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Math 341 - Operations Research 1, or

Math 409 - Calculus of Variations

Also, which out of the two is more helpful generally that might also be used later in my masters and/or PhD? Can I have a little idea about what I'm going to be studying in these two courses? I have so far taken Cal 1, Cal 2, Advanced Cal, ODE, Real Analysis 1 and 2, Algebra, Probability, Statistics etc. And yes, I plan on doing a senior year project/thesis as well. Thank you in advance.

Syed Bukhari
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    You should talk to a qualified adviser at your university. – DanLewis3264 Jun 21 '19 at 18:46
  • I did. I got a 'depends on what you're applying for.' Of course it does. But for a general Math Masters degree. – Syed Bukhari Jun 21 '19 at 18:49
  • But, from my perspective, neither course is essential for postgraduate studies in mathematics. And nor should you be taking courses just to impress admissions tutors. Do some reading on the two topics, and see which one interests you more. Obviously, if you have any intention of specialising in Operations Research, Operations Research 1 would be essential. But if you're focusing on Pure Mathematics, I doubt admissions tutors would care much either way. Calculus of Variations is nice to see but perhaps doesn't require a full course (unless you plan on studying something somehow related) – DanLewis3264 Jun 21 '19 at 18:49
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    OR? That looks more like Computer science or even Business. What about some good Complex analysis course? It is usual at undergraduate level and I see nothing about it in your resume. And "algebra": what does that mean? Linear, commutative,.... Something about Number Theory, too...? I think you may be missing several basic courses usually required for a pure mathematics graduate school... – DonAntonio Jun 21 '19 at 18:50
  • @bounceback thank you – Syed Bukhari Jun 21 '19 at 18:54
  • @DonAntonio the course is just called Algebra which is our core course and introduces cyclic group, subgroups, direct products, homeomorphisms, rings, sub-rings, quotient rings etc. Unfortunately, they don't offer Number Theory anymore, and yes Complex Analysis is a core course which we all have to take in our last semester. – Syed Bukhari Jun 21 '19 at 18:58
  • What you mention is, I think, Group Theory and Ring Theory (basic, apparently). A pity about the Queen of Mathematics, Number Theory...and good you have complex functions. Take into account what your school offers at graduate level to make your choices. – DonAntonio Jun 21 '19 at 19:15

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It depends on what you want to do during your grad years. It really does.

If you want to do OR or Financial Engineering then OR it is.

For a general pure math program you are expected to be able to do a lot of algebra, topology. You are expected to have analysis around your fingertips (Real, Complex, Functional).

For an applied math program it again depends on what you wanna do. Generally incoming class have strong backgrounds in PDEs, Numerical (Analysis, Linear Algebra, ODE and PDEs sometimes Optimizations). Also Modeling Classes, Asymptotic Analysis classes.

In general for math, math programs my PERSONAL suggestions are: PDEs $\simeq$ More Analysis $\geq$ Topology $\geq$ More Algebras $\geq$ Calculus of Variations $\geq$ Operations Research.

Take OR only when you think it will help you with exactly what you want to do. I personally have difficulties believing that it is very useful in getting in a general math program without a focus in OR.

Disclaimer: For people with OR background: I admit that you might have every possible mathematical training that is needed and it is itself a fascinating and difficult subject. However the extent of this answer addresses directly to what a general math program is looking for. Some noted partial exceptions are in the comments below.

Book Book Book
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  • I would echo on some comments on saying that neither these two classes are that important. I do hedge by saying that some math programs are very OR heavy (Cornell, Stony Brook, UPenn); but I do think that Calculus of Variations are probably more widely used in many other institutions as well. – Book Book Book Jun 21 '19 at 19:24
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    As a recent Cornell PhD, I must disagree that Cornell's mathematics program is "very OR heavy". OR (or ORIE as it is called) is its own department at Cornell, and there is no requirement in Cornell's math PhD to take any ORIE courses. – James Jun 21 '19 at 20:27
  • my apologies, thats the department I meant. I could have clarified better I guess – Book Book Book Jun 21 '19 at 20:39