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Looking to Prepare for Metric Differential Geometry

  1. Jun 20, 2012 #1
    This is the course description:

    I want to take this class because the professor comes highly recommended, but I'm a little worried that I won't be entirely prepared for it. Normally this class requires Real Analysis as a prerequisite, and even though the professor explicitly states that Analysis isn't required, I fear that not having that background/mathematical maturity will hold me back.

    I have taken three semesters of calculus and a course on differential equations and linear algebra. These are all of the prerequisites... but if I were to prepare for this course, where would be a good place to start?
  2. jcsd
  3. Jun 20, 2012 #2
    I took a class like that. The only thing we used from real analysis was the implicit function theorem, so it's good to have seen that. But actually, the class itself is where I got a lot more intuition about the implicit function theorem because one of the most natural contexts where it comes up is to prove that some level surfaces of a function on R^3 are "regular surfaces". So, if you're a good student, I think you could handle it already if you really know your stuff from calc 3 and linear algebra.

    It wouldn't hurt to look into real analysis, but as far as the implicit function theorem goes, I think the geometry class would be more helpful for understanding it than the other way around, if it's anything like my experience. There are a lot of real analysis books. Not sure what your style is. My favorite is A Radical Approach to Real Analysis for its historical motivation (take the history with a grain of salt, though), but I haven't read that many intro to real analysis books. From what I've heard, I would probably like Understanding Analysis by Abbott.
  4. Jun 21, 2012 #3
    The obvious answer is to ask the professor teaching the course. I'm sure he'd be happy to help you.
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