What should I focus my efforts on?

[QuietMind]

Hi,

I'm a sophomore physics and computer science major. I go to a "well-regarded" university in the top 20 (I'll keep it anonymous unless you guys think details might help), yet I don't feel like the academic experience has been particularly stellar. I loved my freshman multivariable calculus and intro mechanics course, but since then, my linear algebra, Diffeq, and quantum physics courses have been letdowns. I'm majoring in computer science as well, but those courses haven't been particularly special. In terms of grades, I have a 4.0, but I feel like this is a result of the courses being watered down. This semester, I'm currently on a leave of absence from school due to some circumstances. I've been spending some of my time doing research at an observatory near my house, which is going relatively well for a first time research experience. I have a summer research project lined up as well, but my core concern is that I don't feel tremendously good about my problem solving skills, both in depth and in breadth. I don't feel like if you gave me a problem, right now, that I would be able to provide much in the way of insight.

Lately I've started to self-study a few courses, namely Mathematics for Computer Science through MIT open course ware. I've also considered spending time preparing for math competitions. I never did much of them in high school, but as I got to college I did some problems here and there with friends and I found it to be a lot of fun. I'm a sophomore without a whole lot right now, apart from grades, but I'd like to be strive to stand out from the pack by building up my problem solving skills one way or another. I have a good bit of time right now, and I'm wondering what I should be dedicating my self-study efforts to. Teaching myself courses (that I'll probably have to repeat once in school. I don't know if they support letting you take grad courses early if you can teach yourself the prerequisites) or trying to focus on competitions like the Putnam? I'd like to get an idea of what's worthwhile, or any other advice you may have.

Edit: I forgot to mention my goals. I'm considering physics grad school. But I want to be confident by the time I graduate from college that my problem solving skills are up to snuff, and it doesn't feel like things are on the right track right now.

 

[micromass]

Can you explain us a bit more about your LA, differential equation and QM courses? Who is the intended audience (first year students? Seniors?), and why do you consider them to be watered down.

Also, if you're doing math competitions for fun, then go ahead. But don't expect those to be terribly helpful for grad school. Personally, I have never seen much difference between students who focused on math competitions and ones who did not. Something that actually does help a lot for problem solving and grad school is the Moore method. Students who took at least one class with the Moore method are remarkably well prepared for research and grad school. But if you enjoy it, don't stop doing math competitions though.

 

[QuietMind]

Thank you for the response,

The LA course was supposed to be a proof based course for math majors, the second highest variant of linear algebra available (couldn't take the highest variant due to scheduling conflict). But it is intended for the honors major in math. It just didn't feel like the proofs got very deep, as most of the stuff was was very similar to the textbook examples. I didn't think there was a lot of creativity involved. The professor cut out a chunk of the course for time constraint, cutting out almost an entire chapter (out of 7) that was dedicated to determinants.

Diff EQ was also supposed to be the proof based course for math majors. It just went very slowly. 3 units total: first order, second order, and linear systems. Everyone was getting over 100's on the tests, and it honestly felt like the course could have been completely done in 3 weeks rather than a semester. I redid the course through MIT's opencourseware, and there was about twice as much content in their course. We never did Fourier analysis or the Laplace transform (although to my understanding those techniques are more for engineers, so it might be reasonable not to show up in the variant for math majors)

These two math courses were intended for second semester freshman and first semester sophomore's respectively, which is what I was when I took them.

Quantum Mechanics started off a little simple at first because it talked a lot about each of the historical experiments leading up to the development of the theory (Michelson Morley, Milikan Oil Drop etc). The experiments were very interesting, but there just didn't seem to be a whole lot to do once you understood them, as compared to freshman mechanics where you could always find harder problems. I did enjoy talking to my professor about thought experiments though. This course did get much more interesting once we covered Schordinger's equation, around the 2/3 mark of the course. It was intended for sophomores.

I also did Griffiths Electrodynamics as a directed study. That course I found very challenging, and the other courses were not nearly as difficult in comparison.

You don't think math competitions are a way to improve problem solving skills? Can I ask a little bit more about that? I have at least worked through a good portion of the Art of Problem Solving books and found them to be very stimulating and exciting. Is it that competition problems don't really translate over to courses or research? I was hoping that focusing on, say the Putnam, would help to give me depth rather than just covering more courses on OpenCourseWare. I haven't participated in many competitions so I don't know the feeling of the competition environment, but I do know that I simply enjoy hanging out with a friend and spending a few hours on problems from the AIME or whatnot. I realize that's a high school level competition, but I never really built a strong math base.

This is the first time I've heard of the Moore method. I don't know that my school offers anything like that, but I do plan on taking a course on knot theory where the class size is tiny. I'll be certain to look out for any mention of a class like that though.

 

[jtbell]

Quantum Mechanics started off a little simple at first because it talked a lot about each of the historical experiments leading up to the development of the theory (Michelson Morley, Milikan Oil Drop etc).

Which textbook did you use? This sounds more like an "intro modern physics" course of the sort that is often intended for sophomores, rather than a regular "quantum mechanics" course that uses something like Griffiths's book. That kind of course is supposed to be an overview of various topics, not an in-depth presentation of quantum mechanics alone.

 

[QuietMind]

Thornton Rex "Modern Physics". It was an Intro to Quantum Physics course. Sorry for not clarifying. Funny enough, the "in-depth" Quantum Physics sequence isn't even part of the core curriculum, although I will certainly take it.

 

[jtbell]

Funny enough, the "in-depth" Quantum Physics sequence isn't even part of the core curriculum, although I will certainly take it.

A full QM course isn't required for a physics major, at a top-20 school?