- #31
jbergman
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Not really. Topology is more needed than hard analysis. I believe the Tu book has an appendix, though, that should be sufficient.MichaelBack12 said:
Best way to teach myself differential forms?
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Discussion Overview
The discussion revolves around self-teaching methods for differential forms, including recommendations for online courses, books, and video resources. Participants explore various educational materials suitable for different backgrounds and goals, particularly in the context of physics and engineering.
Discussion Character
- Exploratory
- Technical explanation
- Homework-related
Main Points Raised
- Some participants suggest online courses or videos as potential resources for learning differential forms.
- Several books are recommended, including Flanders' book and a recent book by Tristan Needham, which some participants find well-written.
- Participants mention the importance of knowing one's background and goals to tailor the learning approach effectively.
- One participant highlights the value of Ted Shifrin's notes for being hands-on and example-heavy, which may help beginners navigate abstract concepts.
- There are discussions about the relevance of William Burke's work and his advocacy for moving beyond traditional vector calculus, with references to his published ideas on differential forms.
- Some participants express interest in differential geometry texts suitable for beginners, with multiple suggestions provided.
- Links to various YouTube videos and online resources are shared, indicating a variety of multimedia learning options available.
Areas of Agreement / Disagreement
Participants do not reach a consensus on a single best method or resource for learning differential forms, as multiple competing views and recommendations are presented throughout the discussion.
Contextual Notes
Participants express varying levels of familiarity with differential forms and related mathematical concepts, indicating a range of assumptions about prior knowledge and learning objectives.
- #32
mathwonk
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here is another free set of lectures from a mathematician who tried to present forms to his undergraduates in an unsophisticated way:
https://www.math.purdue.edu/~arapura/preprints/diffforms.pdf
https://www.math.purdue.edu/~arapura/preprints/diffforms.pdf
- #33
martinbn
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When I saw the name of the author I expected to is an intro to differential forms in algebraic geometry, but it is actually a nice introduction to differential forms for someone with basic calculus knowledge.mathwonk said:
- #34
mathwonk
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well, (cough, cough) algebraic geometers are famous for knowing everything.
(maybe make that needing to know.)
(maybe make that needing to know.)
- #35
martinbn
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So, what Mumford said in the preface of his Curves and Their Jacobians book was not a joke.mathwonk said:well, (cough, cough) algebraic geometers are famous for knowing everything.
(maybe make that needing to know.)
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