Programs for Undergraduates
Outside of Brown, many summer math programs are what are known as "Research Experiences for Undergraduates" (REUs). These are designed to give you a sense of what real mathematics research is like (though the specific format can vary greatly). Many programs will require one or more recommendation letters, and it is good to give professors some time to write these. The following summer programs give you an opportunity to encourage younger students to pursue their interest in math.  PROMYS, a strong program for high schoolers held at Boston University. The focus is number theory.
 The Ross Mathematics Program, held at Ohio State University. PROMYS is a descendent of the Ross Program.
 HCSSiM, a program for high schoolers held at Hampshire College.
 Center for Talented Youth, a network of summer programs run by Johns Hopkins University.
There are also semester and yearlong math programs for undergraduates. Here are some of the betterknown ones: Applying to Graduate School  A mathematician's survival guide: graduate school and early career development, by Steven Krantz
 Career advice, by Terence Tao
 Fellowships to apply for:
 Some http://www.ams.org/programs/students/undergrad/undergrad#gradschool
 Assistantships and Graduate Fellowships in the Mathematical Sciences, a document compiled by the AMS each year
 Preparing For Grad School, advice from MIT
 Some grad school advice from Harvard.
 How to get a great letter of recommendation, by Matthew Might
 Recommendations, by Ravi Vakil
 Get into grad school for science, engineering, math and computer science, by Matthew Might
 Thoughts on graduate school, by Noah Snyder (an addendum by Ben Webster)
 More advice for prospective graduate students, by Noah Snyder
 A Graduate School Primer (MAA), by Doug Faires
 Advice on picking a Ph.D. program and advisor
 Choosing a graduate school, by Diana Davis
 Tips for Visiting Grad Schools, by Kimball Martin
Miscellaneous 
