A Y Khinchin was one of the great mathematicians of the first half of the twentieth century. His name is is already well-known to students of probability theory along with A N Kolmogorov and others from the host of important theorems, inequalites, constants named after them. He was also famous as a teacher and communicator. The books he wrote on Mathematical Foundations of Information Theory, Statistical Mechanics and Quantum Statistics are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour.

In his "Mathematical Foundations" books Khinchin develops a sound mathematical structure for the subject under discussion based on the modern theory of probability. His primary reason for doing this is the lack of mathematically rigorous presentation in many textbooks on these subjects. I can remember the vague feeling of dissatisfaction I felt as a student with some of the mathematics in Frederick Reif's "Fundamentals of Statistical and Thermal Physics" and other texts. Khinchin's little book puts everything on a firm mathematical foundation and yet is very readble.

I liked all three of these books but I think I liked this one best. The English translation was done by the eminent physicist and writer George Gamow. Nicely typeset in modern notation with index. This book is also a real bargain.

The literature on wavelets has been growing at an increasing pace, as testified by 129 titles listed in Amazon.com, the great majority which were first published in the last five years. Many of these books are either (i)popular accounts for the general reader, (ii) user's guides for the practitioner or (iii) advanced mathematical treatises for experts. Thus we find very few textbooks where the serious student can obtain an honest introduction to the subject from a recognized authority. This is even more surprising, given that the origins of the subject can be traced back to the mathematics literature in the early part of the 20th century under the names of Alfred Haar, Phillip Franklin and Sir Edmund Whittaker---and later to further work by Alberto Calderon in the 1960's. With the flurry of activity in the 1980's in the French school, the subject came alive and is now a permanent part of the literature in mathematical analysis, growing by leaps and bounds.

The book of Wojtaszczyk is a welcome addition to the literature on wavelets. Without the benefit of glossy pictures or computer output, the author has been extremely successful in presenting a clear and correct approach to the subject for readers who have a minimal acquaintance with mathematical analysis at the level of integration theory and elementary Fourier analysis. Going beyond other introductory works, the book contains a systematic sets of exercises at the end of each chapter, as a sort of "reality check" for the student, to test his/her understanding of the theory.

The first four chapters of the book deal with wavelets in one dimensions, continued in chapter 9. Following the examples of the classical Haar system and the Stromberg spline wavelet, done in great detail, we are introduced to MRA systems as a systematic method for generating wavelet bases of the space of square-integrable functions on the line. An MRA (multi-reolution analysis) is defined by a "scaling function", which satisfies an orthonormality condition, a scaling condition and a smoothness condition in the Fourier domain. Any such function generates an MRA, which in turn generates a wavelet basis. In particular one can generate in this framework the smooth wavelets of Meyer by this method, followed by the compactly supported wavelets of Daubechies. Wavelet theory is first formulated for square integrable functions, but can be extended to other Banach spaces, where it often provides an "unconditional basis", which is not true of the classical Fourier series.

Chapters 5-8 deal with some of the multi-dimensional theory, where several wavelets are necesary to generate the MRA, suitably defined. Chapter 6 contains a self-contained treatment of some important topics in analysis: the Hardy-Littlewood maximal inequality, the Banach spaces H^1 and BMO, the John-Nirenberg inequalty. These are used to develop the property of unconditional basis for wavelets in the spaces L^p and H^1.

The author suceceds admirably in carrying out his stated goal beyond any reasonable expectation: in the preface we read "This is a purely mathematical book, although I constantly try to make the calculations as explicit as possible and I concentrate on theoretical questions that should have relevance in appplications, but regrettably discuss no real applications". With the flurry of literature on the uses of wavelets, these applications are best left to other works.

One can expect that this book will be in print for many years to come.

The book touches the fundamental maths of networking in a simple form. Good for beginners and also advanced people who are tired of trying to remeber some basic formulas when they are needed...

This is one of the best books ever written in the field of AI. In particular with the innovative application of Dempster-Shafer, merged with all the best AI paradigms.

While most AI books contain coursework material or surveys of current algorithms, this book is a mathematical feast.

Be prepared to spend time, to understand the theorem proofs, before applying the theory.

The book is out of print. People who have the book and understand the theory are much ahead.

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.

Of all the books I've looked at to help me review mathematics for my economics PhD (it's been ten years since I did that stuff in college) this book is by far the best I've found. It's written very clearly and things are explained nice and slowly. The problem I have with most books in this genre is that they overwhelm you with zillions of equations and give me a migraine. This book, on the other hand, actually explains things.

I don't know anything about the Cd Rom because I borrowed this book from the library and the Cd Rom wasn't in it. But, I can't say as I really missed it.

This is an excellent book which covers many great ideas and potential methodologies applied to derivative pricing. It should have been published much earlier.

This book gives a quick overview of making money, or losing money more slowly, at various games of chance. Thorpe was best known for "inventing" a system of card counting for blackjack and basic strategy. He wrote the 1962 book "Beat the Dealer" which spawned a whole genre of win-at-gambling books that continue to this day.

"The Mathematics of Gambling" is quite different from those other books. For instance, it does not focus on just one game like most of the others. In fact, it barely explains a game at all. Instead, it describes the mathematical methods that might be used to win at the game more consistently. Think of this book as a starting point to understanding gambling theories.

The book starts with Blackjack, of course, and gives a very brief overview the game and betting strategies. This is mathematically heavy and many details are left out. It is followed by a counter-point of Baccarat which Thorpe concludes mathematically has much less room for winning strategies.

At this point, the book is just getting started. Although most gambling books focus on card games, or just casino games; Thorpe also gives mathematical insight into Horse betting and Backgammon. There are no clear-cut strategies forced upon the reader, just a general pointing in a direction that might prove helpful.

