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Results tagged with mathematics-education
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user 6545
For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/
62
votes
How to memorise (understand) Nakayama's lemma and its corollaries?
It's easiest to understand for local rings, so let $R$ be one with residue field $k$. Nakayama's lemma just says that a finitely generated $R$-module is zero if and only if the induced $k$-vector spa …
- 7,273
6
votes
Are there proofs that you feel you did not "understand" for a long time?
I'd also like to contribute an answer on the fundamental theorem of calculus. The standard proof (to my knowledge, the only proof) of the "first fundamental theorem"
$$\int_a^b F'(x) dx = F(b) - F(a …
6
votes
Are there any books that take a 'theorems as problems' approach?
The little commutative algebra book by Atiyah and MacDonald is one such—the reason it's so little is that probably two-thirds of the results in it are in the exercises. I guess you know the subject i …
2
votes
Making sure that you have comprehended a concept
I think I understand a theorem if I can reconstruct the hypotheses remembering only the conclusion. Likewise, I think I understand a theory if the axioms all seem reasonable and obvious.
However, yo …
2
votes
What are your experiences of handouts in mathematics lectures?
I provide my typed lectures to the students via my website. Looking at a nice, standard linear algebra course, I found that although many people told me they greatly appreciated the notes and used th …