If you want to know more about courses, career options, and life in general for the graduate student in Mathematics, ask your adviser and/or the graduate students themselves. They can tell you about courses you might want to take right now, which entrance exams to take, how to approach graduate schools (whether OSU or others), and what life is like as a graduate student. You might also ask to see a copy of the annual ``Assistantships and Graduate Fellowships in the Mathematical Sciences'' book, produced by the American Mathematical Society.
The Math Department offers two Master of Science (M.S.) degrees, in Mathematics and in Applied Mathematics. You may find that a Master's is sufficient for your career goals, or you may want to try and see if a doctorate should be the next step. (See Section 5.2 for more information on graduate studies in Math.) The department sponsors two doctoral programs, the Ph.D. in Mathematics, and the Ed.D. in Educational Administration and Higher Education with emphasis in mathematics. Again, talking to faculty and graduate students will give you a sense of what is best for you.