"want to be acquainted with all of the different fields" may actually be quite hard - you can't do complex analysis, differential equations in multiple dimensions etc. without having a very firm grip on standard analysis (including all the proofs and definitions that they normally skip in high school).
If you want to build up your math muscles (as a good preparation for actually studying maths), you should have a look at some discrete mathematics books (the one I had was "Discrete Mathematics" by Norman Biggs) as they teach you to think in terms of proofs.
If you want to get a thorough foundation for non-discrete maths, you should start with a good (university math) analysis textbook (No idea what's a good one in English).
Another approach you could take is to take a math book that is targeted at physicists and EE people - those usually skimp on the proofs and don't contain enough detail to understand the fundamentals behind it all, but bring you to the interesting (to physicists and EE people) stuff much quicker than a real math course would.
Oh, and if you hang out on Youtube, be sure to watch the catsters - this is category theory, presented by actual working mathematicians, at an accessible level (and with a cute UK accent too).
i'm not able to dig it up right away - but just a couple of days back there was a blog post by someone who gave a long, very comprehensive listing of topics that take you all the way from basic to postgraduate level math.
It was organized in a dependency graph kind of way.
If you want to build up your math muscles (as a good preparation for actually studying maths), you should have a look at some discrete mathematics books (the one I had was "Discrete Mathematics" by Norman Biggs) as they teach you to think in terms of proofs.
If you want to get a thorough foundation for non-discrete maths, you should start with a good (university math) analysis textbook (No idea what's a good one in English).
Another approach you could take is to take a math book that is targeted at physicists and EE people - those usually skimp on the proofs and don't contain enough detail to understand the fundamentals behind it all, but bring you to the interesting (to physicists and EE people) stuff much quicker than a real math course would.
Oh, and if you hang out on Youtube, be sure to watch the catsters - this is category theory, presented by actual working mathematicians, at an accessible level (and with a cute UK accent too).