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Transfer from University of Toronto to UWaterloo?

  • #1

Main Question or Discussion Point

So I'm in second year physics at UToronto. I'm enjoying the course material, and not bombing at all (GPA 3.32, so yeah could be better, but not terrible). But I'm not really sold on Toronto. I've got some friends in Waterloo; visited the campus several times. I've met some profs there, seen the place, and really like it. And I'm thinking of transferring.

My question is... Is this a bad call? I know it's all relative, but is UWaterloo Physics a step-down from UToronto? (Personally, I don't think so, but what do I know?) Is the hassle of transferring is justified. In my mind, and from a purely personal perspective, it is. But I'd like to hear opinions from others, maybe others who've done the same thing before, if there are any...
 

Answers and Replies

  • #2
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2B Math/Phys student from UW.

Its relative, I have seen people come and fit in just fine, and others switch out within the first month, it all depends on what you have been taught (whether you need to catch up) and whether the school matches your learning needs.

Is it a step down? I would say we are on equal grounds, otherwise we wouldn't be essentially equally ranked. But like you, this is just an opinion and only someone who has been to both can tell for sure, but those choice of words are fighting words :)

I think though that you should consider this. What do you want to do with your degree and does the university offer a unique development in that field? If your thinking theoretical, quantum computing, or nano-tech; you should definitely consider switching to UW since the school is affiliated and offers research opportunities with http://www.perimeterinstitute.ca/" [Broken]

In the end though, the only thing different between our degrees is the crest and the distributor name on the diploma. But you should consider it seriously soon, a lot of school (UW included) will not recognize all of your courses and so deciding earlier will help minimize your chances of repeating similar courses.

Best of luck with your decision!!!
 
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  • #3
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May I ask what both of your entering averages were with respect to the U of T program and Waterloo program? I'm considering applying to these next year.
 
  • #4
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May I ask what both of your entering averages were with respect to the U of T program and Waterloo program? I'm considering applying to these next year.
Hey Kevin, I applied to the following:

UW Math/Phys through the Math Faculty (Co-op)
UW Math/Phys through the Science Faculty (Co-op)
UofT Physics (Regular)

I had an entrance average of 85, got into all three except for the math faculty only offered me regular stream instead of co-op. If you have any questions though, don't hesitate to message me :). Best of luck with your applications next year!
 
  • #5
Hey M1ke_,

All good points. I'm considering doing this immediately. That means I would start at Waterloo in the fall of 2011. I've looked over the transfer section of things, and I think that all my credits are eligible for transfer status. I'll find out eventually, but I don't see any problems.

I agree that both schools are basically dead even. It's not a prestige factor, it's that I don't want to live in Toronto. I like the Toronto, but I'm not a city guy. I know lots of people at Waterloo, have a lot of friends there, visited it a lot, and like the city. I don't think I'll be a temporary transfer. If academics are considered equal, this is a move for personal fit.

Personally, I want to go into experimental condensed matter physics. Granted, UW isn't technically known for this, BUT you have an Applied Physics Specialization. All U of T has is a standard Physics Specialist, and after reading both course outlines, I've decided that UW's seems more, well, complete to my eyes. (Not that I really have the experience to make that call, but it sure seems UW's is more INTERESTING!) I appreciate input from someone in the program.
 
  • #6
May I ask what both of your entering averages were with respect to the U of T program and Waterloo program? I'm considering applying to these next year.
Hey Kevin,

I applied for admission to UofT, McMaster and Queens. All of those schools make you apply as either general arts or science first year (if I recall right), but you can enroll in any program after first year if you have met the requirements; usually, this just means 'pass all your first year classes with at least a 60%, and take any first-year courses in your program'. This is how most schools work, I think. Personally, I enrolled as an arts student (wanted to be a history major, but history turned out to be really, really, REALLY boring (and stupidly easy...), so I got into a real program...)

My application average was 93% from high-school. I got in everywhere I applied. All universities post projected cut-offs online; for science, if your average is mid to high 80%, you will be fine, I think. Sciences are not typically as popular, so it is less competitive. (It's because a B.Sc. is a lot more work than a B.A., but the extra effort is worth it for sure.) This, of course, is different for programs like Engineering, or some specialist programs you apply for from high school. But for general science, you'll have no problems.

Check out these links for detailed and official info:

U of T Physics:
http://www.artsandscience.utoronto.ca/ofr/calendar/prg_phy.htm [Broken]

UWaterloo Physics:
http://ugradcalendar.uwaterloo.ca/group/SCI-Physics-and-Astronomy

If you have other questions, just ask. I may have answers...
 
