchable text and implementations of all algorithms in Maple, Mathematica, and MuPad programming languages. ... Read more

Customer Reviews (2)

well-written guide for building a basic CAS
Excellent book covering the basics of building your own computer algebra system, together with its partner text: "Computer Algebra and Symbolic Computation: Mathematical Methods".The author presents the mathematical fundamentals, practical challenges, formulaic solutions, suggested implementations, and examples in a few programming languages appropriate for someone building their own CAS from scratch in very clear prose.The author makes extensive further reading recommendations for each topic.

At each stage of the development, the author presents the motivation for each feature of the CAS along with formal basics of the math behind the techniques.The author presents the basic practical challenges faced by the computer and algorithms in working with the math.Together, these make the text appropriate for both those with math experience moving into programming, and programmers moving towards math.The author lists step-by-step techniques from a mathematician's point of view for solving the problems, and then continues to give algorithm listings in an easily-read "Math Pseudo Language", complete with flow charts explaining the more complex algorithms.A formal computational complexity analysis of the algorithms is not included.

The author's examples are provided in Mathematica, MuPad, and Maple, but not in C-like languages.The examples, however, are function/structure-based, and are thus clear enough as to be immediately extensible to the reader's language of choice.For an engineer, the examples amount to a practical recipe. The book also contains a CD with the examples & the text of the book as a .pdf.However, this .pdf is only directly accessible to Windows users.Mac users will need to use Windows to run the included Windows app which can access the .pdf and then save it into another .pdf file to use on their Mac.(I've never seen anything like this before!The .pdf files on the CD show up as "Zero KB Symbolic links" on the Mac which don't resolve unless opened in Windows!In the end, I was able to get the .pdf onto my iPhone so I can easily carry the e-book with me when traveling.)

The author provides insight into both the mathematical and computational limitations of the algorithms, the problems caused by the limitations, and frequently gives examples for recognizing the limitations or working around them.

Finally, the author provides extensive references for further reading for details on particular topics.

In all cases, the author's mastery of English prose makes the information easily accessible, which is not at all the case with some other CAS books I've wasted money on...Speaking of price, considering the extreme niche market and the exquisiteness of the text, the combined price of the two books was worth it.

To help the potential customer (as a preview is not available), this book is the one of the two books (which can be effectively read in any order), and covers the basics of CAS's, the included Math Pseudo Language (MPL), defining mathematical expressions as data and functions, solving first order ordinary differential equations, recursion, basic indefinite symbolic integration algorithms, manipulation of general polynomial and rational expressions, and transforming exponential and trigonometric expressions with expansions and contractions.

It's possible I may one day find a more extensive text with more advanced techniques, but the two texts provide a foundation for building my own CAS.

A scholarly text and a seminal reference
Computer Algebra And Symbolic Computation: Elementary Algorithms by mathematician and computer expert Joel S. Cohen is a scholarly text and a seminal reference to the science of computer algebra and programming elementary mathematical expressions both iteratively and recursively. Structures of polynomials and rational expressions, exponential and trigonometric transformations are also covered in this solid teaching tool packed with exercises and sample code. An accompanying CD provides the student with the entire print text, useful internet hyperlinks, and complete algorithms. Highly recommended. ... Read more

Product Description

Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems. The author tackles this complex subject with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated. Introductory chapters look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.

Customer Reviews (1)

A nice introduction, but be careful!
The title does no justice to this book. It is a nice introduction to Geometric Algebra for anyone, not just computer graphics programmers. It shows clearly, that Geometric Algebra is a better alternative to Vector Algebra, which is the mainstream method of dealing with 2 and 3 dimensional geometry.

Geometric Algebra is a far more logical way to deal with geometry than vector algebra. Vector algebra tries to represent geometry by building up everything from points. In Geometric Algebra you have more tools. In fact, you have exactly as many tools as there are kinds of basic geometric objects. In Geometric Algebra you have mathematical representations of points, lines, planes and volumes, exactly the things that come to mind if you think about geometry.

This allows, for example, for a far more logical description of kinematics. To give an example, within 3 dimensional vector algebra a rotation is represented by a vector perpendicular to the plane of rotation, formed out of a cross product.

