When I was in high-school I had a very intelligent and immensely helpful English teacher, who taught me much of what writing skill I possess today. He came in highly excited one morning, to share with us about a new book he'd come across. Evidently, they had, through a computer, discovered an entirely new reality, that was two-dimensional! And this was an actual event, cutting edge stuff.

Well, a few days later, he came in, quite chagrined, to tell us that, as he read further through the book, he realized it was a work of fiction. But his description had been interesting enough to motivate me to read the book.

The Planiverse's reality is that real, and supported by that much scientific and mathematical principle- Dewdney has done his research, to bring us one of the most delightful what-ifs I've found. Imagine reality just like ours, but take out the third dimension. Everything is well supported, every area of life covered, and the drawings immensely helpful. You truly begin to feel for all the characters in the book. But it's not just an exercise in mathematical possibility. It is a rich story, telling of spiritual journey and insight, as Yendred travels to find his answers. And I still remember the ending as grippingly and eerily numinous, as we realize how closely the Planiverse and our Universe are connected, and how limited we are in comparison to the Eternal.

I found this in the ECSU library, and had a wonderful time perusing it when I was supposed to be doing classwork. The only thing disappointing is that it's fiction. Other then that, it's a rather realistic portrayal of some startling events. Putting aside that the computer project come to life thing is pretty obvious, the rest of this stuff is just too original to pass up. Reading the account of two foreign cultures trying to communicate through a computer program, and having the participant on their side being rather of a mystic bent, makes for some very interesting stuff, as simple as kid's adventure, and as inspiring.

One of the greatest books of all-time. I don't want to over-sell it, so judge for yourselves. (heh) Seriously, this is probably the most complete fictional universe ever created. It reads like a dream and when it first came out (and I was a kid) I often wondered whether the events in the book had REALLY happened. It is that well constructed.

Before it originally went out of print I bought two extra copies so that I'd never be without it, I honestly suggest you read it, and if you like it at all - do the same. It will never leave your mind, and you'll be happy about that.

This collection of fifty-six classic problems in probability is a first-rate work. All of the solutions are well written and easily followed. The reasoning is general enough to allow you to go on and solve related problems. Examples are birthday matching, trials until success, cooperation, gambler's ruin, and Buffon's needle.
If you have a soft spot for problems in probability, this book is an inexpensive must.

Published in Journal of Recreational Mathematics, reprinted with permission.

Working through the colorful problems in this book is a great way to (re)learn and apply basic probability principles. There is a great deal of independence between problem so you are never quite sure how tough or easy the next one will be. On the other hand, several of the problems are clearly follow-ons that allow the exploration or expansion of some of the more interesting issues.

Though I've worked through the problems a couple of times, I bought a replacement copy when my original was "permanently borrowed" from my desk at work.

Even if you are not a big probability fan, you are more than likely to find something enjoyable in this book. Some of the problems are wasy, some are hard, and some are just strange, but it makes for a very entertaining diversion for the mathematically inclined.

This book is one of the tomes of probability theory. The material covered is not for the faint of heart though. The text explains things as do most graduate level math texts, in proofs and theory.

This is a GREAT book.
Unfortunately, I lost mine.
I wanted to buy volume 1, third edition, to replace the lost book but I got volume 2, second edition. Because volume 1 is SO GREAT book, I decided to keep volume 2 as well. How can be sure I ordered the needed one?

Although people often recommend K.L. Chung at our math department as an introduction to probability theory, i think that Feller is just another view of the problem. If you prefer a concise writing style then Chung is better. On the other hand, Feller's books are full of examples so that you cannot go through this book without having an accurate picture of the historical developments of probability theory and its many applications (even if sometimes applications are driving the need for theory...). This is anyway something you must have read if you want to get an intuitive understanding of probability theory.

Whatever your preferred writing style is, Feller is probably a "must-read" if you're involved on probability theory, just because of its importance in the literature, not because you like it. Maths are not just about formalism, they're also a matter of culture.

