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Need advice - does this curriculum for Math & Science (at Toronto) look good?

  1. Jan 2, 2007 #1
    I'm about to begin the last semester for my first degree. Somewhere in the first couple of years (I spread it over 5 years as I took time off and worked in the middle) I decided that I would eventually get into the physics program at Toronto. My family did not approve and so I stuck it out with the program I was in at the time. I'm not really bothered by it--I've had a blast.

    Getting back to the story--I always thought that physics was interesting and it would be the road I eventually went for. I was certain that I was going to apply to the physics program when the time came. Then I went back and forth with math. Finally I found a specialist program offered at the University of Toronto which seems to offer enough of both to satisfy me.

    However, I would like feedback from those who have been through a math or science program and know what to look for (particular courses). I want a good coverage of undergrad topics.


    It is the program listed at the very bottom of the page, "Mathematics and Physics(Science program)". The curriculum is:

    First year: Analysis I, Algebra I, Algebra II, Foundations of Physics

    Second year: Analysis II, Advanced Ordinary Differential Equations I, Fundamental Physics Laboratory, Electricity and Magnetism, Thermal Physics, Oscillations and Waves, Introduction to Quantum Physics

    Third year: Partial Differential Equations, Introduction to Topology, Complex Analysis I, Real Analysis I, Introduction to Differential Geometry, Classical Mechanics, Electromagnetic Theory, Quantum Mechanics I

    Fourth year: Mathematical Foundations of Quantum, General Relativity, Quantum Mechanics II, and one of: Applied Nonlinear Equations OR Macroscopic Physics OR Nonlinear Physics

    Additionally, I'm thinking of sneaking in a few computer science credits if they allow for it. I might (rather, should) be exempt from the elective humanities credits as I will already have enough from my first degree ;) I'm particularly interested in the logic, complexity theory and algorithms classes. (By the way, do you know if they would let me take such courses if I had my grades up in the major area of focus?--I go to a community college and we aren't allowed such things. In fact, I think it is mandatory to normally take some credits outside of your major to graduate from UofT with a bachelors! and not just the humanities).

    thanks and happy new year!
  2. jcsd
  3. Jan 2, 2007 #2
    I am slightly confused why you are taking Algebra I and II your first year but then you transition into Differential Equations the following year. You are going to need some heavy Calculus before you are able to fully comprehend differential equations. Although, after reading the description of 'Algebra I' it seems to resemble a Linear Algebra course.

    My mathematics course requirements for high energy physics, consists of three calculus sequences, differential equations/PDE's, Linear Algebra, Vector Calculus and then some upper division sequences (although I also plan to double major in mathematics as well so I will be required to take a lot more mathematics, than that).

    I'll read more about your course and see if I can give you more advice, although I am sure others will provide more informative responses.
  4. Jan 2, 2007 #3
    Thanks for the response, complexPHILOSOPHY

    In addition to the Algebra I and II, there is an Analysis I course in the first year as I listed. It takes up both the fall and winter semesters (a full academic year course).

    The Analysis I description:
    A theoretical course in calculus; emphasizing proofs and techniques, as well as geometric and physical understanding. Trigonometric identities. Limits and continuity; least upper bounds, intermediate and extreme value theorems. Derivatives, mean value and inverse function theorems. Integrals; fundamental theorem; elementary transcendental functions. Taylor’s theorem; sequences and series; uniform convergence and power series.

    They use the Michael Spivak Calculus text for the course.

    This is the higher first-year calculus offering--there is a normal (not as comprehensive on the theory) calculus class for engineers and science students, and an even lesser one for art students. This is the most detailed calculus class that is offered for first-year students at Toronto.

    Is that enough foundation to comprehend the differential equations?

    Also, the Analysis II course will be done in parallel with the differential equations.

    Analysis II description:
    Topology of Rn; compactness, functions and continuity, extreme value theorem. Derivatives; inverse and implicit function theorems, maxima and minima, Lagrange multipliers. Integrals; Fubini’s theorem, partitions of unity, change of variables. Differential forms. Manifolds in Rn; integration on manifolds; Stokes’ theorem for differential forms and classical versions.

    thanks and hope you have a great day
  5. Jan 3, 2007 #4
    I have decided to go ahead and apply. It has been on my mind long enough that I might as well pay the application fee and give it a go. I'm also going to apply to Waterloo.

    My only concern is that I may not be able to handle either of them :(

    I'll be graduating from a college with [hopefully] a 4.0 as I have maintained it up until the final semester (the one which begins in a few days). I study software development. However, I never had a formal mathematical foundation. My curriculum was completely absent of the theoretical CS topics and the math parts (though we covered some algorithms). Additionally, my 4.0 is misleading--I would argue my school has a rather easy curriculum.

    I managed to pull 97%, 86% and 60% in the grade 13 calculus, algebra & geometry, and finite math classes (Ontario, Canada). The calculus one was high, but I studied many many hours for that and did it through correspondence which may have been easier (60% of the grade came from coursework I worked on independently from home, 40% came from an in-person written exam).

    I'm starting to question my real ability. If I am accepted, I will spend the coming summer months reviewing the material from grade 13, and starting some of the program texts on my own.

    Lastly, I do not plan to have a full course load in the first year-- I only wish to take the 3 classes per semester. Perhaps I might add one CS class of my preference in the winter semester.

    I hope that what I lack in talent, I can make up with my hard work (as demonstrated in the current degree program I am in).

    We'll see how it goes ;)
  6. Jan 15, 2007 #5
    The mathematics courses in that program are very in depth and theoretical: in fact, almost all of them are the same ones that people in the Mathematics Specialist program take (i.e. the future mathematicians). If you are more interested in physics and aren't the greatest at proofs, then the Physics Specialist program might be better. At least that will give you the room to take extra math courses if you want, like MAT301 (groups) or MAT327 (topology).
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