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I want to learn DG and RG so I can use them in PDEs. Atm I have no knowledge of either DG or RG (and not that much of PDEs either..) but I have a couple of books (John M Lee and Loring).

If I spend say 1 hour a day on learning this how long will it take? I know this depends on the person, but a rough number? 1 month? 6 months?

What should one skip in learning this field for PDEs? I guess there are certain things I do not need to know (or have time to know).


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closed as not a real question by Quixotic, Pedro Tamaroff, Thomas, Zev Chonoles Jun 28 '12 at 22:39

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

I'm afraid that the dependence of this on the individual (both the amount of time it will take you to learn, and which topics are unnecessary) makes it a poor fit for this website. –  Zev Chonoles Jun 28 '12 at 22:42

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Riemannian geometry is a large field which still has active research going on, and much of it is applicable to PDE. I doubt there's a good answer to this question, because it will depend very closely on what you want to do. Different areas of PDE will use different techniques, and unless you have a very good idea what you want to do there's no way to know what you will need. If you have an advisor, they would be the best person to talk to regarding this.

To quantify a little bit, at risk of loss of generality, you probably wouldn't get much out of a month of study if you know nothing now. At my school we have a 2 semester graduate class in differential geometry, which is essentially the minimum you'll need if you want to do anything serious. Riemannian geometry was about 70% of the curriculum. We also have a 2-semester graduate class in PDE, which again I'd guess is the minimum one needs to do anything serious there. There's no reason you have to take a class, but one way or another you'll need to learn it, so the amount of time should be approximately the same.

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