Justin DeVries
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 Sep 8 awarded Notable Question Oct 11 awarded Yearling Oct 12 awarded Yearling Mar 3 awarded Nice Answer Nov 18 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 $Hom(M,-)$. Nov 13 awarded Critic Oct 24 awarded Popular Question Oct 19 awarded Good Question Oct 12 awarded Yearling Aug 12 answered A chain homotopy that does not arise from a homotopy of spaces? May 30 awarded Nice Answer Mar 9 awarded Fanatic Dec 31 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. Dec 7 awarded Civic Duty Nov 24 answered How to think about CM rings? Nov 23 awarded Nice Question Nov 19 awarded Enthusiast Nov 13 comment Theorems for nothing (and the proofs for free) That's quite surprising! What are some good references for this? Nov 6 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