New Math Hobbyist needs help with direction

[The Rev]

Hi. I've recently gotten interested in mathematics as a hobby, but I'm not sure what I should be studying in what order. I remember in High School we had Algebra I, then Geometry, then Algebra II, then Trig, then Pre-calc and so on. However, we never studied the really cool stuff (like multi-dimensional geometry, theoretical math, etc.), and I was wondering what subjects I need to study, in what order, to build a foundation for those higher math subjects.

I also need to find out what higher math subjects are available to study. (I really know very little about math beyond my basic algebra and geometry in High School, and having seen Good Will Hunting two or three times ).

Anyway, any direction, help, advice, criticism, or good wishes are appreciated.

BTW, right now I am reading through two books, Courant's "What is Mathematics?" and Kline's "Mathematics for the Non-Mathematician" as general mathematics primers, but after that, I'm not sure what a good next step will be.

Anyway, thanks for the help!



The Rev

 

[arildno]

Two areas you need to learn about:
1) Calculus
2) Linear algebra

 

[honestrosewater]

I just came across a book that I think is right up your alley: "Discrete Mathematics" by Norman Biggs. You can search through the book online. It's written for undergrads as an introduction to "higher maths". It has plenty of worked examples and problems- always a plus for self-study. It reads easily and looks rewarding.
mathwonk always recommends a book called "Principles of Mathematics" by Allendoerfer and Oakley. It's out of print, but you can find it used online (try amazon zshops, ebay, and bigwords.com).
What I read of "Mathematics: Its Content, Methods, and Meanings" was fascinating. It introduces a wide range of topics, so you may discover something that especially interests you. I think it's similar to "What is Mathematics".
I think logic helps with everything else. "Deduction: Introductory Symbolic Logic" looks nice- clean and modern, not too much boring extra crap. It doesn't assume any prior knowledge of logic (hence the "Introductory" bit ), uses both trees and natural deduction, and includes Modal and Free logics. I don't like Copi and Cohen's "Introduction to Logic", though it's supposedly the standard (in its 12th edition or something)- I think it has too much boring extra crap.
If you search this site, there are plenty of "what's a good book for learning [blank]?" threads.
You could also check out the math courses on
http://ocw.mit.edu/OcwWeb/Mathematics/index.htm. Their linear algebra professor, Gilbert Strang, is supposed to be excellent- he has video lectures online too. I think they also have forums for courses so students working through a course independently can help each other.
Simply browsing through a few course catalogs (most are online), noting the prerequisites and such, should give you a good idea of in which order subjects should be studied.
This http://www.math.niu.edu/~rusin/known-math/index/tour.html page, from the same site as above, more easy to navigate through than the tour.

 

[Crosson]

Calculus is my main suggestion, it should be enough to keep you busy.

Also of interest: logic and proof. It can be interesting to look back at high school geometry with newfound mathematical maturity, and appreciate the qualities of an elegant proof.

 

[The Rev]

Wow! Thanks for all the help, everyone (especially honestrosewater - great list of books and links - you get an extra thumb up :) ). I appreciate this, immensely!



The Rev