A niche for CRing?

December 14, 2010

Since this project is pretty new, it’s probably worth spending a little time determining its niche. One thing is clear: it’s an undergraduate-level, open-source, collaborative textbook on commutative algebra. But there are a lot of textbooks out there on commutative algebra, even if none (that I’m aware of; please correct me if I’m wrong) are open source.  So we need a raison d’etre to explain exactly why hammering away on this is worth our time, and to determine what we can say in a sales pitch when asking for contributions.

One way we could set a niche is by being really categorical. This is kind of the current approach: the initial chapter (as I write) is on category theory, while the second is on homological algebra. In this sense, the CRing project attempts a broader mission: to educate about general algebra (including abstract nonsense) instead of either simply assuming familiarity with Tor, Ext, and exact sequences and plunging ahead or by sketching details without proofs. As an undergraduate textbook, this level of self-containment is probably a good idea. On the other hand, being really categorical in a proper sense will avoid the “cop-out” of sketching proofs: since this is a collaborative project, we can do a lot.

That’s another sense in which we have a niche. Since there are already several people collaborating (and we hope more will join), editing can proceed at a much faster pace than it could if only one person were working. The use of the git server has made it extremely efficient to keep track of versions and to allow us to work on it simultaneously. As a result, we should probably aim for significant length.

But these are just a few initial, rambling thoughts. Does anyone want to offer any better ideas?


3 Responses to “A niche for CRing?”

  1. Qiaochu Yuan Says:

    How about a lot of examples?

  2. Adeel Says:

    I agree, and was actually thinking the same thing: a ridiculous number of examples. As in, literally put in any example you think of.

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