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Should I transfer to an university if I took all the upper-level courses offered in my LAC?

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Current college: top 15 LAC Entering as: junior Major: physics/math High School GPA: UW: 3.8 W: 4.35 SAT/ACT Scores: 2120 SAT II Scores: 800/800 math/physics (GRE MATH SUBJ 830, PUTNAM 20) <= Should I even mention this? AP nine 5's and two 4's College GPA: 3.65 (I got C+ in Tutorial) Major GPA: physics/math 4.0/3.62 US/Intl: International, male (do not need aid) LOR: I'm overrated by physics profs, so I will get nice ones. Credits obtained until 2016 Spring: 92 credits out of 124 (graduation req.), 44 of which is from AP Math & Physics classes taken until Spring 2016: Math: Complex Analysis, Senior Seminar, Fourier Analysis, Abstract Algebra, Representation Theory, (Senior Seminar), (Field Theory) Physics: Mechanics, Electrodynamics, Thermo Statistical Physics, Quantum Theory, Mathematical Methods of Physics, (Advanced Quantum) The first two physics classes are also upper-level ones, and classes surrounded by () are the ones to be taken in Spring 2016 If I will not transfer, I will have to graduate right after my junior year, since I don't have any new classes to take. I don't have research experience, but I will begin it from the last half of this semester. Although the definition of upper-level courses in my school is ambiguous, I took almost all the highest-level courses in math and physics departments, each of which is a really small department and have not sent their students to nice PhD programs. In order to get research opportunities and take more advanced courses, including grad-level ones, I think I should go to a research university. Questions: Could you recommend me any university (no LAC) which I have chance for and it satisfy the following conditions? - Does not have too much distribution requirements. Since I have taken only Tutorial, Intro Economics and Logic other than math and physics, I'm concerned with distribution requirements. - Has a nice program in either math or physics (so that I will be able to take nice classes/research and have higher chance for PhD) By either taking all physics courses or taking some easier math courses in Spring 2016 semester, I can increase my cumulative GPA to 3.72. But is the spring semester grade really considered? Is it really worth?

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