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 Master of Arts degree, requirements are: 30 units of approved graduate credit, including up to 6 units of thesis credit; 9 to 12 units must be in courses from departments other than Mathematics. At least one year-long course sequence in mathematics which is not co-convened must be included. Master of Arts (Teaching Option): 30 units of approved graduate credit, including up to 6 units of thesis credit; 9 to 12 units should be outside the Department of Mathematics or from the following list of graduate mathematics courses: Math 504, 530, and 596E (Topics in Mathematics for Secondary Teachers - contents will vary, the course may be repeated). At least 12 units of mathematics should not be from that list, and should include a year long course sequence which is not dual-numbered. Each candidate's course of study should be established in consultation with a member of the Mathematics Education Committee.
Students in other PhD programs may earn a PhD minor in Mathematics by completing 12 units of approved graduate course work in mathematics. All the course work must be approved by the Mathematics PhD minor advisor before students begin their course work. To apply for the minor, students must fill out the online form and have it approved before the advisor will approve the Plan of Study form in GradPath, or serve on the Oral Comprehensive Exam committee.
Students must earn a “B” or higher in all coursework, or receive instructor approval that indicates the student's performance in their course merits a PhD minor. If a student does not receive a “B” or higher, and the instructor does not feel the student’s performance merits a PhD minor, the student may appeal the decision. The appeals process is outlined below.
All transfer course work must be approved by the minor advisor, with final approval given by the Director of Graduate Studies. In cases where suitable course work was transferred or where the advisor cannot or will not approve the transfer credit, an examination set by the PhD minor advisor may be substituted. The student may also appeal the decision as outlined below.
Students may also choose two supporting minor subjects, in which case 6 units of approved graduate course work is required for each minor.
Mathematics courses that are required for the student's PhD major or are in the subject area of the student's PhD major may not be used towards the Mathematics PhD minor. (For example, a PhD student in Statistics cannot use math courses that are required for the Statistics PhD or math courses whose content is statistics for the Mathematics PhD minor.)
Some co-convened courses may be suitable as part of the PhD minor, but as a general rule the PhD minor advisor will not approve a plan of study that includes more than 6 units of co-convened courses.
It is highly recommended that students consult with their PhD minor advisor about the suitability of their course work for the minor and for their careers before beginning their coursework.
The PhD minor advisor is currently Professor David Glickenstein.
Appeals Procedure
If a student wishes to appeal any of the requirements mentioned above, the appeal should be made in writing to the Director of Graduate Studies. The appeal will be reviewed by the Graduate Committee and requires a majority vote to succeed. The Committee may place additional requirements/deadlines on the student as a prerequisite for continuing in the program.
Students who wish to appeal the decision of the Graduate Committee must submit an appeal in writing to Head of the Mathematics Department, who will make a decision in consultation with other faculty, as appropriate.
College of Science
University of Arizona - Main - Tucson
Statement of Purpose
Three Letters of Recommendation (letters must be dated and not more than a year old)
Description of past math-related coursework
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
Teaching Assistantships
Domestic Applicants:
International Applicants:
International applicants will not be considered for conditional admission by this program.
4832
ETS Major Field Code(s) for this program: 0703, 0799
30
Minumum credits: 30
Math 910: Thesis (6 units)
Core coursework: See website http://math.arizona.edu/academics/grads/requirements/ms
Language requirements: See website http://math.arizona.edu/academics/grads/requirements/ms
Other requirements:
Students may choose a minimum of 18 units from the following list or from other courses with the approval of the DGS.