This is the long waited 2nd Edition of Trivedi¡¯s classic book on reliability and availability (R&A) analysis of computer and telecommunication systems. It is arguably the best single source book for gaining a comprehensive understanding of both the theories and the best practices of R&A analysis in computer and telecommunication systems. The book not only covers the theories (Markov chains, stochastic reward nets, fault trees, etc.) in detail, but also provides a wide range of real world examples in showing how to apply the theories. After reading the book, a reader would find it easy to start constructing analytical models for R&A analysis of computing systems.

I would highly recommend this book as an excellent advanced undergraduate or graduate course textbook. If you are doing any kind of reliability, availability and performance analysis for computer, telecommunication, or mission-critical systems, you should buy this book as a reference.

This is an excellent introduction to probability and statistics. For those interested in a solid grounding in the fundamentals of software reliability, I would highly recommend Chapters 3 and 6.

I took this course from Kishor a long time ago, using the first edition. The only problem with the first edition was that the bindings wore out: as a result, I've had several copies (including copies of the Indian student's edition I got while it was out of print in this country.) I did not do particularly well in the class; none the less I use the things I learned from his book literally every working day.

I'm about to order a copy of the second edition. Anyone else working with these things should do so also.

The DEFINITIVE text for classical Analysis

This book is the definitive text in classical Mathematical Analysis. It was first published in 1902 and the fact that it is still in print is testimony to it's wide ranging utility and appeal.

It should be noted that this text is not for those who are new to the rigour of Analysis; its presentation is suitable for a final year undergraduate or for the post-graduate student. More importantly, its wide ranging content of proofs and results would also prove useful to the Physicist.

The first part of the book covers the "essentials" of analysis: continuity, differentiability, summation of series, convergence and uniform convergence, and the theory of the Riemann integral. Subsequent chapters quickly but comprehensively develop the theory of analytic functions, the theorems of Cauchy, Laurent, and Liouville and the calculus of residues. These chapters knit very well into the earlier presentation of the basic processes of analysis! The pleasing thing is that despite the passage of time and the advent of hundreds of books on Complex Variable Theory, Whittaker and Watson's treatment still bears a mark of freshness and rigour.

Also included is a comprehensive treatment of expanding functions in infinite series and asymptotic expansions and summability of series. For completeness, the text also covers the theory of linear differential equations and Fourier series.

The second part of the book is what stands it apart from the rest. The authors provide a comprehensive discussion of the major transcendental functions: Gamma, Zeta, Hypergeometric, Legendre, and Bessel to name the more commonly encountered ones. The treatment is rigorous but the copious number of examples provides opportunity to learn the theory and apply it. Lots of apparently obscure results, many that would be useful in Physics applications, are cited as examples.

The latter chapters presents a treatment of Elliptic, Theta and Mathieu functions.

Overall, Whittaker and Watson will continue to be the guiding light for any serious scholar of classical analysis and an excellent reference point for the solutions to the fundamental equations of Mathematical Physics. Even though I am not a practising Mathematician, I find this a pleasant book to dip into: there's always a little surprise and something new to learn.

This book will live forever!

The older I get, the more I realise the truth of what my expert colleagues told me a long time ago: there is ONE book on analysis, and it's called Whittaker and Watson. Shame on CUP for reprinting it in less than perfectly top quality. I guess they know that people will always buy it. It is a book that starts from the very basics of real and complex analysis, and moves on to the very depths of classical special functions. It's a joy to read and to teach from. No respectable mathematical physicist can afford not to own a copy. And it's about 1/4 the price of a typical, low level, textbook.

I decided to purchase this title about three months ago after hearing lots of praise about it on the internet and wanting to learn the subject, and I can now see that this praise was not exaggerated. A hundred years after its first publication, this classic still remains the definitive general reference in the field of special functions and is a very solid textbook in its own right.

