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seen Sep 15 at 3:35

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comment How to introduce notions of flat, projective and free modules?
@Pete: In my mind, the exactness of the tensor product is relatively easy to motivate through change of rings. Say you've got your sequence over $R$ and you've got an ideal $I$. Is it still exact when we think of everything as $R/I$ modules? Well, that's what the exactness of the tensor product will tell you. Of course this becomes very useful once you have localization and completions to play with. For $Hom$, it seems easiest to motivate $Hom(-,R)$ by analogy with vector space duals, and you can build up from there to $Hom(-,M)$ and $Hom(M,-)$.
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answered A chain homotopy that does not arise from a homotopy of spaces?
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comment effective teaching
There is a recent book from the MAA titled "The Moore method : a pathway to learner-centered instruction" that describes five teachers' variations on the Moore method. It may be helpful to look through it for ideas.
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24
answered How to think about CM rings?
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Nov
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comment Theorems for nothing (and the proofs for free)
That's quite surprising! What are some good references for this?
Nov
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comment What representative examples of modules should I keep in mind?
@Dinakar: the top part of the picture is a module M. The labels M_P and M_Q denote the localizations at primes. The bottom part of the picture is the ring R, with primes P and Q labeled. The curves drawn in R represent the support of M. Presumably the thicker lines are indicating embedded primes (non-minimal associated primes), and eta is a generic point (non-maximal prime).
Nov
3
answered Memorizing theorems