[HN Gopher] Differential Geometry: A First Course in Curves and ...
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Differential Geometry: A First Course in Curves and Surfaces [pdf]
Author : ibobev
Score : 93 points
Date : 2025-03-22 13:46 UTC (9 hours ago)
(HTM) web link (math.franklin.uga.edu)
(TXT) w3m dump (math.franklin.uga.edu)
| forgotpwd16 wrote:
| 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.
| sfelicio wrote:
| 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!
| samantha-wiki wrote:
| 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.
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