# Strategies for digging through literature

I hope this question is appropriate for MO - I cannot decidedly tell with soft questions. I was wondering what are the strategies people use when searching for literature on a subject. I shall clarify my question with an example. Suppose, for instance, I want to learn more about $\star$-independence or $\star$-spread and assuming I already do not have a reference for it, how do I go about searching for literature on it. If the latter assumption is relaxed (that is I already have a couple of references on the concept), presumably I can keep looking for cross references and that might, in a small number of steps, exhaust all the literature on the subject. However, I find frequently this is not the case. The problem here is two fold:

1) If I am looking at exploring about a mathematical object/theorem which does not have a name and does not involve any objects which have exotic names, for instance, "A finite union of subspaces of a vector space is a proper subset of the space if the ambient field is infinite" (I hope this is not a bad example and even if it is, that it conveys the underlying issue). Google searching any keywords for an example like this only yields tons of irrelevant entries. This is especially true in cases where the mathematical objects involved have other meanings in english (which can be said about almost every other thing in math e.g. ring, field, ideal, module, etc) and even when this is not the case, it could be a ubiquitous word in mathematics (e.g. vector, space, manifold, etc). So if the concept or theorem does not contain a distinguished word, searching about it is difficult.

2) If the object/theorem is exotic or contains an exotic object like $\star$-independence, google and other search engines suppress special characters and the situation defaults to that in (1). Finally, I find it especially hopeless if you are looking to find say, class number computations of $\mathbb{Q}[\sqrt{2},\sqrt{7}]$.

I would like to know if anyone has any thoughts on getting around these problems. If it's a misplaced question, I would be happy to delete it.

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Community wiki perhaps? –  Andrey Rekalo Nov 17 '10 at 22:20
Since this question is essentially collecting a list of resources and techniques, I think it makes sense for it to be community wiki. I'm hitting it with the wiki-hammer now. –  Anton Geraschenko Nov 18 '10 at 1:44

1. sciencedirect.com --- to search through the journals, and thus by analogy several other publishers' websites

2. latexsearch.com --- still in beta, but it takes TeX / LaTeX code as input, so might be useful for addressing the point raised in your Observation 2.

Another very recent, though not relevant for you website might be: sciverse.com (for image / illustration search in published articles)

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@Suvrit. The problem is not lack of websites. The problem is choice of keywords. In the limiting case, say you know nothing about what you want to search for except the statement of the theorem or the name of the mathematical object, searching through google or any other sites usually produces significantly more irrelevant results compared to relevant ones. Moreover the irrelevant usually get displayed first since more people (read non-mathematicians which are more in number than mathematicians) search for them. –  Timothy Wagner Nov 17 '10 at 22:33
@Timothy: which is why i pointed out latexsearch.com, where perhaps entering the TeX code might help; another choice is to of course ask on math.SE and MO themselves as to what keywords to look for! –  Suvrit Nov 17 '10 at 22:35
@Suvrit: My apologies, I missed the second site. This is pretty cool, I was unaware of it. –  Timothy Wagner Nov 17 '10 at 22:38

There is a site, which is absolutely perfect for asking questions like "what is known about this problem" or "can you point me to a good reference on this and that".

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Self-referential questions are particularly welcome. –  Gerry Myerson Nov 18 '10 at 0:50
This answer got me very excited -- you mean there's another site like this? -- until I followed the link. –  Michael Lugo Nov 18 '10 at 1:15
math.stackexchange has enough knowledgeable participants, I think, that given a good clear title, you'll generally get results there. –  Peter LeFanu Lumsdaine Nov 18 '10 at 1:34
Lots of MO people are regularly active on math.stackexchange and I have seen fairly advanced questions there. But also, I find that on MO, if you display evidence that you have put some effort into the search and if your question is not blatantly on the level of undergraduate homework, people will usually be pretty tolerant. –  Alex B. Nov 18 '10 at 1:36
@Gerry: Where can I find a self-referential question on MO? –  Suvrit Nov 18 '10 at 13:41

I use the MSC codes on MathSciNet to narrow down the search to relevant papers.

See http://www.ams.org/mathscinet/msc/msc.html for the PDF file

You have to use with the old codes as well for older papers.

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@SandeepJ: This is also news to me. Extremely useful, thank you. –  Timothy Wagner Nov 17 '10 at 23:26

I can't answer in general, but I will speak to some examples. For the problem on finite unions of subspaces, I typed finite union subspaces vector into Google, and the top of the resulting list was

On the representation of vector spaces as a finite union of subspaces by J Luh - 1972 FINITE UNION OF SUBSPACES. By. J. LUH (Raleigh). It has been proved in [1] that if a vector space V over a field F is a union of n (finite) proper subspaces ... www.springerlink.com/index/GN711127680W310R.pdf

For the ${\bf Q}(\sqrt2,\sqrt7)$ problem, I typed in class number biquadratic and got a number of results that look like they might be helpful. Typing in class number computation biquadratic, the top result was

A Computation of Some Bi-Quadratic Class Numbers by H Cohn - 1958 2 99191. A Computation of Some Bi-Quadratic Class Numbers. By Harvey Cohn. A fascinating chapter in computational number theory began when Lagrange ... www.jstor.org/stable/2002024

which looks like it might be useful, as do some of the other returns.

I admit that the one with the star in it has me stumped.

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@Gerry: Thanks for the comment. I did similar things for the first two examples. Although for 1, I still did not get as many good hits as I had hoped. One of my professor had commented that this can be proved in an essentially different way in every introductory graduate course. So I was curious to see some proofs. This is not by any means a canonical example of the issues I faced thought, it was just the first one that came to my mind. I found a reference on star-independence since it was "related" to star-spread which is "related" to analytic spread, but it was just accidental. –  Timothy Wagner Nov 17 '10 at 23:48
By the way, if you're still interested in seeing proofs, there's a discussion here: mathoverflow.net/questions/26/… –  Gerry Myerson Nov 18 '10 at 0:21
Thanks. I already asked this on SE and someone linked that page. –  Timothy Wagner Nov 18 '10 at 1:34

If you have a basic article to start with, the "citations" box in MathSciNet often does wonders in finding related stuff.

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I use jstor. This requires a membership; however, if you are currently in college or work at a college your university may have a membership for you already. If not, they probably have some similar service available for free or at least at a discounted price. Your library should have this information so check with them or look on their website.

When I am looking for papers I rarely use Google because it could bring up anything. When on a journal database's website, just type in search terms that are similar to the topic you are researching. Sometimes it can be difficult to find resources. When you are at a loss, ask professionals in your department if they know where you might find resources about the topic you are researching.

I hope this helps!

EDIT: Also, if you are not currently using quotation marks in your google search, try that. You are most likely not using the quotes and that is why you are getting the exorbitant number of results. If you type a string of words, Google will return articles that include any of those words. However, if you type a phrase in quotation marks, Google will return articles that include that string of words. Furthermore, you might try the AND command. This will allow for searching for articles that contain multiple strings of words. for instance "Finite Union" AND "Subspaces" AND "Proper Subset".