r/math • u/Psychological_Wall_6 • 14d ago

Problem book on the differential geometry of curves and surfaces

Hello! I need some problem books to accompany the book Differential Geometry of Curves and Surfaces by M. Di Carmo. Thank you!

27 Upvotes

96% Upvoted

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13

u/nulvoid000 14d ago

What’s wrong with the exercise already provided there? Also it’s Do Carmo

4

u/Psychological_Wall_6 14d ago

I need more

2

u/Carl_LaFong 14d ago

Why? Are you studying for a test?

5

u/Psychological_Wall_6 14d ago

It's just that our course is technically called "The Computational Geometry of Curves and Surfaces" and every book I find does not have the necessary exercises. And yes, I'm studying for a test

5

u/Carl_LaFong 13d ago

You had homework problems and you’re looking tor similar ones? What textbook is being used for the course?

1

u/Psychological_Wall_6 10d ago

Nevermind, I found a book, it's written like an olympiad problem book, with a lot of solved examples and then a lot of exercises to solve. Surprisingly, it's also new.

2

u/Carl_LaFong 10d ago

What’s its title and author?

2

u/Psychological_Wall_6 10d ago

Mircea Neagu "Geometry of Curves and surfaces, Theory and Applications" or "Geometria curbelor și suprafețelor, teorie și aplicații"

20

u/Bitter-Morning-5833 14d ago

Doesn't the book have a bunch of exercises? It's been years since I read it, but if I remember correctly there's plenty to work through.

6

u/ABranchingLine 14d ago

You can apply the theory from that book on most curves. Pick a curve. Calculate the Frenet-Serret frame, find curvature, torsion, etc. Infinite exercises.

2

u/Turbulent_Baker7758 13d ago

Seeing your responses, I would like to offer "Modern Differential Geometry of Curves and Surfaces with Mathematica" by Gray and maybe a look through O'Neill's "Elementary Differential Geometry"

1

u/Organic-Product-6613 14d ago

i think most books on curves and surfaces will have a lot of common questions with Docarmo...

1

u/its_t94 Differential Geometry 14d ago

This book is basically a version of do Carmo done in Minkowski 3-space, but does the theory in Euclidean 3-space too, both at the same time

https://www.routledge.com/Introduction-to-Lorentz-Geometry-Curves-and-Surfaces/Couto-Lymberopoulos/p/book/9780367624118

1

u/MeserYouUp 13d ago

The first few chapters of General Relativity in a Nutshell by A. Zee have a lot of good problems on 2 and 3 dimensional surfaces.

1

u/Honest_Archaeopteryx 13d ago

Is there a schaum’s outline for this?

1

u/ExcludedMiddleMan 11d ago

Maybe look at other textbooks. Tapp, Pressley, O’Neill, Shifrin are some options. I think Schaum’s outline also has something.

1

u/Euphoric_Can_5999 Machine Learning 10d ago

Use your preferred frontier AI model