Interesting. It seems there is a lot of overlap between our programs.
MATH137 seems about the same as our MAT137. Actually, MAT137 is a full-year course, so I guess it's the same as MATH137 and MATH138. Content is identical, I think. Start off with proof by induction, contradiction, and direct proofs. Do a little number theory, then start into continuity, limits, intermediate value theorem, mean value theorem, fundamental theorem of calculus, derivation, integration, Riemann sums, then finish off the year with sequences, series, Taylor and Maclaurin series. Personally, I think that having two half-year classes is easier. Even though the exam was weighted towards the end of the course, there was still a lot of stuff we learned 5+ months before the exam. Y-classes suck.
I think that MATH135 is same as MAT223, Linear Algebra I, which is only half a year. We use Kolman's Elementary Linear Algebra, which is pretty okay, but he tends to use some non-standard notation and definitions which the profs don't like and aren't intuitive. (Eg., instead of invertible and non-invertible, he uses non-singular ad singular, where a singular matrix is non-invertible. So confusing (although if you think about it a minute, it makes sense; it's just no one uses those terms!)... Again, deals with proofs, matrix operations, properties, endless boring Gaussian row reduction nonsense... It's not really tough, but it can get dull at times. Analysis on Manifolds by Munkres has a very well written and detailed first chapter regarding vector spaces and the more theoretical aspects of them. Don't read it if you don't like thinking about n-dimensions though, otherwise it will hurt your head.
This is interesting, m1ke_. It sounds to me like I have a comparable math education to Mathematical Physics students at Waterloo. I had not considered that program because I thought that my math was not the same level required, but I believe it is (this is going by the course descriptions; clearly I have no first hand knowledge). Are these course descriptions comparable:
MAT137Y1
Calculus [72L, 24T]
A conceptual approach for students with a serious interest in mathematics. Geometric and physical intuition are emphasized but some attention is also given to the theoretical foundations of calculus. Material covers first a review of trigonometric functions followed by discussion of trigonometric identities. The basic concepts of calculus: limits and continuity, the mean value and inverse function theorems, the integral, the fundamental theorem, elementary transcendental functions, Taylor’s theorem, sequence and series, uniform convergence and power series.
MAT223H1
Linear Algebra I [36L, 12T]
Matrix arithmetic and linear systems. Rn subspaces, linear independence, bases, dimension; column spaces, null spaces, rank and dimension formula. Orthogonality orthonormal sets, Gram-Schmidt orthogonalization process; least square approximation. Linear transformations Rn—>Rm. The determinant, classical adjoint, Cramer’s Rule. Eigenvalues, eigenvectors, eigenspaces, diagonalization. Function spaces and application to a system of linear differential equations.
MAT235Y1
Calculus II [72L]
Differential and integral calculus of functions of several variables. Line and surface integrals, the divergence theorem, Stokes’ theorem. Sequences and series, including an introduction to Fourier series. Some partial differential equations of Physics.
The MAT235 outline is kinda light; we've done more stuff than that, but they had a snafu with the course coordinator the past couple years, so the content has changed a bit, and they just posted a bare-bones description. Also, MAT235 is same as your Calculus III, just twice as long. I'm not sure if we cover more material, or just more slowly than you.
Given that my chosen route (at the moment) seems to be condensed matter physics and experimentation, would you say (in your opinion, since I can't hold you to anything but that...) that Mathematical Physics would be a good option? Are there many students in your program interested in experimentation, or mostly theory? The Physics components are the same, yes?