General Tips:

  • Turn it in on time (give those professors plenty of time - and reminders - to write those letters). Take the requisite tests.
  • They like to see advanced courses and language proficiency (reading level).
  • Always apply for financial aid.
  • List every little award and honor.
  • Spend some time and thought on the essay.
  • Take advanced courses

The Essay:

  • Be as specific as   possible about your goals and how THIS graduate program will help you achieve them.
  • Find out as much as you can about the school, the faculty, their research. Is there one particular person or area that catches your fancy?
  • Tailor each application to the specific school and program.
  • Talk yourself up - this isn’t the time to be shy! Did you do a research project or clinic that inspired you? Did you have a good teaching/mentoring experience?
  • If there is anything on the “lists” included in the rest of the application you’d like to explain, you should do it here: job experience, strange classes, anomalous grades, other activities not mentioned.

Inform your letter writers, too: if possible, give them a copy of everything - grades, awards, essay, the works.

While you're here:

Learn as much as you can about the different possibilities in the mathematical sciences. Read journals, books, talk to profs, go to colloquia.