I know of very few people who can make mathematics come alive the way Prof. Robert Young (Oberlin College) does. I have been a student of his for the past year-and-a-half. With him my mathematical maturity, integrity, and knowledge have soared. The acquisition of Excursions In Calculus has added tremendously to my growth. Prof. Young's book is a collection of some of his favourite topics in teaching elementary calculus and analysis. Intended for both teachers and motivated students of the calculus, he takes the reader through several beautiful realms of mathematical inquiry and discovery. His topics are diverse: infinite sums and products (including a brilliant presentation of some of the work of Euler, one of his favourite mathematicians), exponential spirals, Wallis's formula for pi, chaos and fractals, Cantor functions, the Weierstrass approximation theorem, and many more with an ambitious appendix on modular arithmetic and related topics such as the celebrated Chinese Remainder Theorem. Prof. Young treats each of his subjects with not only the highest responsibility and technical acuity of a trained professional mathematician, but also with the greatest reverence and passion for the glorious field to which he has devoted his life. The book reads not like a sterile mathematical text but as an intricately woven epic of centuries of mathematical inquiry and the rich personalities responsible. Complete with hundreds of very challenging and non-trivial exercises, this book has something for everyone, whether a motivated student of freshman calculus or a sophisticated mathematician. None will be bored, all will be mystified.

I bought this book to know more about measure theory and probability. It's at a very advanced level (graduate book). Many theorems are proved. The presentation may look a bit boring, but still, it presents everything you need to know.

As the author notes in the Preface, this is an exercise book rather than a problem book; most of the exercises are further developments of ideas in the main text (Korner's book "Fourier Analysis"), and are not supposed to be hard. (The exercises that are hard, are liberally hinted and explained so you can still work through them without undue mental strain.) There are also many alternate proofs of results in the main text.

Nevertheless the book does contain many gems. These are primarily results that depend on some of the same ideas as Fourier Analysis without really being Fourier Analysis. Some of these gems: an "insufficiently asked question of Halmos" (whether there is a uniformly convergent sum that does not satisfy the Weierstrass M-test); a harmonic analysis experiment involving two potatoes and some string; a complete proof of Apery's theorem that the Riemann Zeta Function zeta(3) is irrational; the Feynman trick for evaluating integrals by differentiating under the integral sign; a proof of the Prime Number Theorem; and Karamata's proof of Littlewood's strengthening of Tauber's Theorem.

The index is full of jokes; be sure to read the index and browse any interesting-looking items.

Leadbetter, Lindgren and Rootzen produced this classic text on extreme value theory in 1983. The first text on the theory and application of extremes was the book by Gumbel in 1958. Gumbel only dealt with the original result of Gnedenko which dealt with independent and identically distributed random variables. Galambos in 1978 came out with the first text to cover the dependent situation in detail. This text provided a more detailed and up-to-date account and unified some of the theory. It also provided some applications and gave an account of extreme value theory based on the point processes associated with level crossings. I was very pleased to see the first account of my thesis research on extremes for stationary processes covered in this text.

The book has not yet been revised and there are several recent books that include recent advances in theory and applications.

This text is still a major reference on my bookshelf and is probably the most commonly cited text in the literature on extreme values. As an example in the December 1999 issue of the journal Extremes (which specializes in the statistical theory and application of extreme values) this book is referenced in three of the four articles in that issue.

This book is a classic. From the mathematical bases of factor analysis to its applications, this book has it all. Despite its age, no one who ever performs factor analysis should be without it.

This book provides a nice balance of math, examples, and MATLAB computer. It was of great help for me to understand and code up my own forms of ANNs. The example code provided is a really nice feature. It also puts a great deal of emphasis on relating statistics with ANNs.

This Festschrift for Le Cam was organized by former students and colleagues on the occasion of his 70th birthday in 1994. It did not actually get published until 1997. There are numerous papers written by prominent probabilists and statisticians who worked in the area of asymptotic theory that Le Cam was so well known for. Erich Lehmann provides an essay on Le Cam's years at Berkeley. Diaconis and Freedman talk about the consistency of Bayes estimates in nonparametric regression. Dudley reviews empirical processes. Yang provides an application of Le Cam's work to sodium channel experiments. Stigler provides an historical account of maximum likelihood through the work of Daniel Bernoulli and Leonhard Euler. van der Vaart covers superefficiency. Donoho and Johnstone present some new results on minmax estimation based on wavelets. Many of Le Cam's colleagues at Berkeley contributed interesting articles including Beran, Blackwell, Brillinger and Freedman. There are nearly as many applied papers as theoretical ones in this festschrift. Other well known contributors include Aalen, Millar, de Acosta, Picard, Ferguson, Pollard, van Zwet, Roussas and C. R. Rao.

The book "Financial Derivatives in Theory and Practice" by P.J. Hunt and J.E. Kennedy is yet another textbook on modern mathematics of finance. Although the market seems to be saturated by countless texts on the subject, this book appears to be an original and valuable contribution to the current literature.

The book is divided into two parts: Theory (212 pages) and Practice (159 pages). The first part surveys the mathematics of no-arbitrage pricing theory. It starts by a succinct and rigorous account on stochastic calculus (including basic properties on Wiener process, theory of martingales, and a complete development of stochastic integration w.r.t. continuous semimartingales), written in the spirit of the monograph by Revuz and Yor. The section on SDEs is particularly detailed and covers many topics (e.g. strong and weak solutions, description of the Yamada-Watanabe construction) that are not typically found in texts on finance. All technicalities are treated with due care, and some parts of the text are accompanied with exercises. The first part concludes with two sections on pricing by no-arbitrage and term structure models. Overall this part of the book is masterfully written and it is certain to please a mathematically-inclined reader (I'm not sure about the others).

The second part deals with application of the theory in pricing, with emphasis on interest-rate derivatives. After starting off with an interesting discussion about the real-world modelling issues (risk-free vs. "real-world" probability measure, calibration and dimension reduction), the authors introduce basic fixed income instruments (FRAs, caps, floors, swaps, etc) and proceed by developing no-arbitrage pricing using the standard Black's formula. The next four sections containing material on pricing exotic European derivatives largely follow authors' previously published papers. The book concludes with several sections on pricing exotics and path-dependent derivatives that start with a nice accounts on short-rate (Vasicek-Hull-White) model and market models. The treatment of the latter also gives a systematic development of the drift correction factors for various choices of numeraires. The last section on Markov functional modelling follows one of the authors' papers. One detail that is obviously missing from this part is the treatment of hedging of interest-rate derivatives. Also additional comparisons between existing and the Markov functional model seem to be in order.

Tough the title may not sugest it... and that may be it's problem... it is a profound and easy to read book. Only a word can describe it with justice: It's briliant! Why so much entusiasm? Well...this is a kind of book that one expects to be hard to read... Instead it is Educative and Stimulating presenting it's "mathematics" basis as fun and practical without being superficial. Who may be interested in this book? Any Computer Science student and any programmer wiching to dive in waters larger than common programming. Forget Knuth, this is the one! I do recomend it without hesitation as a MUST in one's library. Just Briliant!

I had read many text books before, never had I read a text book as clear, precise, and straightforward as this one. Just by reading this book, you will pretty much understand everything in the course even if you don't attend the class. The language is simple and easy to understand. Since this book is for an introdutory course, most of the stuff is pretty simple, it might not be the best book for people who studied probability before , but I strongly recommend this book for beginners!