Strategies for digging through literature

Question

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.

Answer 1

In addition to google, google scholar, and google books, I sometimes find the following to be useful:

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)

Answer 2

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".

Answer 3

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.

Answer 4

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.

What goes for Google goes for Google Scholar, Math Reviews, etc.

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

Answer 5

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

Answer 6

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".

You may already know this information, but for those who do not, it may help you narrow your searches down.