Computer Science Books

Like main book "The Mathematica book", this is also paper version of help which is included in the program. But, many people like take a book rather then reading from monitor. The main "The Mathematica book" together with this one, is a complete set for using the program.

I can say that this book is useful. It briefly describes all add-on packages of the program, following by several easy-to-understand examples.

Add-on packages much improve an already powerful program, so using them increase efficiency of every serious task. This book helps one to do this!

Certainly, this book talks about the most powerful feature of Mathematica. It talks about the part of the sotware, that makes it the best mathematics programm that has ever been made until our days. Without the contents of this book (Mathematica Packages) Mathematica becomes a common software like many others that exist today. It will surely help any person to use all the facilities of Mathematica. If you have ever wanted Mathematica to do something for you and people said that it was not possible, you should take a look in this book.

Pictures, programs, proofs and explanations makes this one of the best math books I've seen. For example, Chapter 9 (Penrose Tiles) has 9 pages. In those 9 pages are 25 different pictures, many quite beautiful. There are 3 different programs given which will recreate all of pictures. In the midst of this is a very clear discussion of nonperiodic tilings and Penrose tilings. That's just Chapter 9, there are 25 other chapters, and every one of them just as good. The programs are provided on a CD, so you can experiment with them yourself. More interesting material is at the author's webpage.

Prof.Wagon shares his experience about the difficulties he encountered in ensuring the correctness of the algorithms.

The lessons he offers on the importance of careful thinking and meticulously checking the results of calculations is alone worth the price of the book.

The algorithms in the book require Mathematica 3. They seem to work well with Mathematica 4 as well.

The selection of topics is excellent. This book can provide a great start to a lot fun and learning with Mathematica.

I hope Prof.Wagon brings out a new expanded edition for the current edition of Mathematica soon.

The thing that makes this book great is that it lives up to its title and actually demonstrates practical approaches to using Mathematica. It covers the topics I've seen in other books and many that I haven't seen in other books like optimization and file IO.

This is the only Mathematica book I have seen with enough examples and depth to really show what Mathematica can do. The examples and quizzes are very clever and are a great reference to the subtle kind of tricks you can do to make your programs faster, cleaner, and smaller.

A selection of the diverse examples in the book: Chernoff Faces, Monte Carlo Simulations, Cryptography, 3D molecular-structure renderings, an Eliza program, and a discussion and comparison of functional, rule-based, and procedural programming styles.

Nancy and Colin have brought forward a Mathematica text of exceptional ease in learning. This text is current and has the same easy flow of information that has become the hallmark of this duo. It is well written for a self learning experience or can be adopted to a class setting. Of special note is the presentation of programming techniques, the book starts with the basics and continues to build the readers ability with Mathematica programming.

I have had an opportunity to review all three volumes of Professor Tang's Math Methods book. I must say that his explanations are clear, his examples are good, and he does not burden the reader with proofs for the sake of proofs. This three volume set is written for the practitioner, for students who need to solve problems analytically. I am teaching Graduate Engineering Electromagnetics in Spring 2008 and I am recommending this three-volume set as a resource to students. Mathematical software is useful, but I still believe that understanding the engineering problems through analytic solutions is a prerequisite to being able to solve equations computationally and understanding the solutions.

Bravo to Prof. Tang.

Having taken Mathematical Physics from KT Tang at PLU I used this book before it was published. Everything is laid out neatly and concisely making it very understandable and clear. It was easy to learn things straight from the book. Highly recommended for any engineer, physicist, or any other science related profession that needs knowledge of higher mathematics.

If you are in a situation like me, then this might be the best book. I read some introductory long ago at university. A few years from now I needed to refresh on the subject and get a little deeper. I have browsed or read some other books, but this is now my number one choice for reference. It starts very gently with e.g. spelled out examples on matrix addition. It ends with (by my standards) advanced topics like eigenstructures, quadratic forms, generalized inverses etc. I admire the writing style which is compact, precise and at the same time a little relaxed.

