
[0]: http://www.crcpress.com/product/isbn/9781420067187
[1]: http://seat.massey.ac.nz/personal/s.r.marsland/MLBook.html
1. Modern Algebra by John R. Durbin
2. Introduction to the Theory of Computation by Michael Sipser
3. Machine Learning - An Algorithmic Perspective by Stephen Marsland (not quite on the same level as the above two, but still pretty solid)
I think Tanenbaum's Operating System and Appel's Compilers books both go in this category too, they're big but not compared to their subject matter. But, I've seen enough people disappointed in both to think this is more my personal opinion at play.
http://www.amazon.com/Machine-Learning-Algorithmic-Perspecti...
Code here: http://www-ist.massey.ac.nz/smarsland/MLbook.html
________
the math is mostly the same math that physics and EE majors do for first 2 years, plus probability/stats:
https://www.seas.harvard.edu/courses/cs281/#schedule
http://www.zipfianacademy.com/blog/post/46864003608/a-practi...
http://fastml.com/math-for-machine-learning/
________
the general purpose programming languages mostly used are python, C++, java, and the statistical languages include R, matlab.
there's lots of good threads at /r/machineLearning, including
http://www.reddit.com/r/MachineLearning/comments/2i68f0/tack...
http://www.reddit.com/r/compsci/comments/2jw14w/which_fields...
also some books for people who haven't the rigorous math background yet are Intro Statistical Learning (James et al), the ones by Peter Flach, Steven Marsland, and Witten/Franke:
http://www.amazon.com/Data-Mining-Practical-Techniques-Manag...
http://www.amazon.com/Machine-Learning-Algorithmic-Perspecti...