The book is split into two main parts: the first consists of short (but detailed) overviews of the various sub-disciplines of analysis from which results are required to develop later results, and the second part is devoted to developing the theories of the various kinds of special functions. The sheer breadth of topics and material that this book covers is utterly incredible. The major topics covered in the first part of the book are convergence theorems, integration-related theories, series expansions of functions and differential/integral equation theories, each of which are split into two or three chapters. The reader is assumed to be familiar with some of the subjects here and these chapters are intended more as a review, but they are still quite self-contained and will also appeal to those who have not encountered the subjects yet. (I am only 16 and know no more than ODEs and a little real analysis, but I learned some material from this)

The second section, which is really the heart of the book, starts off with a detailed treatment of the fundamental gamma and related functions, followed by a chapter on the famous zeta function and its unusual properties. The book then covers the hypergeometric functions - the focus is on the 1F1 and 2F1 types, being ODE solutions - which are perhaps the cornerstone of this field, followed the special cases of Bessel and Legendre functions. There are a number of ways of developing and teaching the ideas regarding these functions; this book mainly uses the differential equation approach, starting by defining these functions as solutions to ODEs and going from there. There is also a chapter on physics applications (using these functions to solve physics equations), which is sure to please the more applied math readers. The next three chapters are devoted to elliptic functions, covering the theta, Jacobi and Weierstrass types. (one chapter on each) The two remaining chapters are on Mathieu functions and ellipsoidal harmonic functions. Along the way, some additional functions are also sometimes mentioned in the problem sets. (barnes G, appell, and a few others) About the only room for improvement here would be some analyses of named integrals (EI, fresnel, etc.) and inverse functions (lambert W log, inverse elliptics, etc.), and perhaps more on multivariable hypergeometrics, but these things are not a big deal considering how much else appears in here, and I have not really seen any book out there that covers these anyway.

Each chapter has several subsections, usually one on each major theorem or property of the function in question, and these consist of the main discussion and proof, a few corollaries, and a couple of exercises that illustrate the usage of the theorem. At the end of the chapter, some more sets of problems are given; these mostly consist of proving identities and formulas involving the functions, so answers are not needed, but it would be nice if there was a showed-work solutions book available for students. The problems themselves are very well designed and some really require the use of novel methods of proof to obtain the result. The language is a bit in the older style with some unconventional spelling and usage, but it does not detract from the subject material at all (actually, I personally liked this form of writing), and the price is about right.

The only real complaint I have with this book has nothing to do with its content; it is the printing quality. The text font is simply too small in a number of places and also sometimes looks "washed out;" while it is still readable, such a classic gem as this definitely deserves a better effort on the publisher's part. (one of CUP's other works on the same subject, Special Functions by Andrews et al, has much better printing, although is not as good as this in other respects)

For those interested in the field of special functions and looking for something to start off with, A Course of Modern Analysis would be, hands down, my first recommendation. You cannot really do much better than this.

A.Field's "Discovering Statistics" (using SPSS for Windows)is a must book for not only undergraduate and graduate students but also for the instructors like myself. The language of the book is stimulating the redaer, and Mr.Field's way of explanation is both a creative one and has the sense of humor which makes the book more readable. Its content is well-designed and the reader is able to follow up what each type of analysis is all about, and more importantly how the outcome shoul be interpreted. Although first chapters are written as a refreshment of statistical knowledge, I would like to suggest to the reader to have a primary knowledge about both the basics of research methodology and statistical methods as well as statistical techniques to use them in accordance with the research problem(s).I would also like to point out the fact that some critical issues like "the meaning of standart error" is explained in an efficient way in comparison to that of ordinary statistics textbooks. In short, the book is, indeed, a very helpful one for anybody who wants to use SPSS for this or another reason.

Dr. Field,

Has written a book that should be an example to all others writing about: 1. SPSS and 2. Research methods. As a grad student I have been trying to put together all the stats classes that I have taken and the SPSS class I took and make sense out of it. This book was the final key that brought it all together. Based on logic ... its funny that the science of statistics should be so without logic as far as teaching goes. Again, this book is the way that books on stats and SPSS should be written. My only problems: 1. That while there is a lot covered, I wish that he would go through all (or almost all) of the statistical applications available in SPSS and 2. I would've liked to see a "refresher" on the commands to complete the statistical process talked about, at the end of the chapter. In summary, this book is the only book that I would recommend to those in need of help regarding SPSS and statistics. I can't wait for his new book, co-authored by Dr. Hole.

