Where to go from learning precalc and a bit of calculus?

[mrwall-e]

Hi,

This isn't so much a coursework question, but a 'where to go from here' question. But because I'm not in college, I figured it doesn't really belong in the academic guidance forum. But anyways, on to my question.

Currently, I'm finishing up a 5-week precalculus course at a local community college in which I have a score of a 97 as of right now. On my own time right now, I'm reading the book "How to Prove It", which so far has been very good for a solid, if a bit difficult [for a noob like me], introduction to logic and proof. As one of the "honors" courses last year, I learned quite a bit of set theory, so that section of the book was not too difficult. Also, starting a few days ago, I've been slowly working through Thompson's Calculus Made Easy, which, not only being entertaining, has been quite satisfying difficulty-wise. I'm trying to do all the exercises, but some of the word-problem style ones I have trouble with.

Next year, (as of right now) I'll be skipping two grades to be a sophomore in high school (socially - I know a bunch of people in this grade and I think it'll be okay). My plan is to go to that same local community college and take a trigonometry course, which will hopefully be able to count as my math course in high school grade-wise. Though this may be irrelevant, I'm also planning on enrolling in an introductory course to either C++, Java, or both at that same community college. Topics I'm interested in include physics (obviously ;), the "idea" of quantum mechanics, (may sound strange but) boolean algebra, Galois theory (which was introduced to me by a WPI graduate that interned as a tutor at my school), and other sort-of unrelated things.

This is sort of how I was going to plan the next year or two:

This fall:

Trigonometry (@ CC)
Introduction to C++ (@ CC)

This spring:

Calculus I (@ CC)
Introduction to Java (@ CC)
C++ II (@ CC)

After that, I'm sort of lost as where/what I can study. After taking that Calc I course, would it be way too soon to tackle a book like Apostol, or one of the other books I see recommended here a lot? I know what I want to know, just not how I should get to the point of where I should learn it - if that makes sense.

Thanks for any suggestions.

 

[micromass]

Well, if you're interested in Boolean algebra and Galois theory, why not do some abstract algebra then??

Of course, you'll need to be strong in proofs to be able to tackle abstract algebra, but if you tackled that proof book of yours, then it shouldn't be a problem.

Try to obtain a book like Pinter's "a book of abstract algebra" and try reading it. This will introduce you to the wonderful world of groups and rings

Reading Apostol is also a good idea, but be sure that you're strong in calculus before attempting the book.

 

[mrwall-e]

Okay, thanks so much for your reply. I'll definitely check out that book, I might even have it somewhere (large collection of math/sci ebooks). I just found out I have a meeting scheduled with an academic advisor at the college tomorrow, so hopefully that'll straighten some stuff out. Currently, after finally finishing the download for the course catalog, this is what my Fall semester will look like:

Trigonometry
Discrete Math (Proofs, sets, etc)
Physics I
Intro to Programming With C++

Hopefully in the spring that means I can take Calc I and then be ready for a book like Apostol.

Thanks so much for the advice :)

PS. Can you recommend any other books for proofs and such?

EDIT: I'm only in chapter two of the abstract algebra book and so far it's very ... captivating? lol, if that makes sense for a math book. Thanks for the recommendation!