Im taking a dif-geo class but i haven't done math in 3 years or so. Any suggestions on where i could look up some information or any other resources to put me in a better position for this class? (second year stuff regarding planes etc that i could review)

I really would like to see a relate able Implicit function theorem and proof it seems to be very important in the class. Maybe a even book with a slow pace and some simple examples regarding surfaces. My textbook is almost incomprehensibly complicated and my prof isnt following it that closely.


TEXT Millman and Parker, Elements of Differential Geometry. Prentice-Hall.

SYLLABUS Curves in the plane and in 3-space, curvature and torsion, Frenet-Serret apparatus, surfaces in 3-space, Gaussian and mean curvature, Therema Egregium, Gauss-Bonnet theorem, elements of non-euclidean geometry.

TOPICS The goal of the course is to introduce some of the basic notions of differential geometry in 3-space. We will study chapters 1,2,4 and 6 of the text. We will make several excursions to explore additional topics, provided time permits.

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    $\begingroup$ How about Calculus on Manifolds by Spivak? Unless you deal with some serious abstract diff-geo I think you'd be fine $\endgroup$ – user160738 Jan 27 '17 at 3:01
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    $\begingroup$ Differential geometry is a vast subject, it's hard to know what you need if we don't know what parts of it you're studying. Do you have a syllabus you can share with us? $\endgroup$ – Mnifldz Jan 27 '17 at 3:26
  • $\begingroup$ Sorry i have edited my post to include the syllabus. i have a great geometric intuition in class but i seem to lack the necessary tools to implement them. my prof is great but i find the textbook rather difficult to read and my assignments very difficult and almost always requiring a translator to read them. i feel bad bothering my prof so much feel like i have no idea what i am doing. $\endgroup$ – Faust Jan 27 '17 at 3:48

You seem to be doing a course in "classical" differential geometry (meaning differential forms, topology, and heavy manifold theory are probably not needed). My suggestion is to brush up on linear algebra and some basic multivariable calculus/analysis (where you can review the implicit function theorem), and then read the lovely, highly visual, and amazingly gentle book Differential Geometry of Curves and Surfaces by Banchoff and Lovett. I'd also recommend Kreyszig's Differential Geometry.


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