Questions tagged [differential-geometry]

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5 votes
1 answer

Which books on geometry and topology are best for teaching an intro graduate course?

I'm teaching a graduate (Master's) introduction to geometry and topology (e.g. some basics on manifolds, vector bundles, algebraic topology). What textbooks have you found are best for teaching a ...
David Corwin's user avatar
1 vote
2 answers

Where can I find a good course on tensor calculus not focused on applications and physics?

Where can I find a good course on tensor/ricci calculus not focused on applications and physics? I've been running into lots of tensor-theoretic stuff in differential geometry, so I don't know if ...
John Clever's user avatar
10 votes
1 answer

College undergraduate geometry courses

I am interested in learning how a course in geometry is employed today at undergraduate colleges/universities in the U.S. On the one hand, such a course seems to serve as an optional (rarely required) ...
Joseph O'Rourke's user avatar
9 votes
2 answers

A Question about Theodore Frankel's "The Geometry of Physics"

Locked up in my self-distancing isolation in NYC, I'm reminded of how much I really like Frankel's book, which contains a wealth of beautiful geometry and topology from the standpoint of a ...
The Mathemagician's user avatar
3 votes
2 answers

Monodromy examples for undergraduates

I'm looking to put together a 1 hour talk about monodromy aimed at undergraduate math and physics majors. In terms of prerequisites, I only want to assume the students have seen multivariable calculus,...
Avi Steiner's user avatar
14 votes
2 answers

Does learning classical approach to differential geometry before modern approach help or hinder?

To my mind, there seem to be two main paths to differential geometry. There is the classical approach, focusing on curves and surfaces in $\mathbb{R}^n$, especially $\mathbb{R}^3$. Prerequisites tend ...
J W's user avatar
  • 4,625
15 votes
6 answers

Geometry with a view towards differential geometry textbook

I am scheduled to teach an upper-division undergraduate class on "Geometry" and I get to choose more or less what that means. Common choices seem to be non-Euclidean, hyperbolic, projective, or ...
Mike Shulman's user avatar
  • 6,520