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How bad will not having taken Topology look?

  1. Aug 2, 2008 #1
    I know the importance of Topology, but I need to know if not taking this course in my last year will make a big difference.

    I will be a senior math major and I may decide to go to graduate school. I will take a year off to try to find some work experience to decide exactly what I want to do. Chances are good that even if I end up going for a PhD, I will still end up looking for a position in industry.

    I am taking two graduate courses, Modern Analysis and Algebra, and am looking at one more math elective.

    I can take a class on General Topology or Fourier Analysis (both are at the same time). I have absolutely no experience with applied math, besides the standard diff eq course, so I feel like the Fourier Analysis class could be useful. However, Topology is such an integral subject that I feel that if I don't take it, it will look espescially bad when applying to grad schools.

    My math coursework is not very remarkable, considering I was never very serious about anything until now:
    Linear Algebra, Abstract Algebra
    Adv. Calculus 1,2
    Combinatorics, Geometry
    Complex Variables

    I would prefer to take the Fourier Analysis class. It's material I've never seen before and sounds interesting. I have learned basic Topology in my Adv. Calculus class and would be willing to teach myself for the GREs, etc.

    If I don't take Topology, will this be a huge hole in my transcript, even if I plan on taking an Applied Math route in graduate school?
  2. jcsd
  3. Aug 2, 2008 #2


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    The way I see it, topology is a cornerstone of mathematics, and it's something mathematicians should know. On the other hand, fourier analysis is something that you'll most likely need when going for a job in industry.

    If you choose to take Fourier analysis, you'll most likely be taking a course on topology during your PhD. Similarly, if you don't take Fourier analysis, chances are that the university you attend for your PhD will be offering that class (and if not, you can choose a grad school that does), and you'll be able to take it there. In any case, you'll end up having taken both once you're ready to enter industry.

    Since I would think that topology would look better on your application (though if others feel that Fourier might look better, this being applied math and all, take that into account), I would take that class, then learn Fourier analysis in grad school.

    Also, did you do any functional analysis in those adv. calculus courses?
  4. Aug 2, 2008 #3
    Since you're interested in industrial work, I take it you'll be applying to applied math Ph.D. programs, rather than pure. I think a pure math program would have serious qualms taking on an undergratuate who hadn't taken topology - but by that same token I think an applied program would have the same worries about a student who hasn't taken Fourier analysis (or a PDE class that covered it.)
  5. Aug 3, 2008 #4
    meh you can easily learn pdes on your own, theres tons of book with numerical problems and answers out there. on the other hand having someone check your proofs is something irreplaceable. take the topology class.
  6. Aug 3, 2008 #5
    I agree with that; in pure math there's no substitute for human collaboration... But when applying to grad school, it does matter what's on your transcript. Unless you can prove that you're a PDE whiz, they'll wonder why you're applying in applied math at all.

    Here's an idea - you can't take both classes because of a time conflict, but what if you took topology and also asked the other professor if you could follow their course as an independent study? You couldn't show up for the lectures, obviously, but I'd think it's not too big of a concern since he/she already has lecture notes and course materials made up that you could follow.
  7. Aug 3, 2008 #6
    Thanks for the replies. I think I'm going to stick with Topology for several reasons.

    1. I'll feel that my undergraduate math education is incomplete without knowledge of topology beyond compactness.

    2. I just found out that the professor who teaches Fourier Analysis is not very good, i.e. he doesn't care about teaching at all and that the students usually don't learn anything in his classes, while still earning easy A's.

    3. The Topology professor, on the other hand, is very good and I could gain a lot more from it.

    I'll take the chance assuming that if I do go to graduate school, it will not be for an applied math degree. Pure math interests me and it's probably what I will end up studying.

    If I do get an internship in industry that allows me to see what mathematicians are working on, and I like it, I may change my mind, and I'll worry about what to do then.

    Thank you for the replies.
  8. Aug 3, 2008 #7
    I don't think there's much call for pure mathematicians outside academia, but I'm interested to be proven wrong. Nonetheless, I think topology is the better choice. Good luck!
  9. Aug 4, 2008 #8
    ehh depends on what kind of math. a lot of places do some weird things but still you're right. i personally am hedging my bets
  10. Aug 4, 2008 #9
    I think you made the right choice. If it's an undergrad Fourier class, it will be a nightmare. No measure theory will be assumed, so it will be all handwaving on the professor's part and memorization on the students' part.

    I think that even if you go into applied, you'll be better off with topology. For most applied students at my school (the applied phd is top 20), the pure math coursework is the hardest, so admissions people look to see if you'll be able to cut it. An undergrad course in Fourier analysis would be good for showing interest, but not much more, since you'd have to relearn it the right way once you've had real analysis.
  11. Aug 4, 2008 #10
    I know. If I chose a Pure Math route, I would likely try my hand at academia.

    That's good to know. I feel like I would have a harder time going into Pure Math without Topology than going into Applied without Fourier analysis.

    I'll try to take a PDE class my final semester. Thanks for the replies.
  12. Aug 4, 2008 #11
    I would think :Vector analysis, PDE's,complex variables,linear algebra, abstract algebra,Adv.Calc
    ought to be enough for applied math major.

    Depends on school. When I took PDE's, we covered fourier analysis thoroughly.
  13. Aug 4, 2008 #12


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    you are asking the wrong question. you admit your record is unremarkable for not having taken an interest in your course work and apparently not having done especially well. those are the shortcomings of your record, not the absence of any particular course.

    as to your desired subject, fourier analysis is one of the central ideas in mathematics, touching many many areas, and especially since you are actually interested in it, it would be a good idea to take it and to apply yourself and do well.

    good luck.
  14. Aug 5, 2008 #13
    As someone once said:"If you haven't taken a course in point-set topology, you haven't learnt any maths during your span at univ".

    at least not modern one.
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