I wrote a supplementary blog post to Brad's ( <a href="http://pindancing.blogspot.com/2010/01/learning-about-machine-learniing.html" rel="nofollow">http://pindancing.blogspot.com/2010/01/learning-about-machin...</a>) with the list of books I found useful (no amazon referral links if anyone is worried)  with brief descriptions of each. I work in somewhat different domains and so have a different list of books.<p>I hope someone finds this useful.<p>For those who want a summary,<p>Proof Technique<p>(a)Velleman's "How to Prove It"
(b)Gries and Schneider's "A Logical Approach to Discrete Math"<p>Math<p>(c) Calculus (best "lite" book - Calculus by Strang (free download), best "heavy" books - (d) Calculus by Spivak, (e) Principles of Mathematical Analysis a.k.a "Baby Rudin")<p>(f) Discrete Math (ALADM above + (g) a good book on Algorithms, Cormen will do - though working through it comprehensively is ... hard!<p>(h) Linear Algebra (First work through Strang's book, then (i) Axler's)<p>(j) Probability (see Bradford's very comprehensive recommendations) and<p>(k) Statistics (I would reccomend Devore and Peck for the total beginner but it is a damn expensive book. So hit a library or get a bootlegged copy to see if it suits you before buying a copy, see brad's list for advanced stuff.)<p>(l) Information Theory (MacKay's book is freely available online)<p>Basic AI<p>(m)AIMA 3d Edition (I prefer this to Mitchell)<p>Machine Learning<p>(n) "Pattern Recognition and Machine Learning" by Christopher Bishop,<p>(o)"Elements of Statistical Learning" (free download).<p>(p) Neural Network Design  by Hagan Demuth and Kneale,<p>(q) Neural Networks, A Comprehensive Foundation (2nd edition) - By Haykin (there is a newer edition out but I don't know anything about that, this is the one I used)<p>(r)  Neural Networks for Pattern Recognition ( Bishop).<p>At this point you are in good shape to read any papers in NN. My reccomendations - anything by Yann LeCun and Geoffrey Hinton. Both do amazing research.<p>Reinforcement Learning<p>(s) Reinforcement Learning - An Introduction by Barto and Sutton (follow up with "Recent Advances In reinforcement Learning" (PDF) which is an old paper but a GREAT introduction to <i>Hierarchical</i> Reinforcement learning)<p>(t) Neuro Dynamic Programming by Bertsekas<p>Computer Vision<p>(u) Introductory Techniques for 3-D Computer Vision, by Emanuele Trucco and Alessandro Verri.<p>(v) An Invitation to 3-D Vision by Y. Ma, S. Soatto, J. Kosecka, S.S. Sastry. (warning TOUGH!!)<p>Robotics.<p>(w) Probabilistic Graphical Models: Principles and Techniques (Adaptive Computation and Machine Learning) - not about robotics per se but useful to understand the next book<p>(x) Probabilistic Robotics (Intelligent Robotics and Autonomous Agents) by Thrun, Burgard and Fox<p>PS: I own all these books (except AIMA 3 for which I only have pre pub pdfs)  and if any HN folks in Bangalore want to browse before they buy anything (friggin expensive when you add amazon's postage)  send me email.<p>PPS: on languages, I think Bradford is on the money with regards to reccomending functional languages. I would just say, also know C well. Saved my ass a few times.