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  • #7
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Thanks, I might have some questions after but this will do for now. I was looking at the U of T Mathematics and Physics Specialist and the UW Mathematical Physics. I'm mostly interested in Condensed Matter Physics, I used to be intrigued (and still am) by the High-Energy Physics i.e LQG, String Theory and the like, But I realized that Condensed Matter Physics is very interesting on its own and a lot more applicable. Also the Quantum Nano Center will be done by the time I get there: http://www.nano.uwaterloo.ca/facilities/qnc.html [Broken]. m1ke, do you have any accessibility to those places, PI, IQC, WIN and in the future the QNC building?
 
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  • #8
Thanks, I might have some questions after but this will do for now. I was looking at the U of T Mathematics and Physics Specialist and the UW Mathematical Physics. I'm mostly interested in Condensed Matter Physics, I used to be intrigued (and still am) by the High-Energy Physics i.e LQG, String Theory and the like, But I realized that Condensed Matter Physics is very interesting on its own and a lot more applicable. Also the Quantum Nano Center will be done by the time I get there: http://www.nano.uwaterloo.ca/facilities/qnc.html [Broken]. m1ke, do you have any accessibility to those places, PI, IQC, WIN and in the future the QNC building?
If you're interested in the Math and Physics Specialist at U of T, there are two notes:

1. It is really tough math-wise. First year courses include MAT157 Intro to Real Analysis, and MAT240 Advanced Linear Algebra (I think it's 240, something like that...). 157 is a killer, unless you are really good at Math proofs. Then it could be really easy. I think the textbook they've been using is Michael Spivak's Calculus, which is great by itself for any level calculus. I took MAT137, Calculus! (yeah, it had an exclamation mark there last year; I see they've removed it this year); got a 30% on the first mid-term. First thing I'd ever failed, EVER. But I worked really hard and finished with a 71% (or about 10% above the class average...). Physics is the same as I take as a physics major, PHY151/152. Sabine Stanley teaches 151, and Stephen Julian 152. Both are exceptional professors, but these are still tricky courses.

This isn't meant to discourage you at all. I know a lot of people in that program, and they are doing quite well. And if math is your thing, then you're set.

2. I (personal opinion) think that that program is maybe geared toward theoretical physics more than experimental. You take a lot of maths, advanced upper year stuff. But this (may) come at a cost to taking upper year physics courses that are experimental-based. (Eg., Advanced Physics Lab I, II, or III; Research Projects, Electronics Lab) If you are interested in theory, then Math-Phys Specialist might be a good thing. If (like me!) you are interested in experimentation, it is still a good preparation, but there are easier routes.

Caveat: I should mention I am not a math person; I'm good at math, but not brilliant. This isn't a barrier for physicists though; many physicists were just 'okay' at math. Einstein and Feynman weren't great mathematicians themselves, although they were both so seriously brilliant, I don't think it mattered much. (Ie., even though there may have been several mathematicians around the world that could have derived equations, it took brilliant physicists like Einstein and Feynman to think of doing it!) So, take my opinion with a grain of salt. If you like the Math and Physics route, take it! Don't be bullied by people telling you 'don't take it, it's hard!' U of T is REALLY bad for upper-years telling first-years what not to take. Ignore them, go talk to the Undergrad Coordinator for advice.

(Caveat II: Also, I suppose the fact that I'm transferring out of UofT is worth noting too. Might lead to some bias on my part, but I've tried to avoid any...)
 
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  • #9
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I have Stewart's Advanced Calculus book (vector calculus, multi-variable calculus, differential equations and everything else) which I look through some times. I've learnt some Linear Algebra on my own and Physics.It's kind of odd, I would say I'm fairly good at maths as I help people and fully understand why things happen and why we do this etc. (instead of wrote learning) but I've always had this nervousness when writing a test. It's not serious but I get sick to my stomach and start like fidgeting and sweating. It's really distracting and I waste so much time going over my solutions making sure I didn't miss anything. This then causes me to rush in order to finish and make terrible mistakes.
 
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  • #10
Hmm... Stewart...

Well, Stewart's okay. I'm in MAT235 right now, and we use Stewart's Multivariable Calculus. To be honest, I really hate it. It isn't easy to read, it's too wordy; Stewart takes a really long time to say simple things. Many others in the class feel the same way, as have past students. Stewart doesn't have any proofs either in his books; I've never heard of Stewart's Advanced Calculus textbook, but no Advanced Calculus class here uses it. If there are no proofs in it, then it is NOT and advanced calculus book.

