Physics-based independent Study Ideas?

[flyinjoe]

Hello, I am currently in high school and I recently got the opportunity to do an independent study with one of my teachers and I am struggling to come up with what to study. I have taken calculus 1, 2, and 3, differential equations (with a bit of linear algebra), and calculus-based mechanics and E&M.
I would ideally like to do something physics-based, but I am open to all ideas. I am leaning toward relativity, but I am not sure I would be able to actually do anything with that except learn straight out of the book (most independent study students end up writing a paper).

Do you have any suggestions for topic I should study? What kind of work could I do with what I will learn?

Thank you.

 

[ZapperZ]

Shouldn't you be having this discussion with your teacher?

Zz.

 

[flyinjoe]

Well I did, and he told me to come back with what I wanted to study (he's pretty busy).

 

[ahsanxr]

Here are some options which might be fun to study and should be within reach given your background. They are also very important topics if you choose to pursue physics.

1. Lagrangian and Hamiltonian Mechanics. This is the foundation for pretty much all of modern physics.

2. Special Relativity. A very interesting topic that can be learned with very little background.

3. Complex Analysis. A course of a more applied nature should be accessible. Again, this is a very fun topic that is also useful in physics.

4. Abstract Linear Algebra (focusing on inner products). I've seen way too many physics people who don't understand the fairly simple formalism behind linear algebra and inner product spaces. Understanding of these concepts is crucial for physics, such as quantum mechanics. Doing such a study on your own may be difficult though, since it would require some "mathematical maturity".

You should approach it as follows: Select a book (or books) after some discussion with your teacher which will be at the correct level. Choose some chapters to study (make sure this is a reasonable amount). Go through them very carefully, working through examples and derivations. Do a few problems. This should give you enough material to discuss with your teacher every week. The paper written at the end of most independent studies is usually expository, so after studying these things you can write a short paper maybe summarizing what you learned.

 

[flyinjoe]

Thanks for the excellent information!