- 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
- 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.