Michael Spivak's book Calculus is considered the greatest undergrad calculus text ever written, and it's been around for about 50 years. I've read it, and really enjoyed it, and it helped me to better understand first year calculus.

This is the current edition:
http://www.amazon.ca/Calculus-Michael-Spivak/dp/0521867444/ref=cm_lmf_tit_11_rdssss0

MAT137 uses Salas, Hill and Etgen's Calculus: One Variable. Many people did not like it; I didn't think it was too bad. My marks turned around in the course once I started actually reading the book, so it can't be terrible.

Again, current edition:
http://www.amazon.ca/Calculus-Variable-Satunino-L-Salas/dp/0470073330/ref=dp_ob_title_bk

Edwards and Penney also write very accessible textbooks; they are more geared for students interested in a non-theoretical, computational approach. An introductory text is Calculus, Early Transcendentals:

http://www.amazon.ca/Calculus-Early-Transcendentals-Henry-Edwards/dp/0131569899/ref=dp_ob_title_bk

If you are considering Math and Physics, though, forget Stewart. MAT157 is many times more advanced than it. Read Spivak's book; it's what they actually USE in MAT157. (Note; this is different from Spivak's book Calculus on Manifolds, which is an advanced, theoretical calculus text used in graduate courses (and, formerly, in MAT257 Analysis I, a second-year undergrad math that you will take if you choose Math and Physics Specialist). But, that said, I've skimmed parts of 'Little Spivak' too, and it is really interesting. But you may have to reread a page ten times to understand it. Books of a similar vein are Munkres's Analysis on Manifolds and Rudin's Principles of Mathematical Analysis, also good; I've read part of Munkres, but nothing of Rudin.)

Re., exam nerves. You'll grow out of it. Don't stress out too much. Before you write an exam, it may seem like this big, terrible nasty thing. Three hours later, it's just a piece of paper you scribbled on. Best thing; just write it, close it, then think about it with your extra time. Go back and check AFTER you finish everything. And for god sakes, do the easy questions first, even if they're last on the exam. It builds your confidence, and you'll never lose easy marks by not having them done if you DO run out of time.
 
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  • #11
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m1ke, do you have any accessibility to those places, PI, IQC, WIN and in the future the QNC building?
Not necessarly. PI has open lectures every Wednesday and is literally a ten minute walk from campus, some of topics are fairly advanced though. They also hold large lecture events where they have people from universities like Harvard or MIT to talk about their research. IQC holds open houses, and if you enroll here, I think every year a class (phys 10) which you will be enrolled in, takes a tour of their facilities. WIN on the other hand, is more so a recognized community, they don't per say have a building dedicated to them. I know QNC is going to be the new home of the IQC and head quarters for the nano eng (since every eng needs their own building). There will be labs in there, but we would likely have upper year labs depending on the course you take. Outside of these occurrences, I've heard of people doing a co-op, research courses or summer placement at these places. But in no way can you just walk in to any of them, except for the QNC when its done
 
  • #12
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Interesting, the Stewart's book I'm talking about is older and has a proofs part in the back. I'm not sure, does the Waterloo Mathematical Physics program have the same intensity as the U of T program, sorry I completely hijacked your thread. I'm really enjoy calculus and feel I have a better grasp of it then most people do at my age as I sometimes help people in the Homework Section. Would you think it's a lot easier to get positions at say QNC or IQC having gone to Waterloo? Here is what the Stewart's Book looks like:
 

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  • #13
Interesting, the Stewart's book I'm talking about is older and has a proofs part in the back. I'm not sure, does the Waterloo Mathematical Physics program have the same intensity as the U of T program, sorry I completely hijacked your thread. I'm really enjoy calculus and feel I have a better grasp of it then most people do at my age as I sometimes help people in the Homework Section. Would you think it's a lot easier to get positions at say QNC or IQC having gone to Waterloo? Here is what the Stewart's Book looks like:
Yeah, Stewart's books have proofs in the back. That's not what I'm talking about though. Spivak's proofs are right in the text. The proofs are what you are learning. Here's a breakdown of some first-year math courses:

MAT135: Calculus I - mainly for Life Sciences kids (Chem, Bio, etc.). Not rigorous, no proofs. Multiple choice exam.

MAT137: Calculus - more theoretical. Mix of proofs and computational exercises. See attached past exam...

