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I'll be taking an overload, so I'll be taking 6.0 credits worth of courses (3.0 per semester). I'm only required to take 3.0 more courses in Pure Math to get my degree, so I have room to play around with.

Currently, I will be taking:

Rings and Modules

Field and Galois Theory

Differential Equations

Complex Analysis II

Algebraic Topology

Algebraic Geometry

(Note I'll have taken a lot of 4th year/Grad courses the summer before 4th year such as Functional Analysis, Smooth Manifolds, Banach Function Spaces, and maybe Non-Commutative Geometry)

So I think I'm pretty set on completing my requirements for both my degree and my graduate school application.

But i have room to take electives since I've stacked my first 3 years so jam packed.

I've completed my Arts and Social Science requirements, so I'm just looking for courses that a)interest me, b)may help me in the future if after I (hopefully) complete my PhD and do not want to stay in academia

So the first thing that comes to mind is taking courses in Actuarial Sciences, Stats, etc. I know they are much different than pure math courses, but I'd expect they would help if I would have to look to getting a job on Bay St (toronto).

So some of the courses I'm looking to take:

Accelerated German (for my language requirement for Graduate Studies)

Mathematics of Finance (Actuarial Science)

Financial Markets and Investments (Actuarial Science)

Mathematics of Financial Options (Applied Math)

Probability and Statistics I/II (Stats)

Financial Modelling (Stats)

Would it be wise for me to take some courses in finance and investing if I have the room? I'm usually one to argue that university is definitely -not- a process for a meal ticket for a job, but I'm just trying to weigh the pros and cons of either filling the space I have with electives that could help me in the future, or stick to pure math and just load up on graduate courses that are being offered next year.

I was also thinking, would it be wise to retake courses with all this room? Last year there were two courses where I got a B in for a mixture of both laziness and other reasons. Would it be wise to retake these courses and bring them up to an A or higher?

Thank you for any advice!