*Investment Mathematics* is the best (and perhaps only) book that deals with financial mathematics in a serious and useful way without requiring much in the way of math prerequisits (pre-calculus/linear algebra math ... actually a little bit of calculus knowledge would help, but it isn't absolutely necessary). With the potential audience for such a book, I'm surprised that this is the first review of this book.Unlike other books that don't quite live up to the hype in its backcover descriptions, this book does live up precisely to the descriptions on the cover (and in Amazon's info section). I won't repeat what is written there. To sum up the book very briefly, it covers a wide swathe of issues in financial mathematics that range from basic issues like interest rates and the time value of money all the way up to advanced topics like modern portfolio theory, option pricing, ARCH/GARCH, and Value at Risk.
One thing to note in particular is that this is one of the few finance/investment books that I have seen that goes into detail about downside risk calculations (i.e., "semi-variance"). Most other books, even books that are on a more advanced level, often neglect to deal with the subject or just does some handwaving about it. The authors actually give you the mathematical gist of it in the book.
One of the more useful aspects of this book is not given in the descriptions: It has several sidebars that gives some tips on how to use Excel to implement the models discussed in a practical setting. There are other books that go into more detail (such as *Advanced Modelling in Finance and Investment Using Excel and VBA*) but the authors ought to be commended for putting information about Excel just in case people don't own those other books.
A much more important reason for why I am impressed with this book is that the authors do an excellent and mathematically accurate job of going over the mathematics of finance that doesn't require calculus or linear algebra. I can't think of any other book besides this one that I am familiar with that actually deal with the underlying mathematical logic of finance. Most other books on finance deal with the math on a cookbook level. It is truly refreshing to see a book that helps the reader to see inside the 'black box' of mathematics to see WHY financial formulae and methods are constructed the way they are.
In connection with the point made above, I also appreciated the useful prose, descriptions, pictures, and sidebars that dealt with potentially useful mathematical details and tidbits - like the mechanics of geometric series and the relative positions of the mean, median, and mode, in various distributions - that are not included in most books on finance that I'm aware of. Some of those details may seem basic and trivial, but it is nice to have that information in one place (and/or not have to run to a non-finance math/stat book) and is very instructive for people for whom such details are not trivial.
The only weakness of this book is one of the book's strength: It's lack of calculus and linear algebra. E.g., even when it talks about stochastic models, it really doesn't get into stochastic calculus. On advanced topics such as MPT, option pricing, ARCH/GARCH, etc., the goal seems to be to build intuition. However, this is a rather limited goal. One cannot truly grasp the complexity of those advanced topics without delving into calculus, linear algebra, and advanced probability and statistical theory. For people who are interested in getting a relatively accessible intro into those topics, I would recommend books by people like Paul Wilmott.
So, in summary, I believe that this book will be a useful introduction to financial mathematics pre-calculus/linear algebra. For those looking to get into more advanced topics in financial mathematics, I would highly recommend this book because it gives an excellent overview of those advanced topics and can serve as a bridge to more advanced issues.
In fact, I would recommend this book to some people who consider themselves to be quants dealing with financial math on a higher-level than does this book. Why? Because I strongly believe that many people - even highly sophisticated people - often received cookbook training in financial modeling. Therefore, many people don't understand the basic logical underpinning of what they are doing! *Investment Mathematics* remedies that situation by doing an excellent job of dealing with the mathematical logic of 'basic' financial mathematical models.
Further recommendations: The only other book that I know of that comes close (but is not quite as comprehensive) to dealing with the logical underpinnings of financial formulae/methods and provides useful tidbits on financial math is *Puzzles of Finance* by Mark Kritzman. Another book with a similar zeitgeist (and target audience) as *Investment Mathematics* - but focused in on financial risk - is *Fundamentals of Risk Measurement* by Marrison.
