Self Studying over Summer (high school student)

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I have two main questions:

1. What's next? I have taken several physics courses(covered both mechanics, E/M, wave motion, fluid dynamics, and special relativity) in my high school career. I want to know what i can learn next? (preferably not quantum)

The reason I ask is because I love physics and my school only offers 2 courses on it. I already made an additional one last year. I don't want to go a whole year without my physics :).

*****

2. I have 10 weeks in the summer available in which I can self study information. (Assume dedication isn't an issue) Is it plausible that I could self teach myself AP Calc BC (extremely good at math - missed USAMO by barely anything - also already learned a lot of calc for ap physics), AP Bio (the first 1/2... i understand it to be just rote memorization), AP Econ Macro/Micro, AP Computer Science A (learn java, already know C++), and third year latin (already know 2nd year)?

I will rank the importance of my self studies:
1. Third Year Latin
2. AP Calc BC (pretty much tied with latin)
3. AP Bio
4. Ap Computer Science
5. AP econ macro/micro

If it is not possible to learn all 4 of these then could you please list which combinations would be possible?

Also, any tips on structure of my self study would be helpful specific to these subjects. I am very familiar with self learning things.
 

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  • #2
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It's not for any of us to say what you'll find possible. However, I'd imagine you'll need an extremely high level of discipline to study all of those subjects to an appreciable degree over the summer.

If I may ask, what is the rationale behind your ranking? I'm a little confused by why Latin ranks so highly, given that your passion seems to be physics. Not that there's anything wrong with that, of course, it's a great subject to study, I just would've thought more science-/math-related subjects would've come first. At any rate, if physics is what you're really after, I'd recommend you learn BC Calc as soon as possible, as calculus will open up many more topics in physics. After that, your own interests are what really matter; I don't see a reason why any specific combination of those topics would be particularly easy or hard to learn, relative to any other combination. If you want to get a jump-start on research in physics, I'd suggest CompSci. A lot of physics research involves some level of programming, so you'd be able to participate in that aspect even though you probably don't have the physics or math background to contribute much to those sides of research. If you think you might be interested in biophysics, biology would obviously be good to know, but there's no real rush to learn it: if you want to learn it for personal interest, you can always take it in school or when you enter college, while if you're looking into biophysics research, the AP Biology curriculum is probably too broad and shallow to give you a significant leg up.

Personally, I'd find AP Bio impossible to self-study, since a lot of it boils down to memorization, which would quickly degrade my motivation. That's just me, though. Again, BC Calc is the only real recommendation I can make without knowing your goals, interests, and aptitudes. On a final note, make sure you do leave some time to relax and socialize during the summer. Studying intensely year-round can wear away at the most ardent passions, resulting in burn-out.
 
  • #3
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Thank you for your response! :).

The reason why I ranked Latin first is I am short 1 year for foreign language for my college apps. I think, after looking at various posts about MIT/Caltech/etc., that 2 years of Latin would suffice for college admission into more Math/Science focused schools? If so then Latin would be completely off that list.

Just a list of my goals, aptitudes, and interests-
Goals:
1. Get into MIT/Caltech in an Computer Engineering/Physics double major
2. Understand physics and math enough so I can do research at the state university my senior year (which would be the year after this summer - 2011/2012)
3. Still have some physics that I can spend a year on in class my senior year.
4. Have a little bit of a leg up when going into my Majors

Interests:
1. Physics (specifically particle physics and biophysics)
2. Math
3. Programming
4. Research (related to physics)
5. Biology (specifically human anatomy/physiology)

Aptitudes:
1. Math (If I read a section in a book I understand it without doing problems)
2. Physics (Pretty much the same as Math though I do have to do 1 or 2 problems)
3. Programming (learned C++ in half a year with just self teaching)

Calc BC-
Right now I am signed up to take AP Calc BC and linear algebra (two separate classes) for next year. If I studied Calc BC then I would probably test out of AP Calc BC and switch that class for Calc 3/Differential Equations (1 class). Would there be a potential problem in me doing this? Will I struggle in Calc 3/Diff Eqs at first? Really I am willing to accept any advice you are willing to give.

AP Bio-
I have to agree with you on the memorization part. So I more than likely will not self study bio. The only reason why I listed it is because my school doesn't offer it for next year and I am interested in Biology (though no where to the extent that I am with physics).

CompScience-
I know from learning C++ that a lot of learning a program language comes from practice not actual reading. Would it be feasible to learn Java (through a book and just writing programs on a daily basis) over the summer? About how many hours do you think I will have to put in for writing programs to be truly proficient?

AP Econ-
If I have time then I will get to it. Otherwise its off the table.

I would like to reiterate my question: what is next for me to study in physics?

Thank you for your time :)!
 
  • #4
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Assuming you just finished AP Calc AB, you should learn Classical Mechanics. It's similar to AP Physics B, but instead of Algebra-based math its Calculus-based. Then after you take Calculus BC, you will be able to take Electricity and Magnetism. So for now, make time for Calc BC and Classical Mechanics. There are a series of video lectures for these subjects so you should be set.

