good math books
rw: A few suggestions (if only we all had more time):Do ProjectEuler.net, as it provides a great mesh between algorithm design and mathematics; it might be within your expertise already, however. Look in to getting a good discrete math book or two. My circumstances led me to not use my discrete math book very much for class, so I won't give you a recommendation that I do not have.Go through Scholarpedia. They are doing cool work over there.Get some text(s) on statistical inference, especially Bayesian learning. If you have access to a good library system (say, state-wide library loan), you ought to have no problem getting most textbooks.Seeing as how you're into NLP and AI, look at concurrency and what, say, Google is doing with MapReduce and PageRank (they publish reasonably-understandable papers). In general, push yourself to read peer-reviewed journal articles on the topics of your interest.Peruse some of the organizations that do research into the philosophical and human issues surrounding AI and technology. For example, there's Less Wrong at lesswrong.com. They can come off as quite hubristic, but if you drill through the latent groupthink and individual over-assertiveness, you'll find a gigantic wealth of information on both what rationality is, and how to apply it to your life.Additionally, check out (I've mentioned these before, so I'll quote myself verbatim):"Problems On Algorithms" (Parberry, Gasarch): A slim volume containing ~700 exercises on proving various properties of algorithms. And it teaches you most of what is needed. Download it from: http://www.eng.unt.edu/ian/books/free/"Elements of the Theory of Computation" (Papadimitriou): Classic text. Sure you've heard of Turing machines before, but what do you know about mu-recursive functions? It's very beautiful and if you have a person with whom to read the book and do the exercises, you will gain immensely. It will help unify, in your mind, many of the myriad articles you've probably read on Wikipedia about formal languages and complexity theory.