In parallel to applying to graduate schools, many students also apply to graduate fellowships. These are provided by organizations to fund the graduate study of promising future researchers. Keep in mind that not all of the fellowships are hyper-competitive: for example, about 1000 NSF fellowships are awarded per year. If you win a fellowship, this will give you more freedom to choose graduate schools because funding will become less of a consideration. In addition, your fellowship could exempt you from graduate teaching duties, allowing you to focus more on your classes and research. Applying to fellowships is a bit more involved than applying to grad schools, so getting started over the summer is the best way to get on track. There are several sites that give great overviews of graduate fellowships:
- See http://www.pgbovine.net/fellowship-tips.htm for extensive information and advice about the three most common graduate fellowships.
- See http://grfpessayinsights.missouri.edu/index.php for extensive information about the NSF fellowship.
- See http://djstrouse.com/guide-to-applying-to-us-science-phd-programs-and-fellowships/#more-927 for general advice about applying to grad schools and fellowships.