1. Math (If I read a section in a book I understand it without doing problems)
Still doesn't mean that you should not practice. Sometimes problems are tricky and requires you to think a bit. Practice enough problems until you master the concept and don't limit yourself to the easy ones. Do the same with Physics, because they can get tricky quick.

Good luck!
 
  • #5
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Sorry I probably should have clarified. I took AP Physics C: Mechanics last year and am taking AP Physics C: E/M on Monday. In order to do this I have had to teach myself several topics from AP Calc BC. (I got a 5 on mechanics - lets hope that I can pull off a 5 for E/M)

Still thank you for your response :).

So assuming that I have already covered: mechanics, E/M, wave motion, fluid dynamics, and special relativity. What is next?
 
  • #6
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Calc BC-
Right now I am signed up to take AP Calc BC and linear algebra (two separate classes) for next year. If I studied Calc BC then I would probably test out of AP Calc BC and switch that class for Calc 3/Differential Equations (1 class). Would there be a potential problem in me doing this? Will I struggle in Calc 3/Diff Eqs at first? Really I am willing to accept any advice you are willing to give.
Will there be a potential problem? Absolutely. Is it likely to become a real problem? Probably not, if you make sure you learn Calc2 (i.e. BC) well. A lot of time in Calc2 is spent learning various tricks for evaluating integrals. While this is definitely stuff you should know, you won't be completely blasted out of the water in Calc3 if you don't have them down pat. Calc3 is a different flavor of math from Calc2: while the latter is usually very algebraic and computational, the former is more conceptual and geometric. A big part of Calc3 is learning to think in 3D, understanding what the various kinds of integrals (curve, surface, flux, etc.) really mean, and being able to go between them to solve problems that are often somewhat physical in nature. Being able to actually solve those integrals is important, and if you don't know how, I'd imagine you will do poorly, but I wouldn't call it the focus of the class by any means.

In diffeq, you return more to the algebraic side of things, and again, there is an component that will require you to evaluate integrals. However, the most important concept to remember from Calc2 will probably be power series. Make sure you know what they are, how (and why!) they work, and how to derive them. In Calc2, you go on to learn various methods of testing for convergence; again, this is stuff you will want to know at some point, but not, in my experience, something that will be needed in your typical Ordinary Differential Equations class.

So in summary, it's obviously best if you learn Calc2 inside and out, but failing this, and intuition for what an integral means, a basic understanding of how to evaluate the simpler ones, and some exposure to power series are the most important things to take away.

CompScience-
I know from learning C++ that a lot of learning a program language comes from practice not actual reading. Would it be feasible to learn Java (through a book and just writing programs on a daily basis) over the summer? About how many hours do you think I will have to put in for writing programs to be truly proficient?
You'll find that the more programming languages you know, the easier it will be to pick up new (similar) ones. This will be particularly true if you're starting at C++, one of the more complicated languages, and going to Java, which is the standard intro level language at most schools. Once you get over the syntax (which really isn't that different between Java and C++), you'll mostly just be learning Java's libraries and little nuances. Honestly though, while learning Java should be relatively easy, I wouldn't make it too much of a priority: I've never met an academic physics researcher who heavily utilized Java. C++, Fortran, Python, and Matlab are much more common, due to their being more computationally efficient, easier to use, or both. Personally, I'd recommend learning Python, as it's different enough from C++ to be beneficial to you while being (imho) one of the more fun languages to use. As for how to actually learn, you're correct that practicing will be far more useful than going through a textbook, once you learn the basic syntax and structure from the latter. Think of something that might be fun or useful: a simulation of some physical system perhaps, or a script that you could actually use. Then devote some time to making it happen. There's no rule that says "it's best to spend X hours of day on it," so just go with how you feel on any particular day. You learn best when you're enjoying yourself, so don't try to press on when you're exhausted and burned out, just to have put in a certain number of hours. Keep it light, fun, and playful, and you may be very pleased with the results.

As for what comes next in physics, it sounds like you've gone over most of the topics in an intro level physics course. The big things that are missing are quantum mechanics and thermodynamics/statistical mechanics, so either one of those would serve nicely as the next step. You might have a look at Thomas Moore's "Six Ideas" textbook series, he's an excellent teacher whose style might lend itself well to self-study. Regarding your goals, I'd be wary of a couple of them. Don't get yourself set on going to MIT or Caltech, as they're a crapshoot for anyone without a Nobel Prize and royal blood. Also, don't expect to know enough math and physics to participate in that side of research by next year. It usually takes 2-3 years of undergraduate education to make a significant contribution there. More likely than not, you'll end up either programming or helping out with experiments. Nothing wrong with that: it's just that there's no rush to learn "enough" math/physics to do research, as that's not a race that a vast majority of people can win.
 

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