Differential Geometry: A First Course in Curves and Surfaces [pdf]
10 comments
·March 22, 2025forgotpwd16
Those are (updated) notes for a course with description (taken from prof. Shifrin's homepage):
> This is an undergraduate introduction to curves and surfaces in R3, with prerequisites of either MATH 2270 (2500) and MATH 3000 or MATH 3510(H). The course is a study of curvature and its implications. The course begins with a study of curves, focusing on the local theory with the Frenet frame, and culminating in some global results on total curvature. We move on to the local theory of surfaces (including Gauss's amazing result that there's no way to map the earth faithfully on a piece of paper) and heading to the Gauss-Bonnet Theorem, which relates total curvature of a surface to its topology (Euler characteristic). As time permits, we'll discuss either hyperbolic geometry or calculus of variations at the end of the course.
clircle
I took differential geometry during undergrad but had to drop out of the course as i thought i would fail the final. Great professor, but too much for my 20 year old brain. Id like to try it again in retirement.
samantha-wiki
I was fortunate enough to take this course with Ted Shifrin at UGA, he is an incredible professor (now retired), and it was one of my favorite courses when I was in undergrad.
antegamisou
Suddenly HN has decided that they're not visual learners anymore. Too bad, Keenan Crane from CMU has the best video course series on Discrete Differential Geometry:
https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1...
ofrzeta
This resonates much more with with than the above PDF that jumps right into the first definition.
dist-epoch
For those who don't know, differential geometry is used in the most elegant definitions of physics - quantum field theory.
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blahhh2525
[dead]
bachmidt1007
[flagged]
This is a nice textbook. We used it when I was an undergrad in Brazil and those were some of the most fun classes I've ever had. It gives you a ton of intuition and understanding for classical (extrinsic) differential geometry, and I feel that this experience was very helpful later in learning Riemannian geometry and General Relativity. It also helped a bit when I took an intro course to computer graphics. Solid stuff!