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Mathematics (PHD) 
Program Description

The department offers programs leading to the Master of Arts, Master of Science, and Doctor of Philosophy degrees with a major in mathematics. Concentrations are available in pure, applied, or computer mathematics, in mathematics education, or in probability and statistics. As there are no sharp boundaries between these concentrations, students are encouraged to pursue a broad range of mathematical topics. Programs are planned in consultation with faculty advisers.

To be admitted, applicants must have completed the equivalent of an undergraduate major in mathematics with at least 15 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. Applicants are asked to submit scores on the Graduate Record Examination, including the subject Examination in Mathematics.

For the Doctor of Philosophy degree, the requirements are: 36 units of graduate credit in the major and 12 units in a supporting minor, which may be declared in Mathematics, although outside minors are encouraged. Students will normally either take the first year graduate core courses in Algebra (Math 511A-B), Real Analysis (Math 523A-B), and Geometry-Topology (Math 534A-B), or otherwise learn this material by the end of their first year of Ph.D. studies for the Qualifying Examinations. Qualifying examinations are offered twice yearly, in August and in January, shortly before the beginning of Fall and Spring semesters. Students with prior preparation may attempt the examinations upon entrance to the program, or after one semester. Ideally a student will complete the qualifying examinations by the August following entrance to the Ph.D. program. Students who receive a failing grade twice on any one of the examinations will not be continued in the Ph.D. program. Students who do not complete the three examinations within five semesters and with a cumulative passing grade will not be continued in the Ph.D. program unless the Graduate Committee, upon review of the case, finds extenuating reasons to justify such continuation. Two year-long Mathematics course sequences that are not co-convened and are not part of the required core of algebra, real analysis, and geometry-topology are required. These two sequences must be in two of the three general areas: algebra and number theory, analysis and geometry, mathematical physics and applied mathematics. For most students one of the sequences will be Complex Analysis (Math 520A-B). At least six approved units outside of Mathematics are also required. There is a language requirement which can be satisfied in any two of the following: French, German, Russian, or computer programming. The principal component of the program is the completion of a dissertation involving original creative research.

Ph.D. candidates with other majors who wish to minor in Mathematics are required to take four approved graduate level courses in mathematics and a written examination which covers the content of those courses.

Department/Academic Unit(s)

Mathematics -

The faculty of the Department of Mathematics carries on research (and research seminars) in a variety of purely mathematical and interdisciplinary fields. In algebra and number theory, research includes group theory, rings and modules, algebraic number theory, representation theory, and primality testing. Research in analysis is being carried out on unbounded operators, quantum field theory, integrable systems, dynamical systems, and nonlinear problems of ecology, chemistry, and fluid dynamics. In geometry, there is work on algebraic geometry, moduli spaces, symplectic geometry, and Lie theory. In probability and statistics, projects involve reliability theory, stochastic processes, statistical inference, and nonparametric inference.

College of Science  
Campus where offered
Main Campus - Tucson  
Admissions Contact
Sylvia M Anderson
Graduate Program Coordinator
Sylvia M Anderson
Director of Graduate Studies
David A Glickenstein
Graduate College Degree Counselor
Cindy T Nguyen
Tuition and Fees
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Please refer to the UA Registrar's's Office Special Course Fees for up-to-date information about special course fees. 

Admissions Information

Admissions Requirements

Statement of Purpose
Three Letters of Recommendation (letters must be dated and not more than a year old)
Description of past math-related coursework

Standardized Tests

Required test(s): GRE
Required GRE Subject tests: Mathematics
Recommended tests:
Recommended GRE Subject tests:
Minimum GRE Verbal:
Minimum GRE Quantitative:
Minumum GRE Written:
Minimum GMAT:
Minimum MAT:
Minimum TOEFL: 550
Minimum IELTS: 7

Financial Aid

Teaching Assistantships

Admissions Deadlines

Domestic Applicants:

  • Fall: January 1

International Applicants:

  • Fall: January 1
International Conditional Admission
International applicants will not be considered for conditional admission by this program.
Other Information
The GRE Institution Code for The University of Arizona is 4832
ETS Major Field Code(s) for this program: 0703, 0799
NRC Taxon(a) for this program: Mathematics, Applied Mathematics, Statistics and Probability

Completion Requirements

Degree Requirements

Minumum credits: 36
Core coursework: See website -
Language requirements: See website -
Other requirements:

Minor Requirements

The University requires that PhD students declare a minor. PhD students in mathematics may declare their minor in mathematics or in a supporting discipline. Requirements for the minor are determined by the minor department. Up to 12 units of course work may be in the minor. Students contemplating a minor should consult with the Associate Head for the Graduate Program and their dissertation advisor regarding the suitability of their plans.

Student Handbook  

Program StatisticsInformation about these numbers

Program-level Information
Application Acceptance Rate 49%
Med. Time-to-degree (years) 6.00
Department-level Information
Enrollment Percent Male 75%
Enrollment Percent Female 25%
Enrollment Percent International 22%
Enrollment Percent URM 14%

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Last revised 13 Sep 2017