To be admitted, applicants should normally have completed the equivalent of an undergraduate major in mathematics with at least fifteen units of upper-division or higher level work, including one semester each of advanced analysis at the level of MATH 425A, abstract algebra at the level of MATH 415A, and linear algebra at the level of MATH 413. Ph.D. applicants should also have completed a semester of complex variables at the level of MATH 424. All applicants are required to submit GRE scores*, including the Subject Examination in Mathematics.
To be considered for admission, international applicants whose native language is not English must submit their scores from either the TOEFL (Test of English as a Foreign Language) or IELTS (International English Language Testing System) exams. For the TOEFL exam the minimum score to be considered for admission is 550 for the paper based (PB) TOEFL or 79 for the internet based (iBT) TOEFL. For the IELTS exam the minimum score to be considered for admission is a composite score of 7 with no subject area below a 6.
To be considered for financial support, international applicants whose native language is not English must submit scores from either the iBT TOEFL exam or the IELTS exam. (Applicants cannot be considered for financial support on the basis of the paper based TOEFL exam since it does not test speaking ability.) In addition to the requirements above, international students must have a minimum score of 24 on the speaking section of the iBT TOEFL or a minimum score of 7.5 on the speaking component of the IELTS. In addition to these minimum scores, phone or Skype interviews of applicants are usually required as well as further evaluation of the applicants English once he or she has arrived on campus.
*For the 2021-2022 application year, scores on the subject test of the GRE are optional for applicants, and not required. Applicants are strongly encouraged to take the general GRE exams. The decision to take or not take these exams will not factor into admission decision, but applicants are welcome to include them if they believe they add to their application. Grades and test scores are only two factors taken into consideration in the review for admission; letters of recommendation and statement of purpose are particularly important. Prior research experience is also valuable, but not required and it is understood that these may have been difficult in the last year. Be sure to describe any unusual circumstances in the statement of purpose.