What Advanced Math Should I Teach Myself Next?

[Fragment]

If you can find an older edition(1&2, but they are usually expensive) of Jacobs, then they are great. The newer versions seem more 'watered' down. If you cannot find those, then you should look for Larson or Sullivan, and Gelfand.

 

[Howers]

Granted, but it was still condescending, and that's all I was trying to point out. When I was called out on it, I specified what I meant. I don't think anybody disagrees that Hower could have been more tactful.

And I can only assume that people who ask for something know what they're getting into. The books I linked to assume a level of mathematical maturity on par with an understanding of linear algebra and possible some abstract algebra as well. The OP can probably judge for him/herself based on the level of understanding of that material how much they really know about math.

Oh well. I just think it's a little pretentious to offer advice where it isn't asked for. The OP didn't ask "do I know what I'm talking about". And he didn't make any claims beyond that he had been doing some self-study... certainly nothing to argue with. I don't disagree with suggesting that self-study may not be the most effectual method of doing things, and that making sure you have a strong grasp of the fundamentals is important, but... anyway, I think you guys see what I'm saying.

I see your point, but most students feel they have mastered elementary math in school without realizing what curriculum they are getting it from. Hence, I suggest real books to make sure that is indeed the case. If they have, nothing is lost by looking over free references.

I didn't mean anything by my remark about his age other than surprise. I know gifted people exist... in fact, that's almost all I post about. Its not my intention to slow him down at all, which is why I listed the modern books anyway in case he gets bored. I just think its safe for him to spend a couple of months getting up to speed if it is needed. Lastly, don't project overtones of your own insecurity onto me.

 

[kingdt]

Most of the pure math majors at my school took many college courses when they were in junior high and high school(or international equivalent). I would REALLY recommend trying to take classes from a local university, that way you will really learn the material well and get credit for your work (I mean on transcripts and resumes etc) instead of wasting your time in high school.