When you start thinking about a graduate program, do talk to your advisor and others in the department. However, you can also do some investigating on your own. Here are some ways to get started.
Information Sources On The Web
The American Mathematical Society website has an impressive collection of resources: http://www.ams.org/programs/students/undergrad/undergrad
The Society for Industrial and Applied Mathematics website also provides a lot: http://www.siam.org/students/resources/
The American Statistical Association has an Education section on its website. Click on the "Graduate" tab on the left: http://www.amstat.org/education/index.cfm
The Institute for Operations Research and the Management Sciences website can be useful because it covers a broad range of math-related careers that undergraduates may not be familiar with: http://www.informs.org/Build-Your-Career/INFORMS-Student-Union
National Fellowships
There are several national fellowships that can be applied for over the web, although these are highly competitive and available only to U.S. citizens.
The National Science Foundation Graduate Research Fellowships: http://www.nsfgrfp.org
The National Defense Science & Engineering Graduate Fellowships (funded by the Department of Defense): http://ndseg.asee.org
The National Physical Science Consortium Graduate Fellowships in Science and Engineering (funded by the national labs and the NSA): http://www.npsc.org
The Society Of Industrial and Applied Mathematics has information about fellowships. Scroll down to "For Graduate Students": http://www.siam.org/students/resources/fellowship.php
This site has a wealth of information based on data collected by the National Research Council. While survey data is not the most reliable sort of data and fine distinctions between programs are particularly unreliable, this is a helpful place to start your search. Once you narrow your choices, web sites for individual departments and programs can help as well: http://www.graduate-school.phds.org/rankings
Information Sources Not On The Web
Another useful source of information about individual programs is the yearly article ''Doctoral Degrees Conferred'' in the August issue of the Notices of the American Mathematical Society, which is available in the Science Library. For example, if you plan to work on a doctorate and one of your initial choices is not producing many Ph.D.s or not producing them in areas that interest you, this might be valuable to know.
A visit to one or more of your top choices can be very helpful. Talk to students there and visit the graduate advisor. A Grinnell student who went to that program could be a valuable resource; if you do not know any, department faculty and the Career Development Office may be able to help.
Financial Aid
Graduate students in the sciences can generally count on substantial financial aid. Although the national fellowships mentioned above are hard to get, you should inquire about a fellowship or teaching assistantship at all the schools to which you apply. Research assistantships often become available to students who do well in their initial years.