Field's book is simply the best volume written yet for beginning users of SPSS (Statistical Package for the Social Sciences). Unlike most stats or software books, Field uses humor, wit and quirky real world examples to provide an easy and enjoyable read. The version I purchased came with a CD including all the data used in the book's examples. Chapters 1-4 are great primers for stats and Field does eventually take the reader into some more sophisticated analyses including Logistic Regression and Factor Analysis. Step by step instructions are supplemented by screen captures and graphs. This is an invaluable book for anyone faced with the challenge of learning SPSS for a class or for business. I would recommend it over any of the 15 or so books I've read regarding SPSS -- including the official manuals!

This is an introductory book. It also fits in introductory level of Mathematical Statistics. The prerequisites are introductory calculus and linear algebra. Most theorems are proved in calculus style but there are some gIt can be shownsh that are not proved. So some readers may not be satisfied with the book, especially Math majors.

Logical steps are shown in detail; else logical gaps are contained within a level such that a first time reader can fill in the gap with a pencil and paper. Occasional mix with Bayesian perspective is also a feature. Answers to odd-numbered exercises are provided except ones that ask derivations and proofs. Exercises that require some tricks are provided with hints. In these respects, this textbook is suitable for self-study.

Upon completion of the entire material, I feel concepts are developed well up to Hypothesis testing Chapter 8 where the presentation of material reaches climax and its level of exposition is somewhat higher than other chapters. Thereafter, simple linear regression is treated in detail, but coverage and detail of materials seem to deteriorate from the following general regression section, nonparametrics and thereafter. Kolmogorov-Smirnov Tests section is treated nicely though. Anova section lacks in coverage. The new simulation chapter is presented more like a demonstration rather than an introduction.

I have never seen the previous 2nd edition (unfortunately Dr. Degroot is no longer with us), but according to the preface of this 3rd edition, Dr. Schervish describes 8 major changes from the previous edition. Notable are some material removed from the previous (likelihood principle, Gauss-Markov theorem, and stepwise regression), some added (lognormal distribution, quantiles, prediction and prediction intervals, improper priors, Bayes test, power functions, M-estimators, residual plots in linear models and Bayesian analysis of simple linear regression), more exercises and examples, special notes, introduction and summary to each section, and so on. I find the last in the list is somewhat disturbing, especially introduction parts that are often redundant with the very next paragraph. On the other hand, I find that special notes provide good insights.

I wish they included introduction to Statistical Decision theory, full coverage of regression analysis to be usable such as diagnosis, transformation and variable selection, coverage of Multivariate Normal distribution, more coverage and depth in nonparametrics and simulation, and lists of recommended readings for further study at the end of each section with comments.

There are a noticeable number of typos as of this first printing I have. I sent suggestions for typos and was impressed that Dr. Schervish updated errata list within a few days at his homepage. I wish all authors were like him being responsible.

I used to hate statistics, but this book is pretty clear and concise, and gets the idea across very quickly and easily. The exercise questions were of reasonable difficulty, and are put forth in a clear manner, unlike other books which present the questions in round-about manner. The examples tend to follow on or build upon from the earlier chapters, so it is best to tackle the book in the order as prescribed by the chapters.

I have looked at many introductory books to probability and statistics and this one is definitely the best. It is very clear and readable and yet gets to pretty advanced stuff.

