good math books
hamilton: Everyone has given really great recommendations.  I second caffeine's PROCESS.  The way I learned most mathematics is from working through problems on a white board I bought.  From there I got a great grasp of probability theory and linear algebra, which gave me the legs to study statistical learning.While I have nothing to add on the math front, on the intuition / implementation front you should definitely check out Chris Manning's (currently) free textbook on Information Retrieval.  He delves into the history, technical details, and state of the art of IR.  Let's hope he opens up his NLP book as well (great CS prof at Stanford).If humanly possible, I'd recommend making a friend who can help you solve confusion or quandary about certain problems.  This is probably less likely for most people, but if you DO know someone with domain knowledge, I'd buy them dinner and pick their brain.  I've fully traversed the learning curve from both wrestling with problems and talking to people much smarter than me.http://www-csli.stanford.edu/~hinrich/information-retrieval-...