In that case, I think you'll want to study mathematical logic, theory of computation, incompleteness/undecidability and model theory, to improve your ability to contribute to the open problems that Eliezer thinks are most plausibly relevant to Friendly AI. Skimming our recent technical papers (definability of truth, robust cooperation, tiling agents) should also give you a sense of what you'd need to learn to contribute at the cutting edge.
A few years from now, I hope to have write-ups of a lot more open problems, including ones that don't rely so heavily on mathematical logic.
Something closer to cognitive science based AI, which Paul Christiano and Andreas Stuhlmuller (and perhaps others) think is plausibly relevant to FAI, is concept learning. The idea is that this will be needed at some point for getting AIs to "do what I mean." The September workshop participants spent some time working on this. You could email Stuhlmuller to ask for more details, preferably after reading the paper linked above.
Sorry for the late reply; my mid-semester break just started, which of course meant I came down with a cold :). I've (re-)read the recent papers, and was rather surprised at how much of the maths I was able to understand. I'm feeling less confidant about my mathematical ability after reading the papers, but that is probably a result of spending a few hours reading papers I don't fully understand rather an accurate assessment of my ability. Concept learning seems to be a good backup option, especially since it sounds like something my supervisor would love ...
I'm starting my Honours next year, and would like to do something towards helping MIRI with Friendly AI. I would also prefer to avoid duplicating any of MIRI's work (either already done, or needed to be done before my honours are finished midway through 2015). I decided to post this here rather than directly email MIRI as I guessed a list of potential projects would probably be useful for others as well (in fact, I was sure such a thing had already been posted, but I was unable to find it if it did in fact exist). So: what sort of Friendly AI related projects are there that could potentially be done by one person in a year of work? (I suppose it would make sense to include PhD-length suggestions here as well).
Some notes about me and my abilities: I am reasonably good with math, though my understanding of probability, model theory and provability logic are lacking (I will have a few months before hand that I plan to use to try and learn whatever maths I will need that I don't already have). I am a competent Haskell programmer, and (besides AI) I am interested in dependent type systems, total languages, and similar methods of proving certain program errors cannot occur, although I would have to do some background research to learn more of the state of the art in that field. I would (hesitantly) guess that this would be the best avenue for something that a single person could do that might be useful, but I'm not sure how useful it would be.