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I had the same experience as a math undergrad. Too many professors seem to have forgotten what it was like to be a student. They write books that are great re
by benrbray 6y ago
I had the same experience as a math undergrad. Too many professors seem to have forgotten what it was like to be a student. They write books that are great reference material for their colleagues but which are utterly opaque to a student who is still working to build their foundation.
Textbooks often format proofs as a sequence paragraphs, but this really obscures the logical structure of the argument. As a student, I found it very helpful to write down proofs as nested lists [1,2] instead.
Admittedly, now that I have more experience, I do like my proofs to be more terse when I'm communicating them just to myself.
[1]: https://benrbray.com/static/notes/separating-hyperplane-thm_jun17.pdf https://benrbray.com/static/notes/separating-hyperplane-thm_...
[2]: https://benrbray.com/static/notes/minimax-approx_nov16.pdf https://benrbray.com/static/notes/minimax-approx_nov16.pdf
- Jtsummers 6y agoYour examples are, more or less, how I was taught to construct proofs. It's just much clearer and easier to read/follow than the prose-style in that Wikipedia page. And you can always supplement one with the other, just like the code example. Technically unnecessary since there was a prose description of the algorithm, but from a readability/understandability perspective it's immensely useful.