Calculus on Manifolds
Michael Spivak
11 people recommended it in 9 threads, 2009–2023.
What people on Hacker News said
This gives you a rigorous treatment of calculus, which hopefully you have some familiarity with.
Working successfully through those three is quite sufficient to understand proof-based college math!
For me, the eye opening thing was that any n-dimensional body is a transformation of the n-dimensional standard cube.
And from Spivak his small gem "Calculus On Manifolds" made quite a dent on me.
These books changed my life in the best of ways.
I'm working through Calculus on Manifolds. Partly as mathematical weight training, partly because the aspect of quantum field theory that trips me up is usually the field bit.
Apart from the classic calculus textbook, he has written Calculus on Manifolds which is also a nice introduction into differential geometry.
Where it comes up
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