I'm going to try to do some research next summer with a math professor who does math finance, so I'm trying to build a skillset that will allow me to follow along in his research. Besides NA (then parallel computing), calc-based probability and a class in PDE, all of which I hope to take this year, what other class would you recommend?
Hard to tell, as I don't know which courses are offered at your department... But, try to browse other alike threads on this forum, you'll find much advice on the preparatory materials/courses for doing quantitative finance related work from other (much more knowledgeable in that than myself) members of the forum. As far as CompSci related stuff, I'd add a suggestion to take some sort of advanced computer architecture course: if you intend to work on implementing numerical algorithms, where each cycle counts, it greatly helps to understand the architecture of modern processors - stuff like pipelining and superscalar execution, exploiting memory hierarchy etc. (again, you could easily recognize is the course good by the textbook used - if they use Patterson/Hennessy books, they are good to go).
As far as Burden & Faires concerned: Remember to stay persistent along the way, it's not an easy read (and it's rather lengthy book), but it's very rewarding. Also, the book is definitely not about pseudo-code only: you'll find
here implementations of all algorithms in C, Fortran, Java, Pascal, Maple, Matlab and Mathematica; so take your pick, and if all of these are not enough for you, then drop me a note and I can send you my own implementations in Fortran and Matlab (mostly un-commented but still in most cases somewhat simpler than author's versions, I wrote these in my two readings of the book - I've actually found implementing algorithms along the way as the best way to proceed with the book, and I'd strongly suggest the same, but when you're done with your own implementation, it's always beneficial to compare it with others).