The application process...
is entirely electronic through the UA Graduate College.
Applications open in late October.
Application Deadline: January 10, 2027
*NOTE* Applications can be accepted after the deadline. Please contact the graduate office to inquire after the deadline.
Admission Requirements
To be admitted, applicants are expected to have completed the equivalent of an undergraduate major in Mathematics, with a minimum of one semester each 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. A full year of Abstract Algebra, Real Analysis, and a semester of point set topology are preferred, and graduate coursework is valued.
PhD applicants should also have completed a semester of complex variables at the level of MATH 424. GRE scores are not required, but applicants are welcome to include them if they believe they add to their application.
International Students
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. There are additional requirements for students who are Teaching Assistants. The Graduate College does not accept Duolingo scores for demonstration of English Proficiency.
Students who wish to receive a Teaching Assistantship as part of their financial support and have graduated from domestic institutions must also demonstrate English proficiency as per Graduate College requirements. Attendance at an English-speaking institution does not qualify a student to be a Teaching Assistant.
The English proficiency requirement can be fulfilled the following ways:
Official Test Scores
Tests that satisfy the requirement are listed below, along with their minimum passing scores. A passing score from any one of these tests will satisfy this requirement.
- TOEFL IBT Speaking Section:
- For tests taken prior to January 21, 2026: minimum speaking score of 24
- For tests taken on or after January 21, 2026: minimum speaking score of 5 on the TOEFL 1-6 scale
- TOEFL PBT: those who took the revised test after 2017 will be asked to take CEPT-OPI
- TOEFL Essentials Test Speaking Section: score of 11
- IELTS Speaking Section: score of 7.5
- CEPT-OPI: score of 44
- CEPT Full Academic Communication Skills Section: score of 44
- PTE Academic – Speaking skill: score of 80
- Completion of ESPE
Please note that the TSE/Speak and TBEST exams are no longer administered but will be accepted as long as the minimum passing score was met (TSE/Speak – score of 50 or TBEST – score of 6.8) and the student has not been out of the country for more than one year since taking the test.
The Graduate College does not accept Duolingo scores for demonstration of English Proficiency.
International students are encouraged to complete a free online survey, after which applicants that are well matched for success in our program will receive an application fee waiver.
Application Procedure
On the graduate online application, you will be required to submit online the following items. Prior research experience is also valuable, but not required.
You should arrange for at least three letters of recommendation. The letters must be dated and may not be more than a year old.
Your statement of purpose should describe your interests in mathematics generally, and in The University of Arizona in particular. If you have done a research project of some kind, you should include some description of it in your statement.
Both domestic and international applicants must submit transcripts from all previous colleges and universities attended. Unofficial transcripts are accepted for the initial application. Official transcripts will be required upon admittance and the applicant will be notified by the Graduate College.
This list should include all your mathematics coursework at the junior level or higher. For each course please include the course number as it appears on your transcript, the topics covered and the textbook used. If the course is a graduate course, you should indicate this.
International applicants whose native language is not English must also submit their scores from either the TOEFL (Test of English as a Foreign Language) or IELTS (International English Language Testing System) exams. The minimum requirements for the scores can be found under the "International Students" section of this page. The test date must be within two years of the intended term of enrollment to be considered valid. You will be required to either upload a copy of your TOEFL (or IELTS) score report during the online application process or arrange to have ETS (Educational Testing Service) send your scores to us electronically. (School code: 4832; Department code: 0703) The Graduate College does not accept Duolingo scores for demonstration of English Proficiency.
You may take both the GRE and the GRE Subject Test in Mathematics, however they are not required. If you have chosen to take the exam you may either upload a copy of your GRE score report during the online application process or arrange to have ETS (Educational Testing Service) send your scores to us electronically. (School code: 4832; Department code: 0703)
The University of Arizona College of Science in cooperation with the University of Arizona Graduate College is sponsoring fee waivers for this program for all domestic students entering Fall 2026. Under “Sponsor/Program Affiliation”, please select “Endorsed Math PhD” for the fee waiver request.
