Sources for Graduate Funding
Whether you hope to be a research mathematician, a teacher, or something in between, applying for funding is an important part of professional life. Whatever kind of school they're at, college professors use funding to go to conferences, buy computers, get research or teaching assistants, get course releases so they can (fill in the blank: do research, design a new course, etc.). Plus, of course, funding gives you status, power, and cold hard cash.
There is one definite, tried-and-true strategy for getting grants: apply. Apply for as many as you can stomach. As a good rule of thumb, try to apply for at least one grant each year. If the grant gives you feedback, use that feedback in your next round of applications. If not, don't take failures personally--just try again. Remember that nothing succeeds like success: getting one grant makes it easier to get your next one, so keep at it.
I have attempted to collect as many sources of graduate funding as I could. This list is not exhaustive; please let me know if you learn of any other sources. (I found most of the items on this list from the list at the Division of Sponsored Programs here at the University of Iowa.) Also, I will update links very very infrequently; please let me know if you find any that are out of date.
I classified these funding sources in the way that made sense to me. However, it may not be perfect. I encourage you to skim all of them in case you find a grant that might meet your needs in a place you hadn't anticipated. (If you do, please let me know so that the next person has an easier time finding it.)
Finally, let me know what sources of funding you receive!