Mathematical Literature and Resources

Note: Most of the resources below are access-restricted. The University of Illinois, like most major universities, has license agreements that provide access to these sites to its users. Access is controlled by IP number. From within the \url{illinois.edu} domain access is automatically granted without any login. To access the resources from outside the domain, start from the Online Reference Collection link at the UIUC Library website, type the name of the resource (e.g., "MathSciNet") in the searchbox, then click on the resoure. This will bring up a login window (log in with your NetID and password), and establish a connection to the resource via the Library's proxy server.

Finding articles

MathSciNet (http://www.ams.org/mathscinet). The premier source for published math articles. Nearly all published math literature since the 1950s is indexed and reviewed in MathSciNet. Many of the more recent entries have links to full text versions of the article.
Zentralblatt (http://www.zentralblatt-math.org/zmath/en). Similar to MathSciNet, but has better coverage of older (early 1900s) literature.
JSTOR (http://www.jstor.org). Complete digitized archives of some fifty math journals, with many going back a hundred years or more.
ArXiv (http://front.math.ucdavis.edu). Preprint archiv.

Finding books and general resources

UIUC Library: Online Reference Collection (http://www.library.uiuc.edu/orr). Links to restricted databases/resources. Most interesting among these is World Cat, the mother of all library catalogs which contains the collections of all major libraries in the world. Type "World Cat" in the search field to access this catalog.
UIUC Library Catalog (http://www.library.uiuc.edu/catalog).
Library of Congress (http://catalog.loc.gov) The mother of all libraries.
Amazon (http://www.amazon.com).

Finding information about a math topic

MathWorld (http://mathworld.wolfram.com). A gigantic mathematical encylopaedia, hosted by Wolfram Research.
Wikipedia (http://www.wikipedia.com). MathWorld and Wikipedia often are the two top hits when googling mathematical topics. Depending on the topic, one or the other might provide better information, so it's worth looking at both.
Google (http://www.google.com)

Cool sites

Online Encyclopaedia of Sequences (http://www.research.att.com/~njas/sequences/). An absolutely amazing tool - it even has a "webcam".
Inverse Symbolic Calculator (http://oldweb.cecm.sfu.ca/projects/ISC/ISCmain.html). Real number lookup. Does for real numbers what the Online Encyclopaedia of Sequences does for the sequences.

General references

Math History Archives (http://www-history.mcs.st-andrews.ac.uk) An enormous resource of historical information and biographies of thousands of mathematicians.
Math Resource collection from Penn State (http://www.math.psu.edu/MathLists). Very extensive collection of Mathematics Department websites from around the world.