Within Geometric Algebra a rotation is represented by ... the rotation itself! How? through the introduction of a bivector that defines the plane of rotation. The size of this bivector then represents the magnitude of the rotation. This is much more logical than artificially constructing a vector perpendicular to the rotation. In fact, the vector method often fails, not only within 4 dimensions, but already in 2 dimensions. You cannot represent a rotation in 2 dimensions with a vector perpendicular to the plane of rotation, because, in 2 dimensions there are not enough dimensions to do that. Moreover, it creates a wrong habit. In 3 dimensions you have 3 translation directions and 3 rotational directions. This creates the false illusion that, in general, the number of rotational degrees of freedom in any dimension is equal to the number of translational degrees of freedom. This is already false in 2 dimensions, wherein you have 2 translational degrees of freedom, but only one rotational degree of freedom. Within a 4 dimensional space there are 4 orthogonal translations possible, but no less than 6 orthogonal rotations. Or, simpler, when you look at the corner of a room in 3 dimensions, 3 lines meet, and 3 planes meet. But at a corner of a room in 4 dimensions 4 lines and 6 planes meet. Such things are surprises for people trained in thinking in terms of vector algebra. Geometric Algebra makes these kinds of things immediately clear. Also such things like understanding the distinction between ordinary and dual spaces are much clearer to see in Geometric Algebra than in Vector Algebra.

The nice thing about this book in particular is that it shows the most basic of calculations, and writes them out explicitly. This is why I bought the book. This could, in principle, be an ideal preparation for more advanced books in Geometric Algebra.

The reason why I do not give this book more than 3 stars is because the book has some shortcomings and contains errors. The most serious one is in the derivation of the equation m^n= B sin(theta) on page 138 - 139. Because of the misplacement of a minus sign, the whole derivation is clumsy, illogical and, of course, wrong. The final result is true, but the derivation is wrong. The author knew what the result had to be. And, since such an elementary derivation of this result did not exist anywhere else, the author had to find it himself, but made a mistake. That is really a pity, because, since this is the first book on geometric algebra on this elementary level, this particular derivation might give the impression that Geometric Algebra itself is far less elegant than it is.

The mistake the author makes, is thinking that -1-cos2(theta)= - sin2(theta).{With cos2(theta) I mean cos(theta) squared. And with a2 I mean a squared}

So, let me take this opportunity to rectify this, and restore the faith in the elegance of Geometric Algebra.

Begin simply with 1 = mm = mnnm=(mn)(nm)=(m.n + m^n)(n.m + n^m)=(m.n + m^n)(m.n - m^n)=(m.n)2 - (m^n)2.

Therefore (m^n)2=(m.n)2 - 1 = cos2(theta) - 1 = - (1 - cos2(theta))= -sin2(theta). The rest of that derivation then proceeds as in the book.

This derivation is a really nice illustration of the power of Geometric Algebra. By just beginning with the number one, and writing it out in geometric products, the identity the author tries to show, follows.

There is another shortcoming of this book. It does not contain exercises or problems. What I really would like is that every chapter would end with a collection of exercises and problems, with all solutions or the odd numbered solutions in an appendix. Just explaining various results of Geometric Algebra, and showing the details of how to work them out, is not enough to learn the subject, even at this elementary level. Especially with such a novel thing like Geometric Algebra it is essential that you 'get your own hands dirty', and experience yourself solving a problem that would be difficult to do with the old method. Mathematics in particular can ONLY be learned by actually DOING it, through actual problem solving. And the power of a new method only becomes clear by experiencing that you, yourself, are solving a problem that would be difficult, if not impossible without this method.

Since it is the only book that teaches Geometric Algebra on this level I know of, I recommend it, mainly because of a lack of alternatives. That is a negative reason. A positive reason is, that it really succeeds in showing the power of having a COMPLETE algebra of geometric objects at your disposal. This book shows clearly, thatvery many derivations that are clumsy and difficult to make in vector algebra, become easy and elegant in Geometric Algebra.

Consider also this. Before Newton and Leibniz developed integral calculus, people had to remember formulas of areas and volumes of spheres, cylinders etc. By just learning integral calculus there was no need any more to remember them. You could find many such formulas with only a few strokes of the pen. Moreover, integral calculus made it possible to find formulas for areas and volumes etc. that were not known, and were impossible to find.

In exactly the same way, Geometric Algebra replaces the need for remembering many theorems of geometry. On top of that, it gives a tool to find many geometric theorems that are virtually impossible to find with vectors, and vector algebra. Moreover, it transforms clumsy derivations in other fields into elegant one's. The one example that comes to my mind is the representation of 3 dimensions in quantum mechanics by Pauli matrices or Dirac matrices, which are, according to Geometric Algebra, much better seen as bivectors, trivectors etc. This book gives a very elementary introduction to just that, without being bogged down with details of physics. ... Read more

Product Description
Solving problems in quantum mechanics is an essential skill and research activity for physicists, mathematicians, engineers and others. Nowadays, the labor of scientific computation has been greatly eased by the advent of computer algebra packages, which do not merely perform number crunching, but also enable users to manipulate algebraic expressions and equations symbolically. For example, the manipulations of noncommutative operators, differentiation and integration can now be carried out algebraically by the computer algebra package.