MAT157: Introduction to Real Analysis - All Proofs. Very theoretical. Required for the Mathematics and Physics specialist at UofT.

Clearly, you have a better grasp of calculus than many people. However, the calculus you do in (I assume) canadian high school is no where near the level of serious university calculus. Remember, most people in the Mathematics and Physics Specialist program at UofT got 95%+ in high-school calculus. (I am not a believer that UofT is a better school that others; it's simply not true at all. However, people think it is, and it tends to attract some very bright students.) I was one of the best math kids at my high-school too; I always helped other kids understand stuff. At UofT, I am average on a good day.

I think the mathematical physics program at Waterloo is about on par with UofT's. But m1ke_ can answer for sure.

Here is the final exam I wrote last year in MAT137. I believe the consensus at the time was that it was of medium difficulty, only because the course coordinator wrote a whopper of a third midterm and the class average got totally wrecked, so he had to compensate with an easier than average midterm.
 

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  • #14
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Yea, I've always heard that U of T has outrageously difficult tests...
 
  • #15
m1ke, do you have any accessibility to those places, PI, IQC, WIN and in the future the QNC building?
You also really don't need to be worrying about whether you can wander around PI during your free time. The work done there on a daily basis is way, way, WAY beyond either your or my level. Also, in first year, your priorities will be more along the lines of:

1. Party
2. Studying/Cramming/Finishing late assignments
3. Party
4. Sleeping

This is a general list, but you see my point, I think.

University offers many opportunities for undergrads to get involved in advanced physics though, so don't worry. There are usually weekly physics talks from visiting profs. My first year physics professor Sabine Stanley (seriously, if I could sell you on attending UofT for physics, simply having her and Stephen Julian as your first year profs could be enough incentive by itself; look them up on the UofT physics website (just google it...)) organized tours of fellow professors labs (with free pizza!) for her first-year students.

Also, don't worry about hijacking my thread! I got my answer (m1ke_'s comments were actually quite helpful; thanks!), and you might as well use it to ask questions. Honestly, if you're considering either school, best people to get info from are the people who go there.

Almost more than that, though, please consider the location of the school! I am applying to transfer to Waterloo not because I dislike UofT, or my program. (Well, you get enough lab reports back with a 79% instead of 80%, and you might start hating it...) I found that while I like many of the attractions and facilities the city of Toronto offers, I simply don't want to live downtown. I've been to Waterloo a bit, and felt right at home there. Easy choice. So think about that at least as much as program requirements. It is a crucially important yet often overlooked part of university application.
 
  • #16
Yea, I've always heard that U of T has outrageously difficult tests...
Maybe. Depends on the person. Many people get 100% on exams all the way through. (Very few, though; they're the true geniuses...) If you work hard, study, you can do very well regardless. But you will hear many excuses from people who do poorly. Maybe they're true, maybe they're not. But that's the way it is, so instead of complaining, study more! There, enough said...
 
  • #17
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Hey, Steven is right that you should not worry about getting around places like PI. In the time I've been here, I've been to those places collectively about 4 times, half of them from volunteering through science faculty events. As for your question about it being easier to get a position, I could not tell you because I've never heard of anyone getting offers, all that I know is that they do offer positions during coop and summer. Although, I don't think they would. The idea of PI and IQC is to bring together great minds and make progress in the fields of quantum computing and string theory, so the concept of being bias would contradict their very foundations. Outside of that, it would be against the law for them to not hire someone qualified for any position, based on their educational backgrounds.

As for books/courses, it depends whether you enter physics or math/phys as well as which faculty you apply to. Ill do a similar break down of my first year math for math phys through the science faculty.

Math 137: Calculus 1 (Stewart Text book) - essentially a detailed recount of what you learned in grade 12, including proofs and theorems that you would disregard in high school (ie mean value theorem, L'Hopitals Rule, etc) and then extending into integration. You'll be in sections with Honours Math and Computer Science students. Exam is 65% of final, fully written with proofs.

Math 135: Linear Algebra I (Introduction to Linear Algebra, by D. Norman) - Introduction to spanning and linearly independent sets of vectors; systems of linear equations and their solutions; linear mappings; matrices and their properties; vector spaces; subspaces, bases, and dimension of vector spaces; determinants and matrix inverses; eigenvalues, eigenvectors and diagonalization. You take it a semester before everyone else, so you will be with only other math/phys students. Exam is also 65%, fully written and mostly proofs.

