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Prereq for Differential Geometry

  1. Feb 8, 2012 #1
    I am an Astrophysics undergrad, and will be taking Classical Differential Geometry I & II. Are there any classes that will make understanding Differential Geometry easier. I can chose from:

    -Introduction To Abstract Algebra
    -Introduction To Mathematical Analysis
    -Introduction To Real Analysis I
    -Methods Of Numerical Analysis I
     
  2. jcsd
  3. Feb 8, 2012 #2
    See if any of those courses includes an introduction to manifolds, preferably differentiable manifolds. I think that would be valuable, but maybe not neccesary, background knowledge. I am personally taking a course on differential topology this semester, partly to prepare for a course on analysis on manifolds, which I suspect includes differential geometry.
     
  4. Feb 8, 2012 #3

    George Jones

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    This depends on how the differential geometry courses are taught.

    You might not need any of the other courses for differential geometry. You might need some of the other courses, not so much for their material, but to build up sufficient "mathematical maturity". Finally, you might need some specific material from some of the analysis courses.

    What is the difference between "Introduction To Mathematical Analysis" and "Introduction To Real Analysis I"? What are the prerequisites for the differential geometry courses?
     
  5. Feb 8, 2012 #4
    Course descriptions are:

    MATH 4540 - Classical Differential Geometry I
    Smooth curves in Euclidean space including the Frenet formulae. Immersed surfaces with the Gauss map, principal curvatures and the fundamental forms. Special surfaces including ruled surfaces and minimal surfaces. Intrinsic Geometry including the Gauss Theorem Egregium.

    MATH 4550 - Classical Differential Geometry II
    Tensors, vector fields, and the Cartan approach to surface theory, Bonnet's Theorem and the construction of surfaces via solutions of the Gauss Equation. Geodesics parallel transport, and Jacobi Fields. Theorems of a global nature such as Hilbert's Theorem or the Theorem of Hopf-Rinow.
     
  6. Feb 8, 2012 #5
    MATH 3190 - Introduction To Mathematical Analysis
    This course is intended to introduce students to higher mathematics. The techniques of proving theorems, including proofs by induction, will be emphasized. The course will include elementary set theory and equivalence relations and a discussion of the real number system. Proofs of some basic theorems from algebra, calculus or number theory will be studied.
     
  7. Feb 8, 2012 #6
    Mathematical Analysis and Real Analysis will both help you develop proof skills and might get into manifolds and whatnot. If anything, take one of them to develop maturity.
     
  8. Feb 8, 2012 #7
    Thanks everyone
     
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