This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explanatory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages Mathematica and Maple while some problems are implemented in C++.

Modern developments in quantum theory are covered extensively, beyond the standard quantum mechanical techniques. The new research topics added to this second edition are: entanglement, teleportation, Berry phase, Morse oscillator, Magnus expansion, wavelets, Pauli and Clifford groups, coupled Bose Fermi systems, super-Lie algebras, etc. ... Read more

Product Description
The book gives a thorough introduction to the mathematical underpinnings of computer algebra. The subjects treated range from arithmetic of integers and polynomials to fast factorization methods, Gröbner bases, and algorithms in algebraic geometry. The algebraic background for all the algorithms presented in the book is fully described, and most of the algorithms are investigated with respect to their computational complexity. Each chapter closes with a brief survey of the related literature. ... Read more

Customer Reviews (1)

Not a book for the weak of (algebraic) heart
Winkler presents an extremely concise overview of the major algorithms ofpolynomial algebra.In order to understand the text fully you must have avery strong background in abstract algebra.Even then you'll probably findyourself re-reading sections of the book in an attempt to reach anunderstanding.The advantage of this book over more explanatory texts(like Geddes) comes from the meticulous quality of the proofs andalgorithms. ... Read more

Product Description
Timing issues are of growing importance for the conceptualization and design of computer-based systems. Timing may simply be essential for the correct behaviour of a system, e.g. of a controller. Even if timing is not essential for the correct behaviour of a system, there may be good reasons to introduce it in such a way that suitable timing becomes relevant for the correct behaviour of a complex system. This book is unique in presenting four algebraic theories about processes, each dealing with timing from a different point of view, in a coherent and systematic way. The timing of actions is either relative or absolute and the underlying time scale is either discrete or continuous. ... Read more

Customer Reviews (1)

Comprehensive and accessible overview of the field.
Over the past decade, there have been significant advances in the area of formal methods that concerns itself with the specification and verification of timed systems. Many of the formalisms, methods, and techniques that had previously been used strictly in relation to untimed systems, have been extended to incorporate timing aspects as well. This book, somewhere in between a monograph and an advanced-level textbook, narrowly focuses on one of these methods, an algebraic one.

The method used is that of the Algebra of Communicating Processes [1,2,3], abbreviated ACP, and often just called "process algebra" by authors from the ACP school. Process algebra (a term I will strictly use here in the narrow sense of the ACP method) is a formalism that emphasizes the definition of and calculation with processes by means of equational logic. No fixed process model is imposed, and indeed many models have been proposed and studied. In practice however, mostly a bisimulation model based on structural operational semantics is used.

The authors start out with a general introduction to untimed process algebra, and then gradually incorporate timing aspects. In particular, two directions of research are methodically explored. Firstly, the choice of the time domain, where they examine both a discrete domain and a dense domain (basically modeling moments in time as natural numbers, and as real numbers). Secondly, the distinction between relative and absolute timing is made, the difference being whether references to time are specified with respect to an "absolute clock", or with respect to the amount of time that has passed since the last event within the process. All resulting four possibilities (discrete-relative, discrete-absolute, dense-relative, and dense-absolute) are studied in detail in four corresponding chapters, and in a very uniform manner indeed, which enables the reader to compare all four directions closely, and understand the issues involved. This is all the more encouraged by the authors, who go to great lengths to show the relations between the various theories. Finally, the authors conclude with two chapters that show how the framework set out in the previous chapters can be extended with other well-known concepts from process algebra, like the silent step or the state operator.

Throughout the book, the authors give a large number of example specifications and (partial) verifications, many of them non-trivial. Even while these examples are impressive, I must note that none of them are "real life" in the sense that our colleagues in industry would be impressed with them. I suppose such examples would not have fit the scope of the work, so it is only minor criticism, but I would love to see a companion volume on the applications of timed process algebra, in a framework of comparable maturity. A more serious issue for me was the complete lack of references to or comparison with related work outside the ACP school (for example to the timed extensions of CCS and CSP). Especially where the tradeoffs between the many options possible are discussed, one becomes very curious on how the corresponding issues in related work have been handled. I was annoyed by this, and feel it is a painful omission, equally so whether one views this work as a textbook or as a monograph.