Math 138: Calculus 2 (Stewart Text) - a continuation of Calculus 1 picking up at more advanced integration. Applications of integration. Intro to Differential Equations. The rest of the course looks at sequences and series. Exam style from Calc 1 applies here.

After first year, you have to buy very little books. All my math courses last semester were course notes; which in total maybe came to $100.
 
  • #18
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?
 
  • #19
I am so sorry... That is wayyyyy too long of a post.
 
  • #20
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Why does the U of T Math/Phys programs sound much more difficult then the Waterloo Math/Phys, you said you took Real Analysis in first year...
 
  • #21
Why does the U of T Math/Phys programs sound much more difficult then the Waterloo Math/Phys, you said you took Real Analysis in first year...
The UofT program is "Mathematics and Physics (Science Program)". It's through the math department. It- oh, well, wait, I'll just show you:

Mathematics and Physics(Science program)

Consult the Associate Chairs, Undergraduate Studies, Department of Mathematics and Department of Physics.

Specialist program:

(14-14.5 full courses or their equivalent, including at least one full course at the 400-level)

First Year:
MAT157Y1, MAT240H1, MAT247H1; PHY151H1, PHY152H1
Second Year:
MAT257Y1, MAT267H1; PHY224H1, PHY250H1, PHY252H1, PHY254H1, PHY256H1
Note: PHY252H1 and PHY324H1 may be taken in the 2nd or 3rd year.
Third Year:
1. APM351Y1; MAT334H1/MAT354H1, MAT357H1
2. One of: MAT327H1, MAT347Y1, MAT363H1
3. PHY324H1, PHY350H1, PHY354H1, PHY356H1
Fourth Year:
1. Two of: APM421H1, APM426H1, APM436H1; MAT446H1
2. Two of: PHY450H1, PHY452H1, PHY454H1, PHY456H1, PHY460H1
3. One of: MAT477Y1; PHY424H1, PHY478H1, PHY479Y1

NOTE:
1. Students who are intending to apply to graduate schools in mathematics would be well-advised to take MAT347Y1
2. Students are required, as part of their degree, to take a course with a significant emphasis on ethics and social responsibility such as: PHL275H1/PHL265H1/PHL268H1/PHL271H1/PHL273H1 or similar courses in other departments.
3. Students planning to take specific fourth year courses should ensure that they have the necessary third year prerequisites.


PHY=physics course (Waterloo: PHYS)
MAT=math course (Waterloo:MATH)
APM=applied math (Waterloo:AMATH)
PHL=philosophy (er, don't even know...)

You can check out program requirements here:
Physics:
http://www.artsandscience.utoronto.ca/ofr/calendar/prg_phy.htm [Broken]
Courses are listed here if you want to browse them:
Physics:
http://www.artsandscience.utoronto.ca/ofr/calendar/crs_phy.htm
Math:
http://www.artsandscience.utoronto.ca/ofr/calendar/crs_mat.htm

I think that part of the thing is (sorry m1ke_, nothing personal) that the UofT MathPhys specialist, well, it is harder. Math-wise. I'm a physics major, and take the exact same physics courses. But the math is the difference maker. And, honestly, I try to get out of taking any maths I can.

Also, I believe at Waterloo, there are two versions of the Mathematical Physics program, one through the Math Dept, one through the Physics Dept, and they differ slightly. It may well be that the Math Dept version is comparable to UofT.
 
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  • #22
NOTE: I AM NOT A MATHPHYS SPECIALIST... I am but a lowly physics major. Those program requirements are also on the program page.

Also, I think that UofT is noted somewhat as having a really tough math department. This doesn't necessarily mean good (doesn't mean not good, either), but yes, the math at UofT is tough. But if you take the hardest math courses, you get the best profs. Observe:
Difficulty:
MAT135<<MAT137<<MAT157
Teaching Quality:
MAT135<<MAT137<<MAT157

Logical, no?
 
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  • #24
In comparison to the physics courses, Waterloo appears to have a better selection: http://www.ucalendar.uwaterloo.ca/1011/COURSE/course-PHYS.html.
I agree. Certainly more diverse. This is part of my decision.

Waterloo's program seems to be more built like an engineering program. For example, they seem to have many more lab components. Also, the UofT physics program doesn't make you take statistical mechanics, optics, and a couple other things that are required at Waterloo.

Do I detect a note of favouritism toward Waterloo in your posts? (Wouldn't be a bad thing.)
 
  • #25
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A little, I'm just worried about the lack of mathematical rigour, but I don't think Real Analysis is necessary. Complex Analysis is.
 

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