GR courses and Physics vs Math

Over the 17 years I have taught so far at UofT, I have had a lot of questions from Physics, Math, and Engineering specialists and majors about choosing General Relativity courses. The following are my answers to the most common questions I get asked about GR courses and Physics vs Math, written from the perspective of the professor currently teaching PHY483F/PHY1483F.

Is my math preparation sufficient?

*gulp* Is this really a physics course?

Yes, this is definitely a physics course. Even though I may look scary on paper, I work hard to be non-scary and humane to students -- in general, in class, and one-on-one. This course is one of the more conceptually advanced courses we offer in our UofT Physics programme, but it is not epically difficult. I and the TA help you learn the concepts gradually, through engaging lectures and materially useful tutorials designed to build confidence. I provide full online lecture notes in LaTeX, which I update both before and during the semester. Homeworks teach you how to calculate with pen and paper, and also how to automate tedious computations using Maxima, a free computer algebra package. Undergrads (PHY483F) form the majority of the class; the remaining 30% or so are grad students (PHY1483F). Most undergrads are Arts & Science students; a few are Engineers. The grad students are mostly in Physics/CITA with some in Astro. The only specific MAT background anyone needs is (a) basic 2nd year linear algebra, (b) a solid understanding of div, grad, and curl in spherical polar coordinates, the multipole expansion, and EM waves from 3rd year electromagnetism, and (c) an exposure to variational calculus from 3rd year classical mechanics. So if you have the two prerequisites PHY350 and PHY354 or similar, you should be fine. Generally, I do not recruit math for its own sake in my physics teaching; rather, I teach mathematical tools (sparingly) from a physics perspective when they are useful for explaining how the physical universe ticks. Note: my appointment to the Math Department is status-only; the Physics Department pays 100% of my salary and therefore enjoys 100% of my loyalty.

Physics GR vs Math GR

Should I take Math GR or Physics GR?

The answer depends largely on what you want to do next year. Are you planning to apply for PhD programmes? In Math or in Physics departments? Suppose that you want to apply to do a PhD in Department A at a variety of other universities. The general rule of thumb is that a graduate admissions committee member speed-reading your academic transcript would rather see core competencies in their discipline demonstrated via courses taken in Department A at your current university than in Department B, even if A and B are cognate disciplines. A more precise answer would depend on the country and on the institution. If you are not planning on going to grad school, pick whichever courses fulfil your intellectual curiosity the most and give you the most transferable skills for whatever else comes next.

Are PHY483 and APM426 similar enough that taking both of them would be repetitive?

There are certainly significant overlaps between the short-form descriptions of PHY483 and APM426. But if you delve deeper, you should expect to see significant differences. For example, they have different prerequisites. The acid test would be to ask your Department's Undergraduate Office whether you can take both PHY483 and APM426 for credit. If you can, the two courses are not largely identical. The general strategic solution to any course choice conundrum is as follows. Each teacher is responsible only for our own courses, not for what other teachers do with theirs (although of course we do monitor that). So the smart strategy is to obtain a detailed syllabus in advance from whoever is teaching each course you want to compare and decide between. After you have studied and compared detailed syllabus info, you will be in a better position to ask us specific questions.

No, really -- how can math GR and physics GR be different? Isn't it all just GR?

At a broad brushstroke level, the main difference is that PHY483 teach you the physics and astrophysics of general relativity, while APM426 teaches you the mathematics of general relativity. Both are valid and interesting areas of study, but they are motivated and framed differently, and different conceptual and technical tools are emphasized. (After all, Physics and Math are distinct disciplines, even though they both contribute a great deal to each other's intellectual health.) The overlaps tend to be more in the equations studied and their solutions rather than the motivations, contexts, and applications. Finally, be aware that the precise split between Physics and Math varies between institutions, and general conventions of how to seat academics in different departments can vary considerably between countries.

What do you teach in your course?

If you visit the official departmental course listing page for PHY483F and click on Link to Course Homepage, you get to my course website. Study all of it, especially the syllabus.