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Difficulty of Topology vs Differential Geometry

  1. Aug 24, 2011 #1
    So I need to decide by tomorrow, whether I'll be taking topology or diff geo, (along with real analysis and advanced linear algebra). I've sat in on both classes for the first lecture, and I'm still not certain which class would be more difficult. My diff geo class has no exams, and instead requires a presentation and an expository paper at the end of the semester. Anyone know what that might entail? Topology is, however, the typical problems sets and exam format.

    I feel like I'm already overloading on my math classes, so I would like your opinion on which class to take.
  2. jcsd
  3. Aug 24, 2011 #2
    Tough call. Is it an introductory topology course (i.e. point-set topology)? Keep in mind that topology is an absolutely fundamental subject in mathematics; it would be very good for you to have some experience with it. As far as difficulty goes, I suspect that you might have an easier time with the topology course (not to mention that having a topology course under your belt would make diff. geometry easier in the future).
  4. Aug 24, 2011 #3
    Indeed, topology is much more important than differential geometry (that doesn't mean that differential geometry isn't important, but just that topology occurs more often).
    Furthermore, topology goes very well with your real analysis class, so the two classes will complement each other.

    It's also better (and more natural) to do differential geometry from a topology point-of-view. So if you're set on doing differential geometry, then you need topology sooner or later anyway.

    As for difficulty, I would say that both subjects are as difficult.
  5. Aug 24, 2011 #4
    Inkit, I think if you post the syllabi and what each class intends to cover, people will have a better time advising you. Both are introductory classes.
  6. Aug 24, 2011 #5


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  7. Aug 24, 2011 #6
    Agree 100%.
  8. Aug 24, 2011 #7
    I don't know anything about differential geometry, but I think topology is probably a prerequisite?

    I mean how do you even talk about a differentiable manifold without knowing the basic terminology of a point-set topology course?

    Wait I read your OP again and yeah if you're taking your first actual real analysis class then taking differential geometry might be a problem... because differential geometry is doing analysis on spaces more general than Euclidean space?
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