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What should I focus my efforts on?
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[QUOTE="QuietMind, post: 5444859, member: 584429"] 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. [/QUOTE]
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