Should I Choose a Physics or Math & Physics Major for Theoretical Physics?

[rso]

Hello,
Next month I will begin my first year at the University of Toronto for my undergrad and I have a question regarding which major I should declare at the end of the academic year.

I intend on pursuing physics into graduate school (likely more on the theoretical side) and so the two specialist programs that appealed to me were the Physics (obviously) and Physics and Math programs (a specialist program is essentially a major but with more time invested in the subject).

The two specialists are nearly identical with regards to the physics courses taken with the exception of 4th year in which the Physics specialist requires an extra experimental course (e.g. computational physics). The points of differentiation are of course the math courses. Without going into excessive detail, the Math and Physics specialist involves more advanced courses (with I assume more emphasis on rigorous proof) such as Real & Complex Analysis, Differential Geometry, and advanced ODEs & PDEs. Additionally, it includes 2 applied math courses in 4th year: General Relativity and the Mathematical Foundations of QM. The physics department also offers a Relativity course but I don't think it is available every year and I imagine the math in the course would be less rigorous.

I currently plan on enrolling in the Math & Physics specialist as I imagine having a greater understanding of more abstract math would only be beneficial if I continue on into theoretical physics. Additionally, the guide to being a physicist mentioned taking more advanced math classes and I enjoy math itself as well (although not as much as physics .

So, I was just wondering if I could hear some opinions regarding which program would be more ideal. Would the advanced math courses be worth taking or would they somehow detract from my physics education? Any opinions would be appreciated.

Thanks in advance

 

[CAF123]

I was in a similar situation to you some time ago, deciding on Physics or Mathematical Physics.
This time last year, I emailed the theoretical physics department about some of my questions and they said if you definitely wish to pursue the more theoretical side of physics, then do Mathemtical Physics, if you prefer the experimental side, do Physics or if you want to keep your options open, do Math Phys and change later if needed.

The person I was speaking to you has since become my director of studies and I definitely feel the earlier maths courses have benefited me. Early on in the degree programme, I can see there is certainly an emphasis on the mathematics, but as the years progress, ie 3rd,4th year, Math Phys majors do physics courses that are more theoretical that require just that extra maths.

 

[PhyConnected]

I think you should start off with MAT157/240/247 sequence first and see whether you can get used to it. Many people simply drop out within a week or so.
In my year, 150 people enrolled for MAT157 and by the end of second year there was 25-30 people left. (so there's even less people in Maths and Physics)

If you're able to handle it, then I'd say definitely go for the Maths & Physics Specialist as the program is pretty much superior than a pure Physics Specialist in every way. You essentially take all the same Physics classes with a larger variety and more rigorous Maths courses that are oriented to Physics students.
For instance, in addition to the 4th year APM courses you mentioned, you'll also be taking a full year PDE course called "Differential Equations for Mathematical Physicist", instead of the one semester non-specialist course. I guess I don't need to emphasize how important PDEs are in Physics.

The extra rigor in the Maths courses usually becomes useful at a later stage.
Take MAT247 as an example. You'll learn a lot more about Hermittian operators in MAT247, which will become useful in PHY356 when they talk about the formalism of Quantum Mechanics.
All the properties that the Physics students take for granted will be proved rigorously in MAT247, which I imagine would be more satisfying for a Mathematically inclined student. It may not essentially help any of the calculations, but it certainly gives you a more complete view of the theory.
The stuff about manifolds and tensors in MAT257 also becomes useful in General Relativity.

You can always take PHY407 or PHY405 as well but from what I gather those courses are of little value.
Doing a project course is also probably more useful than taking the advanced labs.

 

[jimmyly]

I made a very similar post a month ago. And i am going for the math & phys. I plan on finishing in 5 years because some of the upperlevel phys and math courses clash but i think the extra math will benifit me.

 

[rso]

Thanks for all your responses. Based on your advice I think I will stick to my plan of enrolling in Math & Physics. I have heard much of the infamy of MAT157 so I have begun reading Velleman's How to Prove It. Additionally, I have some transfer credits from doing IB in high school so I will have a reduced course load first semester to make the transition to university level Mathematics and Physics easier.