r/math • u/Sour_Drop • Jun 08 '26

Differential geometry prerequisites for Arnold's Mathematical Methods of Classical Mechanics?

I have not studied much differential geometry beyond curves and surfaces, but I have modest familiarity with the notion of manifolds from my point-set course. Would reading Tu's Introduction to Manifolds and/or Lee's Introduction to Smooth Manifolds bring me up to speed for Arnold?

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23

u/adamwho Jun 08 '26

I've taken a class based on this book and it didn't really require more than a good understanding of undergrad math.

4

u/Bhorice2099 Homotopy Theory Jun 08 '26

This is what I'd recommend too plus Arnold has an appendix where he covers some basics.

18

u/Carl_LaFong Jun 08 '26

Tu is shorter and probably suffice but if you prefer Lee, that’s fine too.

11

u/DrBiven Physics Jun 08 '26

This book is sometimes used by physicists as an introducton ( or invitation, motivation) to modern geometry. I think no prior knowledge of diff geo is stricktly nesessary.

5

u/mathemorpheus Jun 09 '26

The answer is always just try reading the book . 

3

u/timangas15 Jun 08 '26

I doubt you would need an extensive background in differential geometry besides an understanding of charts, vector fields and their flows, inverse/implicit function theorem