There are a lot of people out there who do statistical analysis but who do not possess the mathematical knowledge underpinning a lot of what they are doing (i.e., linear algebra and some calculus). Most of the time people can get away with using stastical software as a sort of 'black box' and not worry about the math. But there are situations when having the background knowledge is crucial.

This book does an excellent job of facilitating self-study of the math underpinning multivariate statistical analysis ... namely, linear (matrix) algebra and some calculus. Each chapter has a set of questions and ALL of the answers are provided in the book (handy for self-study). The one slight critique of this book I can give is that I wish the book did more on the calculus aspects. However, that is a minor comment and the knowledge that this book imparts of linear algebra to self-learners is extremely valuable.

College-level collections strong in either science or computer science - into the intermediate studies levels - will want to add MATHEMATICS OF DIGITAL IMAGES: CREATION, COMPRESSION, RESTORATION, RECOGNITION to their collections. These three elements are key to digital imaging - and the math needed to carry out all these components are explored in a textbook which offers both theory and practical applications and exercises. College-level courses will want to consider this as a classroom text on the subject, but specialty libraries will also find it a popular pick for advanced self-study.

Diane C. Donovan
California Bookwatch

This book is quite academic in tone, but practical in content. It is more of a math book that uses imaging in its examples than a book about imaging that uses math as a tool. It does a good job of starting from the beginning in any mathematical topic it explains, going through an explanation of the theory including proofs, and almost always showing at least one imaging example to explain each mathematical topic. Exercises are included, but these are not generally proofs in the classical sense. Instead, you may be asked to draw a diagram or image proving a theorem, or be asked to explain how a particular image proves a theorem. Answers to selected exercises are in the back of the book. Because this book has such good explanations on subjects such as the SVD and information theory, it might be useful to students that are not that interested in imaging simply because the analogies made to imaging make the mathematical theory quite clear. However, the last two parts of this six part book are very much aimed at those who are interested in image processing. I notice that the table of contents is not shown here, so I do that next:

Part I - THE PLANE
1. Isometries
Introduction; Isometries and their sense; The classification of isometries
2. How Isometries combine
Reflections are the key; Some useful compositions; The image of a line of symmetry; The dihedral group; Appendix on groups;
3. The seven braid patterns
Constructing braid patterns
4. Plane patterns and symmetries
Translations and nets; Cells; The five net types;
5. The 17 plane patterns
Preliminaries; The general parallelogram net; The centered rectangular net; The square net; The hexagonal net; Examples of the 17 plane pattern types; Scheme for identifying pattern types;
6. More plane truth
Equivalent symmetry groups; Plane patterns classified; Tilings and Coxeter Graphs; Creating plane patterns;

Part II - MATRIX STRUCTURES
7. Vectors and matrices
Vectors and handedness; Matrices and determinants; Further products of vectors in 3-space; The matrix of a transformation; Permutations and proof of determinant rules;
8. Matrix algebra
Introduction to eigenvalues; Rank and some ramifications; Similarity to a diagonal matrix; The Singular Value Decomposition;

Part III - Here's to Probability
9. Probability
Sample spaces; Baye's Theorem; Random variables; A census of distributions; Mean inequalities;
10. Random Vectors
Random Vectors; Functions of a random vector; The ubiquity of normal/Gaussian vectors; Correlation and its elimination;
11. Sampling and inference
Statistical inference; The Bayesian approach; Simulation; Markov Chain Monte Carlo

Part IV- Information, Error, and belief
12. Entropy and coding
The idea of entropy; COdes and binary trees; Huffman text compression; Huffman code redundancy; Arithmetic codes; Prediction by partial matching; LZW Compression; Entropy and minimum description length;
13. Information and error correction
Channel capacity; Error-correcting codes; Probabilistic decoding; Bayesian nets in computer vision;

Part V- Transforming the Image
14. The Fourier Transform
The DFT; The CFT; DFT connections;
15. Transforming Images
The Fourier Transform in two dimensions; Filters; Deconvolution and image restoration; Compression
16. Scaling
Nature, fractals, and compression; Wavelets; The Discrete Wavelet Transform; Wavelet relatives

Part VI - See, Edit, and Reconstruct
17. B-Spline Wavelets
Splines from boxes; The step to subdivision; The wavelet subdivision; The wavelet formulation; Band matrices for finding Q,A, and B; Surface wavelets;
18. Further methods
Neural networks; Self-organizing nets; Information Theory revisited; Tomography

Maybe you like the idea of this book but you are wondering, does it live up to the promise, will you actually read much of it, is it just too big? The answers are yes, probably yes, and no.