And that is the whole issue with this book. If you are looking for the one-true-path to gambling winnings, look elsewhere. If you want, instead, to read about mathematics applied to betting games this is the book to start reading. The writing is precise and clear and the math is not too horrid. Especially helpful is the time Thorpe spends setting up the underlaying math to working out a potentially successful strategy. Also, the final section on money management is excellent even if your game of chance is the stock market. A game Thorpe also wrote about in "Beat the Market".

This book is a short overview of some of the important mathematical techniques used to study genome sequences. In spite of the length of the book, the author does a fine job of introducing these techniques. Students of computational biology will especially benefit from its perusal.

The first section is a brief overview of the structure of DNA, m-RNA, and t-RNA. Recognizing that DNA is two large for direct analysis, restriction fragments are discussed in the second section, with emphasis on the restriction-enzyme fingerprint. The author's goal is to find the probability of occurences of a 6-letter word in a strand and the mean distance between occurrences of this word (assuming no overlap between the words or the occurences and equal probabilities for the bases). The effect of successive pair correlation (Markov chain effect) is considered briefly. This is followed by a calculation of the probability that a base pair is contained in a given clone. The author omits any discussion of algorithms for optical mapping, but does give a brief discussion of restriction maps.

The mathematics becomes more rigorous in chapter two, wherein the author analyzes a chain that exists as a set of cloned subchains with unknown overlap. This is the 'fingerprint assembly' problem the object of which is to produce a physical map of the full sequence. The fingerprint of the clone is a collection of lengths of a particular restriction fragments. This algorithm involves a sequence of contiguous clones called 'islands'; and 'contigs', which are two or more clones. The average number and size of islands are calculated assuming that the clones have equal length and identical overlap threshold. The method of anchoring is also discussed as a second method for obtaining the physical map of the genome. The author then considers the problem of covering the whole sequence by first placing n markers on a genome and covering by intervals centered at these markers. This is the restriction-fragment-length polymorphism analysis, the combinatorics of which the author solves by using Laplace and Fourier transforms. He also considers adaptive and non-adaptive pooling, in order to find a particular set of proteins on a large fragment.

The third chapter addresses sequence statistics, with the author addressing the nonhomogeneity of sequences and the correlation dependence in the bases. The chi-square test is discussed is some detail and the author discusses the accuracy of the Markov chain assumption. Noting that very long chains would be needed to determine the parameters for the expressions for the conditional correlations, he uses the maximum likelihood method to find the intrinsic correlation length, and then estimates the parameters by modeling the parameter set.

The author then studies the isochore regions and discusses their detection via the Jensen-Shannon entropy. Asking whether there are correlations between these long regions and within them motivates him to consider the long-range properties of DNA. This leads to the examination of a long fragment of a single strand of DNA, and with the assumption that strand-symmetry holds, the correlation coefficients are studied, with the decay properties of the auto- and cross-correlation discussed. Then, distinguishing only dual pairs, the author considers the probability that a pair is separated by an integer after an integral number of steps, a calculation that reduces to finding the largest eigenvalue of a 'transfer matrix', a procedure well-known in statistical physics.

Next, a consideration of simple sequence repeats leads to a difference equation that is solved by the method of moments. Windows of bases are then discussed, in order to improve on the statistics. Correlations within and between windows are calculated. Interestingly, the consideration of long-range correlations gives a power-law dependence for the correlations, which is related to the Hurst index for self-similar patterns. Readers get their first taste of hidden Markov models in this chapter, which are currently very popular in sequence analysis. Even more interesting is the discussion of walking Markov models, wherein a first-order base-to-base Markov chain is chosen to depend on a hidden parameter, and the time evolution is shown to satisfy a Fokker-Planck (diffusion) equation. Spectral analysis and information theoretic criteria are also discussed.

In the next chapter of the book, the author considers the most important part of sequence analysis, namely the comparison between sequences according to their linear ordering. The problem is to find the probability of a common subsequence of two linear chains with a given length. The first calculation assumes that the matches are mutually exclusive, and the result is an upper bound on the probability. The author then considers the matches to be independent events, and again bounds are given for the probability, the so-called Chen-Stein estimate). He also gives an estimate of the probability in terms of an asymptotic series. Extreme value methods are then used to calculate the expectation value and the variance of the length of the longest match. An interesting exercise is assigned for the reader; namely of finding the effect on the Fourier and Walsh power spectrum with the assumption that the base correlations are fractal in form. The alignment problem is then generalized to include replication errors, mutations, etc. The chapter ends, appropriately, with a discussion of multisequence comparison. The author poses the problem as one of finding the best match of a word to an n-tuple of words, which he tackles first using 'information content'. The category analysis of separating subsequence configurations into clusters is briefly discussed via simulated annealing, discriminant analysis, Bayesian analysis, and neural networks.

The last chapter is a short introduction to the biophysics of DNA. The Hamiltonian for the dynamics of DNA is given, thermal equilibrium is assumed, and the partition function is calculated. This is followed by a discussion of the dynamics at low temperature when the energy is given by RNA polymerase instead of the heat bath, and the dynamics is solved via the Lagrangian using Bessel functions.

This is an excellent introductory book, although mostly oriented to people with a reasonably good mathematical background. Searle covers most, if not all, the matrix algebra that you may need to fully understand applications of mixed linear models. Chapters one to eight cover the essential operations (addition, multiplication, determinants, etc) as well as more advanced concepts (rank, canonical forms, inverse, etc). The rest of the book (chapters nine to fifteen) covers applications to statistics as well as advanced topics that can help you to understand how do some of the statistical packages work inside. The only mathematics book that I have read from cover to cover. Definitively a classic.