To knowledge seekers, the ability to understand and beat a system is the entire game. In this book, Skiena describes how he and some of his students wrote a computer program to win money betting on professional jai alai matches. Along the way, he explains the origins of the game and some of the basic rules, the fundamental bets that can be made as well as the meaning of statements such as pari-mutuel betting. His program does work well, in that he quadruples his money in a short time. Once that is done, he gives the money to a university charity, hoping to make his money from writing this book.
The fact that such a program could be created is not surprising. Jai-alai is a sport where individuals compete one-on-one or in teams of two, and the betting patterns determine the payoffs. It is much easier to simulate these types of matchups and predict the outcome than it is for team games. Baseball managers have been doing such modeling for years. If my memory serves me correctly, the first to do it in major league baseball was Davey Johnson, who kept detailed statistics on all pitcher-batter matchups. All of his decisions concerning who to put up to bat were then based on playing the percentages. That is essentially what Skiena does, although with a different twist. Pari-mutuel betting is where those who wager are betting against each other, so the patterns of wagering determine the payoffs. The patterns of betting are also factored into his predictions. These conditions make it possible for someone to make money creating such a system, but only as long as no one else is doing it. If others begin to use the same system, then the players are betting against each other, destroying the opportunity to make a profit. Therefore, his very act of publishing this book probably means that his system can no longer be used to win at jai-alai betting.
This is an excellent example of how basic mathematical modeling is done. Use data of previous results to form a model of what has happened in order to predict what will happen. Skiena writes with a wit and rigor that is rarely seen in mathematics. Very little mathematics background is needed in order to understand the explanations of the behavior of the program and why it works.
I found this book so interesting that I stayed up very late finishing it. It reads like a novel, but teaches you a lot about mathematics. Instructors in mathematical modeling and computer programming can find many interesting ideas for classroom exercises in it. As long as no one takes it too seriously, it is all in good, clean fun.

It's an enjoyable read. Pretty light on mathematics and software engineering though. You can easily get through this book in an evening or two and refresh some of your thoughts on modeling and statistics. Steven Skiena keeps a web site ...that's worth a peek and has reading material on this work there. Wish the book had shipped with a CD though so you could play around with his model and simulate a few games of Jai Alai for fun.

This is a fascinating book. It captures exactly the excitement of starting out in programming and working on a project in your spare-time simply because the project seems like a fun, cool thing to write, such as a program for predicting the outcome of football games. Even if you don't come from a mathematics/programming background, I think you'll find the book very interesting. Chapter 4, "The Impact of the Internet", alone, is worth the cost of the book.

I can't say more than what already been said by other reviewers. To recap,

F = {all excellent combinatorial optimization books}
cost(this_book) <= cost(y) for all y in F.

;)

I had this book on my shelf for two years before taking a serious look at it, and only wish I had read it much earlier in life. Christos Papadimitriou has written quite a gem! On one hand this book serves as a good introduction to combinatorial optimization algorithms, in that it provides a flawless introduction to the simplex algorithm, linear and integer programming, and search techniques such as Branch-and-Bound and dynamic programming. On another, it serves as a good reference for many graph-theoretic algorithms. But most importantly Papadimitriou and Steiglitz seem to be on a quest to understand why some problems, such as Minimum Path or Matching, have efficient solutions, while others, such as Traveling Salesman, do not. And in doing so they end up providing the reader with a big picture behind algorithms and complexity, and the connection between optimization problems and complexity.

After reading this and Papadimitriou's "Introduction to Computational Complexity" (which I also highly recommend), I now consider him one of the best at conveying complex ideas in a way that rarely confuses the reader. I also had the priviledge of attending one of his talks on complexity, and he seems just as effusive and transparent as a lecturer as he does a writer. Ah, for once I bought a Dover book that did not disappoint.

One could buy this book for different reasons: interests in combinatorial optimization, of course; interests in what Papadimitriou has to say, since his thoughts on this subject are definitely invaluable; perhaps the price is a good reason alone.
Whatever the reason, however, I think that would be a rare event to remain duped.

I was preparing my exam in Computability and Complexity when I first used it. I've been wonderfully surprised by the amount of definitions, algorithms, concepts I've found in this book. I think one could use this book for a simple course on Algorithms, on Computability and/or Complexity, on the whole Combinatorial Optimization, and the book would be always and costantly useful.

The chapters on algorithms and complexity, or those on NP completeness have proved to be gems. The chapters on Approximation and Local Search are great, and they feature a bunch of detailed and excellent quality stuff (e.g. there is a detailed treatment of Christofides' algorithm to approximate the TSP, that is quite an idiosyncratic topic).

All in all, a very great book, with a value exponentially greater than the very insignificant price.