Hey guys,

I took some math in college and am now going back to explore it some more; I think there's some chance I'll want to do grad work in something mathy.

Anyway, I've taken the calc sequence, linear algebra, and ODE's. Really didn't like ODE's, liked linear algebra, and think I'll like some optimization/game theory type courses.

I'm taking Real Analysis I now and can take Real Analysis II, Game Theory, or Probability in the second semester this summer. For what it's worth, I really like the cardinality stuff we've covered (like C(0,1) = C(0,2)).

I'm also taking classes in the fall/spring semester at a good college so I should be able to take any standard math class. I want to maximize my exposure to topics so would like to avoid taking classes that are fairly similar (like algebra + number theory seems like a bit of a waste to take in the same semester).

Anyway, sorry this is so tl;dr but would love to get some advice from the math guys. Happy to clarify anything that's unclear.

Thanks a lot,
Mariogs

Why do you think these are similar?

Algebra is a pretty key subject, well worth considering (compulsory imo). Not knocking number theory at all but unless you're particularly interested in number theory its a stand-alone subject that you can leave out.

Can you be more precise about this? There are lots of "mathy" things for which you don't need much of any of the formal mathematics.

I'm not sure why you think algebra and number theory are similar enough that it's a "waste" to take them in the same semester.

If I'm reading this right, you're a non-degree seeking student, so your concerns have little to do with the formal requirements of classes that one must take to get a degree in math, but instead you're interested in preparing for applying to graduate school in some field, but you're not really sure what that field is.

I think you should figure out the grad school part first, and then the math course question will work itself out.

I thought they were similar because, where I went for undergrad, abstract algebra was a pre-req for number theory, and *I thought* a lot of number theory results rely on algebra...

Thoughts on what I should take for my 2nd class this summer and then during the year? Was thinking something like:

Game Theory (summer)

Abstract Algebra
Probability Theory
Optimization
Complex Analysis

Not sure whether I should sub in topology or geometry for one of the above...thoughts?

Thanks for the help, Chezlaw.

@Aaron,

I know I like math, but it's hard to know what specifically I want to do math-wise without taking more math. Sort of a catch-22...to know what I want to do more of, I have to just go out and take more math...

It's sort of true, but it's also not that true.

Is your intention to get a Masters or PhD? Are you interested in getting one in math or merely a "mathy" field (perhaps something in computer science or finance)?

Looking further down the horizon, what do you intend to do with whatever degree you're getting?

Number theory uses algebra, but it also draws on ideas from geometry and topology. Yet taking a class in number theory is nothing like taking a class in any of algebra, geometry, or topology.

Sounds good. Not sure what geometry covers at this level but personally I'd miss this out even if there's lots of fractual stuff and especially if its back to the Greeks.

Is the topology course one you should consider doing later? may just have been where I studied but it was an advanced course (not one I ever did but sounded interesting).

Do you have access to rough course outlines for the geometry and topology courses? If so, could you post them?

Not sure where you want to go, but if you wanna go into finance, I can recommend probability and measure theory. I really liked both myself.

MATH W4051x Topology 3 pts. Prerequisites: MATH V1202, MATH V2010, and rudiments of group theory (e.g., MATH W4041). MATH V1208 or W4061 is recommended, but not required. Metric spaces, continuity, compactness, quotient spaces. The fundamental group of topological space. Examples from knot theory and surfaces. Covering spaces.

Will post geo later. No interest in finance fwiw...

I would advise to take Topology and leave out Optimization. Other than that I like your choices.

Anything up to quotient spaces in the Topology class description you will need to know if you go further in math. And fundamental groups is a very interesting topic.

Optimization is applied and quite specific, and tbh probably kinda boring. I'd say you can always learn it later on your own if it turns out to need it.

I was going to suggest the same, topology instead of optimization. I was a little worried that the topology course would be too big of a jump, but judging by that outline it should be fine.

No one has mentioned statistics yet--if you want to go to industry you might want to supplement your knowledge with some statistics--say, a course on regression and a follow up course, say time series or data mining (or both).

If were going down what best for the carear route then maybe consider some programming courses.