This is not to say that there are no analytic solutions presented in this book. Quite the opposite: I found the fact that a good third of the space is taken up by investigations into analytic models somewhat disappointing, as that is perhaps the area where Mathematica gives you the least advantage over other platforms.
The part dealing with finite difference and Monte Carlo schemes is excellent, however. The mathematics of the models is introduced in a very clear and concise fashion, and after this no-nonsense introduction you get straight into coding things up in Mathematica.
Against the background of the high-quality discussion of the issues that do find their way into this book, the number of currently important topics that are lacking treatment is regrettable. I would have particularly liked to see examples of inverse problems, letting Mathematica do the work of calibrating model parameters to more market observables than e.g. just constant stock volatility. Wouldn't we all love to use Mathematica for the calibration, as well as the evaluation and benchmarking of such hotly discussed models like stochastic volatility models or local volatility models? How much time we could save by not having to code all these steps in C++ or worse environments! It seems it would have been a small step for the author to take us that little bit further along, but a large step for the majority of the readership who doesn't share the author's proficiency in the use of Mathematica. Still, if this more advanced level of usage is your aim, the book will at least start you off on the right track.
For a reader familiar with or interested in using Mathematica for (mostly Equity) derivative modelling and valuation, I cannot recommend a better book in the market.
Even for readers not familiar with Mathematica, the treatment of finite difference methods, the need for multiple time step techniques, and the analysis of errors arising from using these techniques is well worth a careful read. The treatment of how various trees binomial, trinomial etc. fall out as special cases of more general discretisation methods is one of the clearest I have seen.
Wall Street modellers will do well to review their algorithms and implement many of the techniques offered in this book. Easy accessibility of the code (CDROM accompanies the book) for Mathematica users is of course a big plus.
Altogether, an excellent addition to my derivatives library.