the road to learning useful math
caffeine: Could you be more specific about what kind of math you've been seeing in the papers that you'd like to understand (and/or link some of the papers)?  What you need to know is on this list http://www.gatsby.ucl.ac.uk/teaching/courses/ml1-2009/cribsh...  for the most part.  Because math is layered, once you've got three or four layers of unfamiliar abstraction, it gets very hard to figure out what's going on.The way to get around this initially is by brute force.  For example, say you have a matrix function (from matrices to matrices).  The formula uses the exponential of a matrix, and you're not sure what that actually looks like.  So find the definition, and write it out.  Think about what that means, maybe do a couple of examples to get a sense of it. Write out your matrix function with this definition expanded (which probably means you'll write it element-wise), so that you know what each element of the output matrix is as a function of the elements of the input matrix. Work a couple of examples, think about it.Eventually, you get familiar with the exponential of a matrix, and you do the mapping in your head - so your brain has just acquired a new abstraction. The process above applies to basically every mathematical structure you'll run into.  Sometimes you'll have to recurse a few levels.It's not about books, it's about process.  You can know how to do lots of math problems and still not grok papers - and you can learn to quickly grok papers and be able to implement them / reason about them without being very good at math problems (I'm in the 2nd bunch). In terms of books, you only really need Wikipedia / Wolfram MathWorld, plus maybe one of the standard math references like Kreyszig or Boas.  Learning to use Mathematica can make your life much easier as well.One last comment:A book that totally changed my relationship to math is Peter Szekeres' Modern Mathematical Physics: Groups, Hilbert Space, and Differential Geometry. The explanations are uncompromisingly lucid, written in plain english, with minimal symbol walls.  The book takes you essentially from zero, and introduces nearly all the math that underpins modern physics.  This book really changed my conception of myself - I've lost my fear, when reading papers, that maybe this is the one I'm not smart enough to understand.  When that fear goes, the stress goes - and you know it's just a matter of learning the definitions.  Then it becomes pleasurable, like a puzzle.