Later, TA's have more responsiblity. Typically, the TA's prepare their own lectures and assignments, and may write their own tests. Graduate programs in mathematics want students with strong mathematical talent and the personal qualities needed for success in a demanding field - qualities such as commitment, willingness to work, intellectual curiosity. Letters of recommendation, from those who have taught the student advanced mathematics, are very important indicators of probable success. This is because these teachers can compare the applicant with other students who have gone on to graduate study.
Grades are important - especially grades in advanced math courses.
Finally, GRE scores allow some comparison of applicants from different colleges. Visit the school, sit in on some classes, talk to the faculty, and, most important, talk privately to several graduate students. The University of Kentucky offers Master's and Ph. D degrees in both pure and applied mathematics. The program emphasizes frequent informal mathematical contact between students and faculty.