Math 511A: Algebra (3 units)
Math 511B: Algebra (3 units)
Math 523A: Real Analysis (3 units)
Math 523B: Real Analysis (3 units)
Math 534A: Topology-Geometry (3 units)
Math 534B: Topology-Geometry (3 units)
Math 500A: Research on the Learning of Mathematics for Teachers (3 units)
Math 501A: Symbolic Logic (3 units)
Math 501B: Symbolic Logic (3 units)
Math 504: History of Mathematics (3 units)
Math 505C: Algebra for Elementary & Middle School Teachers (3-4 units)
Math 505D: Data Analysis and Probability for K-8 Teachers (3-4 units)
Math 505E: Number and Operations for K-8 Teachers (3-4 units)
Math 505F: Geometry and Measurement for K-8 Teachers (3-4 units)
Math 506A: Research on the Learning of Mathematics (3 units)
Math 506B: Research Methods in Math Education (3 units)
Math 506C: Research on the Teaching of Mathematics (3 units)
Math 507C: Problem Solving for Secondary Mathematics Teachers (3 units)
Math 507D: Modern Algebra for Secondary Mathematics Teachers (3 units)
Math 507E: Principles of Calculus for Secondary School Teachers (3 units)
Math 507F: Probability and Statistics for Secondary Math Teachers (3 units)
Math 509C: Statistics for Research (3 units)
Math 513: Linear Algebra (3 units)
Math 514A: Algebraic Number Theory (3 units)
Math 514B: Algebraic Number Theory (3 units)
Math 516: Commutative Algebra (3 units)
Math 517A: Group Theory (3 units)
Math 517B: Group Theory (3 units)
Math 518: Topics in Algebra (3 units), may be repeated)
Math 519: Topics in Number Theory and Combinatorics (3 units), may be repeated)
Math 520A: Complex Analysis (3 units)
Math 520B: Complex Analysis (3 units)
Math 527A: Principles of Analysis (3 units)
Math 527B: Principles of Analysis (3 units)
Math 528A: Banach and Hilbert Spaces (3 units)
Math 528B: Banach and Hilbert Spaces (3 units)
Math 529: Topics in Modern Analysis (3 units), may be repeated)
Math 532: Topological Spaces (3 units)
Math 536A: Algebraic Geometry (3 units)
Math 536B: Algebraic Geometry (3 units)
Math 537A: Global Differential Geometry (3 units)
Math 537B: Global Differential Geometry (3 units)
Math 538: Topics in Geometry and Topology (3 units, may be repeated)
Math 539: Algebraic Coding Theory (3 units)
Math 541: Introduction to Mathematical Physics (3 units)
Math 553A: Partial Differential Equations (3 units)
Math 553B: Partial Differential Equations (3 units)
Math 554: Ordinary Differential Equations (3 units)
Math 556: Applied Partial Differential Equations (3 units)
Math 557A: Dynamical Systems and Chaos (3 units)
Math 557B: Dynamical Systems and Chaos (3 units)
Math 559A: Lie Groups and Lie Algebras (3 units)
Math 559B: Lie Groups and Lie Algebras (3 units)
Math 563: Probability Math (3 units)
Math 564: Theory of Probability (3 units)
Math 565A: Stochastic Processes (3 units)
Math 565B: Stochastic Processes (3 units)
Math 565C: Stochastic Differential Equations (3 units)
Math 566: Theory of Statistics (3 units)
Math 567A: Theoretical Statistics I (3 units)
Math 567B: Theoretical Statistics II (3 units)
Math 568: Applied Stochastic Processes (3 units)
Math 571A: Advanced Statistical Regression Analysis (3 units)
Math 571B: Design of Experiments (3 units)
Math 573: Theory of Computation (3 units)
Math 574E: Environmental Statistics (3 units)
Math 574G: Introduction to Geostatistics (3 units)
Math 574M: Statistical Machine Learning (3 units)
Math 574T: Time Series Analysis (3 units)
Math 575A: Numerical Analysis (3 units)
Math 575B: Numerical Analysis (3 units)
Math 576A: Numerical Analysis PDE (3 units)
Math 576B: Numerical Analysis PDE (3 units)
Math 577: Topics in Applied Mathematics (3 units, may be repeated)
Math 580: Mathematical Models in Biology (3 units)
Math 582: Applied Complex Analysis (3 units)
Math 583A: Principles and Methods of Applied Mathematics (3 units)
Math 583B: Principles and Methods of Applied Mathematics (3 units)
Math 585: Mathematical Modeling (3 units)
Math 586: Case Studies in Applied Mathematics (3 units)
Math 587: Perturbation Methods in Applied Mathematics (3 units)
Math 588: Topics in Mathematical Physics (3 units, may be repeated)
Math 593: Internship 1-6 units
Math 595A: Math Instruction (3 units)
Math 595C: Research in Applied Mathematics (3 units)
Math 595D: Research in Mathematics Education (3 units)
Math 596A: Topics in Mathematics (3 units)
Math 596B: Mathematics Mentoring Methods (3 units)
Math 596C: Mathematics Instruction for English Language Learners (3 units)
Math 596F: Topics in Math for Elementary and Middle School Teachers (3 units)
Math 599: Independent Study (1-6 units, may be repeated)
Math 636: Information Theory (3 units)
Math 697B: Applied Mathematics Laboratory (3 units)
Math 699: Independent Study (3 units)
Math 900: Research (2-6 units, may be repeated)
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. These two sequences must be in two of the three general areas: algebra and number theory, analysis and geometry, mathematical physics and applied mathematics.
The 30 units must also include 6 units in courses from departments other than Mathematics. As with the PhD degree, the requirement of 6 units from outside the Mathematics Department may also be satisfied with an internship. See the Priori Acceptable list for approved courses. Students may take a course outside of this list with the advanace approval of the DGS.
MS students must complete one professional development requirement chosen from this list:
All students in the Mathematics MS program are required to have a Graduate Faculty Advisor (also called Major Professor)
Please refer to the Graduate Student Handbook for students who are pursuing this program of study.