I'm somewhere a long this path, so I can share my experiences. Something worth playing with is Coq, I enjoyed doing the most of course here. One benefit is that it uses a consistent notation to represent things and not too many unfamiliar symbols. It introduces things like the Peano axioms and other interesting stuff. It will also nail down commutativity, transitivity and other useful concepts. Not sure how useful it is, if you haven't done some programming.
For learning important symbols and terminology, I would look at Set theory. Knowing the difference between "member of" symbol and "subset of" symbol of is fairly basic stuff, I just picked it up by osmosis. Predicate calculus also crops up a fair bit, I got taught it in my computing degree. I've got Conceptual Mathematics because I found a fair amount of the maths around functional programming languages was expressed in terms on Category Theory. It was good for the first few chapters but my interest waned at some point and I find it hard to get back into,
I'm interested what other people would recommend.
As far as programming goes, pretty much anything that can be done with Game Maker 7, I can do, and I know a bit of Python. Formal logic-wise, I have Greg Restall's "Introduction to..." (I have a B.A. in Philosophy, on of the modules of which was formal logic). Thank you for the advice.
This will not be a long post; I have a simple question to ask: if you wanted to educate yourself to graduate level in mathematics, but didn't actually want to go to university, what would you do? I would ask for text-book recommendations, but I don't want to limit your responses (however, bear in mind that the wikipedia articles on, say, cardinality or well-ordering go over my head – they may skim my hairline, but over they go). Also bear in mind that while I personally have A-levels (British qualifications) in both Maths and Further Maths (which is to say, I know some calculus at least), there are probably plenty of people on lesswrong who don't and who desire the same information – so assume as much ignorance as you feel necessary (it's a shame, actually, that there isn't a sequence here on lesswrong for maths). What do you advise (if you think the query ill-defined, I would like to know that as well)?