I've browsed maybe half of the chapters. Each one is clear, easy to skim through, with a lot to dig into if you want. So far I've found not one "book report" just summarizing recent work. I've found fascinating helpful interpretations of subjects I don't know -- and challenging positions on subjects that I have my own view of.

Of course you can find fault. The book leans more to applied math than I'd like. And what about functional analysis?

Overall, I am stunned to think I wavered on buying this. I almost passed it up. It would have been a big mistake.

This book is a look to the future of mathematics based on the trends in mathematical thinking at the present time. I did not read all the articles in the book, so my review will be limited to those I did. The article "Experimental Mathematics" by D. Bailey and J. Borwein is an overview of a somewhat controversial activity in mathematics. This activity, characterized as "experimental" mathematics, has, the authors argue, enabled very interesting mathematical problems to be eventually solved. They outline in the article the recent discovery of how to calculate the the nth digit of Pi without computing any of the first n-1 digits without multiple-precision arithmetic and needing only low memory. The calculation scheme was based on a formula that was discovered by a computer, the first time this has happened.according to the authors. Experimental mathematics can be viewed as "real-time" discovery of mathematics, as well as letting us visualize the mathematical structures involved using computer graphics. Mathematicians interested in network modeling will appreciate the article by F. Kelly entitled "Mathematical Modeling of the Internet". Interestingly, his approach makes use of dynamical systems, with the goal of studying the behavior and stability of the TCP/IP protocol. The most interesting section of the article is the section on packet marking strategies. One can find surprising connections between strategies for packet marking, packet shaping, and network QoS, with techniques in option pricing from financial engineering. This is particularly true for frame relay networks. This connection was not discussed in Kelly's article, but I have found these connections in developing my own network models. Kelly gives good insight on how to apply techniques from optimization theory and dynamical systems to study the behavior of modern networks. The network modeling of the 21st century will have to contend with wireless, DWDM, and other more exotic technologies. By far the most interesting articles in the book were the two articles "Geometric Aspects of Mirror Symmetry" by D. Morrison and "A Chapter in Physical Mathematics" by K. Marathe. The constructions that take place in the areas discussed in these two articles have to rank as the most fascinating in all of mathematics. And most interestingly, the ideas had a powerful influence from theoretical physics. One can say without question that physical ideas coming from quantum field theory/high energy physics justify a rephrasing of the words of the famous physicist Eugene Wigner. One could now speak of "the reasonable influence of physics in mathematics". Physical ideas have permeated many different areas of mathematics and will continue to do so. Some mathematicians have classified this influence as "physical mathematics" because some of the mathematical constructions have not been justified rigorously. Several brilliant mathematical developments have occurred in the last two decades resulting from ideas from high energy physics, such as quantum invariants of knots and three-dimensional manifolds, Seiberg-Witten theory, mirror symmetry in algebraic geometry, and supersymmetry and index theorems. These exciting results could be described best as kind of a "quantization of mathematics", and the future will hold more of the this line of thinking. Every construction in mathematics will have a quantum analog, with a correspondence between mappings/structures in "ordinary" or "classical" mathematics and unitary transformations/noncommutative structures in the "quantized" version. An example of this kind of development is occurring today in the field of non-commutative geometry. "Mathematics Unlimited-2001 And Beyond" is a brief glimpse of what will be an exciting century for mathematics. Quantum computation will no doubt become a reality soon, and its computational power, coupled with the needs of the information age, will push mathematics to new dizzying heights. What was called experimental and physical mathematics in the book will continue to have their niches; but "pure" mathematics will also hold its ground and continue to solidify and advance. The mathematical adventure is just beginning......

