I mean this book is really thick: http://www.amazon.com/Asset-Price-D...=1366085365&sr=1-1&keywords=Stephen+J.+Taylor An example of math/stats theory that I think I should know to develop a profitable day trading strategy would be Monte Carlo.
Not worth the paper it is printed on ... For example: p.28 (from amazon look inside): "Finding prospective quantitative trading strategies is not difficult. There are: * Business school and other economic research web sites. * Financial web sites and blogs focusing on the retail investors. * Trader forums where you can exchange ideas with fellow traders. After you have done a sufficient amount of Net surfing or trading magazine riffling, you will find a number of promising trading strategies. ... " Either this guy is a total moron or ...
http://www.amazon.com/Mathematics-Poker-Bill-Chen/dp/1886070253 http://www.amazon.com/Fixed-Odds-Sports-Betting-Statistical/dp/1843440199
Since you were asking for maths/ stats books, this is one of the best introductory stats/ ML books IMO: http://www-stat.stanford.edu/~tibs/ElemStatLearn/
Don't waste your time reading books ... Take a look into papers in http://arxiv.org/archive/q-fin to get some rough idea what math can be applied and then cherry-pick math lecture notes for the topics you are interested in. (Fortunately, the math used in q.finance is rather primitive ...)