What High School Courses Should I Take to Prepare for College and Research?

[dogpoint]

Hi all,

I am currently a junior. I am taking the standard AP Physics C this semester, and in the spring hope to take a formal Classical Mechanics course at a local college (to cover lagrangians, hamiltonians, calc or variations, all that good stuff). Next year, I will hopefully take a similar upper level, theoretical electricity and magnetism course and possibly a quantum mechanics course.

However, I am open to tweaking my schedule. Are there are any other courses that would be good to take now to get a "head start" for college and research? Anything to self study, less formally?

Thanks!

 

[Rocket50]

Have you done AP Calculus BC? If you have or haven't, it is worth going through a book like Spivak. After, try to cover multivariate calculus or differential equations or linear algebra.

For physics, try to self-study classical mechanics (Kleppner or Morin) and electricity & magnetism (Purcell).

 

[dogpoint]

I took AP Calc BC last year. This year I'm doing an honors sequence of multivariable calc, linear algebra, and introductory analysis at a local college. I've been self studying ODE'S using MITopencourseware in my spare time. Any suggestions for relevant math next year/over the summer? I was thinking either formal real analysis or differential geometry. Thoughts on which one would be more applicable?

As for the physics book suggestions, thanks a million! I'll definitely check them out.

 

[Rocket50]

Honestly I'm not a fan of local college courses. They were way below the level that I found in self-studying or at university. Maybe you would want to study those math courses again (should be much easier now).

 

[dogpoint]

Well, I am taking them at a University, a "top 10 school" or something like that ("top five," I think, actually? Whatever, rankings are arbitrary anyway). I just sort of got used to saying "college" because I'm taking them through the undergraduate division. They're pretty rigorous and challenging, and very theoretical/proof-based for the math ones. Anyway, sorry about the linguistic imprecision.

 

[Rocket50]

Well, I am taking them at a University, a "top 10 school" or something like that ("top five," I think, actually? Whatever, rankings are arbitrary anyway). I just sort of got used to saying "college" because I'm taking them through the undergraduate division. They're pretty rigorous and challenging, and very theoretical/proof-based for the math ones. Anyway, sorry about the linguistic imprecision.

I'm so used to "college" implying a local college within 5 miles of your house. First of all, you're a very lucky person. Few people have access to such universities in high school. Then I guess you've gained a very good education from there.

Then you're pretty much set. You don't have to review those subjects and focus your attention on the physics courses.

You said learn "real analysis formally". Didn't you already learn from something like Rudin at your university?

 

[dogpoint]

Ha yes, truly, I'm quite lucky to have such resources available.

As for analysis, the course I'm taking is technically "introductory analysis." The college (er, university) also offers a more advanced study of real analysis.

 

[Rocket50]

Ha yes, truly, I'm quite lucky to have such resources available.

As for analysis, the course I'm taking is technically "introductory analysis." The college (er, university) also offers a more advanced study of real analysis.

Well, if you have the opportunity to take it, you might as well. If not, you can self-study it if you want. What textbook did it use in the introductory analysis course? Also, what are your aspirations? A double major in mathematics and physics?

 

[dogpoint]

No textbook, just my professor's notes. Which makes it a little hard to compare to other sources. The same prof also teaches the Real Analysis course and uses his own notes. I'll definitely do a little self-studying from Rudin's to supplement the 'introductory analysis' stuff though (just found a pdf for free- exciting!).

Yeah, probably a double major in math and physics at this point. And a Phd in theory, hopefully. I like pure math (namely topology and differential geo, from what I've seen) but mostly I'm interested in mathematical physics.

 

[Rocket50]

No textbook, just my professor's notes. Which makes it a little hard to compare to other sources. The same prof also teaches the Real Analysis course and uses his own notes. I'll definitely do a little self-studying from Rudin's to supplement the 'introductory analysis' stuff though (just found a pdf for free- exciting!).

Yeah, probably a double major in math and physics at this point. And a Phd in theory, hopefully. I like pure math (namely topology and differential geo, from what I've seen) but mostly I'm interested in mathematical physics.

I guess you can go through Rudin and fill up the gaps along the way. So if you're looking for a math subject to self study, I think the next logical choice would be Abstract Algebra, for which you can use Artin. If I were you, I'd be focusing a little more on the physics though since you're relatively behind on it.

 

[dogpoint]

Hmm very true, I've been focusing mostly on math recently. On the physics end of things, I'm trying to work through an introduction to general relativity currently- that introduces relevant tensor calculus as it emerges. But perhaps it would be best to start with more formal classical mechanics now as well, rather than wait to take it as course in the spring. I found a free one online so it's definitely convenient. Thoughts?

 

[Rocket50]

Hmm very true, I've been focusing mostly on math recently. On the physics end of things, I'm trying to work through an introduction to general relativity currently- that introduces relevant tensor calculus as it emerges. But perhaps it would be best to start with more formal classical mechanics now as well, rather than wait to take it as course in the spring. I found a free one online so it's definitely convenient. Thoughts?

Maybe that's a little ambitious. Classical mechanics (Kleppner or Morin - I used Kleppner first) and Electricity and Magnetism (Purcell) took me about 1 year (although I was doing some math with it around that time as well).

 

[dogpoint]

Hm we'll see. I think I could cover classical mechanics this semester, then do E&M the next. My school offers a "quantum mech for mathematicians" in the fall that might be good to take also.

Anyway, thanks for all your help and textbook suggestions! I appreciate it a lot.

 

[Rocket50]

Columbia university?

1 per semester is a good goal. Good luck!

 

[dogpoint]

Ha yep, good guess. Thanks!