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Yesterday I attended a seminar talk titled "Cluster presentation of reflection groups", and before it I tried to ask Google what is a "cluster presentation" --- but all one can find on this request is about databases or social studies.

Another example: try to find something on "geometrical groups" and not "geometric group theory".

I think this is a very common problem, when you are interested in some area you don't know anything about and trying to find some texts on it --- but it's very hard if you don't know what exactly to look for. Of course if you have someone to ask, it's not a problem anymore, but usually you don't.

So the question is: how to start learning an advanced topic if you don't have any texts or guidelines about it (and have nobody to ask except for MO community)?

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    $\begingroup$ In the old days, before the internet, I used to wander through the math library glancing at random math books that seemed interesting. This gave me a sense of where everything was. I would also browse through newly arrived journals and sometimes even bound volumes of old ones. This gave me a sense of what was out there and what things were called. Then if I wanted to learn something specific, I had some sense of which part of the library to look in and I would just look through the books or journals I suspected were relevant. And do this while you're young. You won't have the time later. $\endgroup$ – Deane Yang Oct 22 '11 at 14:25
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    $\begingroup$ In the case of a seminar you can try to look up some articles by the speaker and see if you can find any useful references. $\endgroup$ – Pieter Naaijkens Oct 22 '11 at 14:25
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    $\begingroup$ Why would you be interested in "Cluster presentations of reflection groups" if you don't know what the words mean? Surely whereever you are, there must be some talks of which you can understand the title, at least? $\endgroup$ – Igor Rivin Oct 22 '11 at 14:37
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    $\begingroup$ @Deane Yang - well, the library in SPbSU (Russia) doesn't allow to "wander through" --- you can only ask for specific book, but that's all. And it also doesn't have any new books and journals. $\endgroup$ – Andrei Smolensky Oct 22 '11 at 14:41
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    $\begingroup$ Andrei, that's quite disappointing to learn. I find random luck to be a great way to stumble onto new things I like and want to learn about. Anyway, posting a question on math.stackexchange.com or MO seems like a reasonable thing to do when you have some vague idea of something you want to learn more about. $\endgroup$ – Deane Yang Oct 22 '11 at 14:58
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This is just about your first frustrating seminar talk. You might borrow a book by James Humphreys, Reflection Groups and Coxeter Groups. I borrowed this because of this course announcement: http://www.ma.utexas.edu/users/allcock/teaching/Coxeter_groups/Coxeter.html and first homework http://www.ma.utexas.edu/users/allcock/teaching/Coxeter_groups/index.html by Daniel Allcock of U. T. Austin.

I got plenty of stuff on Google with: presentation "reflection groups" so it is the word "cluster" that is a bit too specific.

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How basic is basic? An ideal presentation announcement will mention the intended audience, as well as what prerequisites will be assumed and not covered. A bibliography also will give a few clues.

If the subject has old enough roots or foundations, one can turn to certain compilations for motivation and partial explanations that are pitched to a more general audience which possesses graduate level experience. I personally like Encylopedic Dictionary of Mathematics from MIT press; others like A Princeton Companion To Mathematics; hopefully this thread will produce a few more titles.

Gerhard "Ask Me About System Design" Paseman, 2011.10.22

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