With regard to specific schools, I don't think you should be worrying about it yet! Concentrate on figuring out what you want to study
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With regard to the different subjects:
In mathematics, you will spend most of your time proving things. A standard undergraduate program will give you courses in analysis (real and complex), algebra, differential equations, topology, probability and combinatorics, number theory, and other subjects. Within a math program you will not get much in the way of applications in core courses.
Theoretical physics, at least at my school, is not very well-separated from any of the other physics programs. You will have to do a lot of laboratory work. You'll get courses in classical dynamics, electromagnetism, optics, modern physics, thermodynamics, and quantum mechanics, as well as courses in single-variable and vector calculus and linear algebra. You'll also likely have a course in mathematical methods, and perhaps another in complex variables, which will cover various tools useful in physics. You won't get to see much of the abstract side of mathematics.
Engineering programs will focus on applications. Lots of labs, and math classes focused on tools. You will also have physics courses specialized for engineering applications, and "core" engineering courses (as you can probably tell, I'm much less-familiar with engineering programs; you probably don't want to listen to me about this!).
Currently I'm a fourth-year math-physics double major student in Canada. I have enjoyed the combination immensely; over the summer, I worked at the university doing research in theoretical particle physics, and now I am starting an honours project in analytic number theory (which is about as far as you can get from physics within math!). If you are interested in both fields and willing to do work, then I highly reccomend such programs! It involves laboratory work, and requires you to quickly switch from thinking about physical problems to abstract mathematical problems, but if you are motivated, the fields can complement each other quite nicely. The main disadvantage to such programs is the limitations they force to choices of elective courses in each field (there are some really cool math courses that I don't have time to take!).
For reference, here is a list of math and physics courses I've taken (and am taking):
1st year:
math - single-var calculus, linear algebra
physics - kinematics & thermodynamics (lab), electromagnetism (lab)
2nd year:
math - vector calculus, linear algebra, abstract algebra, ordinary differential equations, mathematical methods, probability & combinatorics
physics - modern physics (lab), optics (lab), quantum mechanics
3rd year:
math - real analysis & intro. to topology, complex analysis, group theory, game theory, differential forms
physics - classical dynamics, thermodynamics & statistical physics, modern physics ii (lab), lab course
4th year:
math - number theory, automata, group theory ii, honours project in number theory
physics - electrodynamics, quantum mechanics ii & iii, cosmology, particle physics
Hopefully this will give you some idea of what sort of diversity in courses you will see in the two fields. This includes essentially all of the honours courses in a standard honours physics program, modulo typical math courses, which are replaced with elements from an honours math program. There are a couple of courses missing that are in an honours math program at my school: rings and fields (which you get some of in the second year algebra courses), and some additional math electives.
Princeton was kind enough to give me an interview. But that maybe becuz I am from Burma (ever heard of this country?).
