David Madore's WebLog: Math on the Web

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(Friday) · Last Quarter

Math on the Web

One thing which regularly annoys me is how difficult it is to find mathematics on the Web at the level I'm interested in. One can easily find a lot of undergraduate-level stuff, and a lot of research papers, but there seems to be a gap between the two at which there is little available material online. For example, just now, I wanted the precise definition of a Gorenstein ring (or a Gorenstein singularity, or whatever: it's the word Gorenstein which interests me, in any context). Now there are tons of research papers which deal with resolution of Gorenstein singularities or classifications of them, or whatever: but they never bother to recall what a Gorenstein singularity is, because everyone is supposed to know that (in order to make any sense of the paper or to have any interest in it). And on the other hand, this is way too advanced for most online courses: what I would need is a general treatise on Cohen-Macaulay rings (such as this book by Bruns and Herzog, of which I have a copy at my parents' house but none where I am now).

Of course, there is MathWorld, which is often useful (especially when it comes to formulæ of kinds): here it gives a definition of a Gorenstein ring (I won't link to it because I don't wish to Google-feed it), but I can't make heads or tails of it — I'm sure they omitted something. And this isn't just bad luck in this particular case: it's really quite typical of their definitions in relatively high-brow domains. When there is an entry in the Wikipedia, it's usually more useful, but, unfortunately, the word Gorenstein doesn't appear in the Wikipedia (I guess I'll have to write the entry when I find out precisely). In general, the Wikipedia isn't very good when it comes to mathematics because there isn't a convenient way to typeset mathematical formulæ in it.

(That's what research libraries are for, you say? Yes, but it is presently 4AM, and all research libraries I have access to are closed. And how can I go to sleep without knowing the correct definition of a Gorenstein ring? Now you understand my dilemma!)

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