Although almost everything presented in their book has been published before, the authors deserve significant credit for bringing together the most successful concepts in timed process algebra within a coherent and uniform framework. Whereas isolated publications have sometimes suffered from subtle and unexplained differences in definitions and approaches with regard to each other, this book succeeds in painting the bigger picture. In my opinion this is a clear sign that timed process algebra has grown up to be a mature theory, existing not only in the strict domain of academic research, but also ready for classroom teaching, and hopefully, industrial application.

Looking upon the work as a whole, I am pleasantly surprised by the combination of academic depth on the one hand, and the great number of examples and exercises given on the other. This makes it very suitable as a classroom or self-study textbook, for advanced undergraduate students, or for researchers in need of an introduction to timed process algebra. These textbook qualities are augmented by a large appendix containing a mathematical background primer. It would be incorrect however to view this work as a textbook only; it is just as much a monograph of timed process algebra, giving a comprehensive and accessible overview of the field.

References:

[1] J.A. Bergstra and J.W. Klop. Process algebra for synchronous communication. Information and control, 60(1-3):109-137, 1984.
[2] J.C.M. Baeten and W.P. Weijland. Process algebra. Cambridge tracts in theoretical computer science 18. Cambridge University Press, Cambridge, 1990.
[3] J.C.M. Baeten and C. Verhoef. Concrete process algebra. In S. Abramsky, D.M. Gabbay, and T.S.E. Maibaum, editors, Handbook of logic in computer science, Volume IV, pages 149-268. Oxford University Press, Oxford, 1995. ... Read more

Product Description

This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; introduces nonspecialists to screw theory in the geometric algebra framework; explores new developments in the domain of Clifford Fourier Transforms and Clifford Wavelet Transform; presents a detailed study of fluid flow problems with quaternionic analysis; examines new algorithms for geometric neural computing and cognitive systems; analyzes computer software packages for extensive calculations in geometric algebra.

Product Description

Modern computer algebra systems are revolutionizing the teaching and learning of mathematically intensive subjects in science and engineering, enabling students to explore increasingly complex and computationally intensive models that provide analytic solutions, animated numerical solutions, and complex two- and three-dimensional graphic displays.

This self-contained text benefits from a spiral structure that regularly revisits the general topics of graphics, symbolic computation, and numerical simulation with increasing intricacy at each turn. The text is built around a large number of computer algebra worksheets or "recipes" that have been designed using MAPLE to provide tools for problem solving and to stimulate critical thinking. No prior knowledge of MAPLE is assumed. All relevant commands are introduced on a need-to-know basis and are indexed for easy reference. Each recipe is associated with a scientific model or method and an interesting or amusing story designed to both entertain and enhance concept comprehension and retention. All recipes are included on the CD-ROM enclosed with the book.

Aimed at third- and fourth-year undergraduates in science and engineering, the text contains numerous examples in disciplines that will challenge students progressing in mathematics, physics, engineering, game theory, and physical chemistry. Computer Algebra Recipes: An Advanced Guide to Mathematical Modeling can serve as an effective computational science text, with a set of problems following each section of recipes to enable readers to apply and confirm their understanding. The book may also be used as a reference, for self-study, or as the basis of an on-line course.

Customer Reviews (2)

A good overall text

I took this class with one of the authors, George McGuire. The text strongly supports self learning, and has a range of engaging excercises for someone new to using a Computer Algebra system. It should be noted however, that this text exclusively focuses on MAPLE, and many of the harder questions rely on the user making large intuitive leaps in how to program MAPLE, and definitely relies on a large amount of knowledge not explained in the text.

cd format mac incompatibility fixed (for me)
Contacted Springer who manufactured cd in microsoft format incompatible to mac today (26Feb2002).

...These authors are masters. Each author, I find from surfing on the web, has a computer learning lab. The early reading introduces the fact that without the constraints of paper, undergraduates can learn to compose solutions to more realistic problems, eg. golf balls do not go on parabolas but do depend on your irons and crosswinds.

My last read text by the same authors, "Nonlinear Physics with Maple" edition 1 was a really inspiring book full of exercises. A master of solitons, Ablowitz, wrote (with) "Complex Variables" available at [Amazon.com]. Riemann Hilbert problems chapter 7 ought to further flesh out "Nonlinear Physics with Maple" last chapter concerning inverse scattering method in a to me readable manner. ... Read more

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Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them.Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators.The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications. ... Read more