Self study curriculum for physics and math?

[aexyl93]

I was wondering if there's some kind of curriculum I could follow to self-learn undergraduate physics and math. I'm a senior in high school, I took Pre-AP physics last year and am taking AP Physics this year. I also took a computer science class and am taking another one this year. I self-learned basic calculus such as single-variable derivatives and integrals, and solids of revolutions, though I haven't quite started multi-variable calculus. I'm also reading a few books on relativity and quantum mechanics.
This year I have three free class periods which may soon be four, that I can use to study math and physics.

My main question is, are there are any curricula I can follow to learn undergraduate math and physics? I'm not really sure where to start, what to study, or what order. Also, is there any place I could get problems to practice what I learn? I also have access to the library at a local college, would that be a good place to get materials for self-study?

I want to learn as much as I can before school ends. I want to learn all the major topics topics in math and physics.

 

[G037H3]

calculus -> classical mechanics ->etc.

I want to learn as much as I can before school ends. I want to learn all the major topics topics in math and physics.

err, what?

 

[aexyl93]

calculus -> classical mechanics ->etc.

I want to learn as much as I can before school ends. I want to learn all the major topics topics in math and physics.

err, what?

Did I say something wrong? Maybe I phrased it wrong. I want to use the most of my time at school for learning math and physics. I also want to eventually learn about and understand most, if not all major topics in math and physics.

 

[G037H3]

Oh, your post made it sound like you wanted to learn all the major topics before school ends. lol.

 

[jtbell]

Go to the website of a university that offers an undergraduate degree in physics. Look up the requirements for a BS or BA in physics. Note the prerequisites for the courses and the sequence in which they are listed. Many universities also list sample course schedules for physics majors.

 

[aexyl93]

Well, I am sort of hoping to cover undergraduate math and physics before school ends. Maybe not in-depth but a general understanding of the concepts and work. Though I guess that still sounds a bit crazy?

 

[hadsed]

I'd say if you've already finished up to multivariable calc then just learn that plus linear algebra, which will be very useful to you in more advanced courses.

 

[ephedyn]

I think jtbell's response is the most relevant, and hased pretty much answers specifically how you can get ready for university mathematics. I'll just spoonfeed a bit more information.

Personally I'd learn calculus and LA concurrently, then ordinary differential equations. I actually think it's better to have a solid foundation of these 3 than to have a vague idea of many math topics. Been there, done that, I'm now in my first semester of my freshman year and wish I had received this piece of advice.

You will have to pick up a textbook. Your background sounds very similar to my junior year in high school, so I'll recommend accordingly. I haven't found 'the' calculus textbook(s) that fits me - there are so many of them! (Courant, Apostol, Widder, Kaplan are the better ones, IMO - and there are also 2 books by Edwards & Penney, which are OK) But I like Tenenbaum & Pollard for ODEs, and Hoffman & Kunze for linear algebra most.

Physics is a much more orderly affair. The topics are usually organized neatly for you in a general college physics textbook. If you can finish reading Fundamentals of Physics (Halliday, Resnick, Walker) or an equivalent, say, College Physics (Serway et al), you should have a pretty good idea of every area of physics. I really like the Feynman Lectures on Physics for this purpose too, but I feel that it's 1 level harder than the above - so if you have the patience to finish calculus through multivariable/vector calculus, LA and ODEs, you could start from there for physics.

Nothing can go wrong if you finish in the order of the syllabuses put up on OpenCourseWare.

 

[aexyl93]

I looked at MIT OpenCourseWare and I think i'll follow that. But what do I do for exercises and practice problems? Part of the assignments use problems from different textbooks.

 

[ephedyn]

I feel strongly that OCW should never be used as a standalone resource. You should probably buy the said textbook, or find free problems online.

 

[hadsed]

For someone who's self-studying math and taking classes as well, I'd say get Stewart's calculus. I got mine for a measly 2 dollars because I bought an older edition, and it's great. I also own Spivak's calculus as well, but this is difficult to work through especially if you haven't been introduced to proofs or if you just don't have enough time. Also, you can always go back and learn it through Spivak after mastering at the level of Stewart, which is still a bit challenging in its own way. Stewart will teach you all that you need to know to do physics and be able to move on in your maths, and since you'll be taking these courses again in college you can always tackle the harder stuff later. Plus it's a good reference to have I think, and includes differential, integral and multivariate calculus and a tiny bit of ordinary differential equations as well.

 

[Sankaku]

Well, I am sort of hoping to cover undergraduate math and physics before school ends.

I hope you have a lot more hours in your day than us regular people. For math, as well as videos from MIT and Berkeley, try here:

http://www.uccs.edu/~math/vidarchive.html

As jtbell said, just look at any good University curriculum to see what order you need to go in...