As a graduate student many years ago, I bought the last shelf copy of the first edition to Caswell's text on matrix population models for our bookstore. After 10+ years of using the book, both in research, and teaching, I'm glad I did. The 2nd edition is a lucid and masterful update, with several nice touches that should be appreciated by both newcomers and experienced modelers. In particular, some of the more turgid text from the first edition has been clarified, and expanded, and several new very important chapters have been added (yes, using branching process theory you can handle demographic stochasticity with matrix models). A superb book, made even better by the inclusion (at last!) of some basic MATLAB code for some of the more esoteric calculations. My only complaint (related perhaps to the 'code') is that the many good 'worked examples' are not treated more fully. I'd have liked to have seen the actual matrices involved, or some further detail, in some cases, rather than a figure or table summarizing the results. However, a minor complaint - perhaps easily solved by a companion website with code for each example in the book 9something I'm probably going to do on my own, but should be standard these days for any technical text).

There is often a false dichotomy drawn between differential (or difference) equation models of populations and agent-based (artificial life, individual-based, configuration) models. Agent-based models can represent more of the complexity of biological systems at the expense of analytical tractability. Matrix population models form a bridge between the two approaches.

Caswell shows how you can elaborate differential equation models to represent much of the population structure and characteristics of interest within a population. His descriptions are clear and easily accessible to biologists as well as people from the more quantitative fields of science.

The new edition of this book is due out in April 2000. I am looking forward to it.

Simple, precise and organized are the perfect adjectives for this book. It's amazing how the book guide you in an easy way through it chapters.
Im an Industrial Designer and I recomend this book and this software for all people envolved in product design.

Mechanical Desktop 4.0
Mechanical Desktop 5.0

One could burn a great deal of thesaurus time searching for the right superlatives to describe this book. The third element in a series that will hopefully never end, it is an exciting combination of computer science, philosophy, and playfulness. Dr. Pickover can rightfully be labeled the "philosopher king" of the computer world.
As was the case in previous books, the primary focus is on the computer generation of images, but in this work the author skips down other avenues of mental exploration. Computer generated mazes, fractal music, fractal ant farms (think about whether the ants or the farms or both are what is fractal), caging fleas in Hyperspace, virtual reality, and strange chess problems are just some of the items that are discussed. Short pieces describing strange forms of art creation appear at regular intervals.
The only place where this reviewer thinks that the book stumbles is in the short science fiction story. However, it is conceded that this may be an instance of personal prejudice. This reviewer is a longtime reader of the genre, with an emphasis on the so-called big three of Asimov, Clarke, and Heinlein. It may be unfair to compare anyone to those three.
The level of difficulty resembles a sine curve. Some passages require a good deal of knowledge in the area of math/computers, while others can be understood by anyone. All topics are well referenced, so anyone who wishes to explore further will have no trouble doing so. Questions designed to initiate further thought occur at the end of each essay.
Whatever your background and interests, you will find something of value in this book and both of the two previous ones, "Computers, Pattern, Chaos, and Beauty" and "Computers and the Imagination." To paraphrase an old advertising slogan, "no one can read just one."

Published in Journal of Recreational Mathematics, reprinted with permission.

Pickover presents numerous brief chapters providing excursions into computer art, mathematics, physics, and whatever other topic happens to be tangentially related to anything he cares about. In the hands of a less astute person Mazes for the Mind would be meaningless drivel. But Pickover is like a wonderful uncle you see a few times a year for holidays; he is full of fascinating tales to share. Anyone who is interested in how math shows up in odd places, and who has some familiarity with relatively advanced topics like chaos theory, number theory, topology, etc. should find plenty to occupy their minds in this work. Though some of the sections are too brief, the quick tours through each topic are generally enjoyable.

I'm most interested to see what other Pickover works are available.