Graduate Programs
Welcome to the webpage for the graduate program of the Department of Mathematics at the University of Utah. We offer a Ph.D. and Master's degrees in many different areas of mathematics. The faculty at the University of Utah are active and involved with the students and have many diverse research projects. Our former graduate students have gone on to mathematical careers both in academia and in industry. We invite you to explore our graduate program information, our math department, university, and living in Utah.
See the links below for more information about our programs.
DEGREE OPTIONS
Click on program title to expand.
Ph.D. Program in Mathematics
The Ph.D. Program in the Department of Mathematics enjoys an excellent reputation in a diversified set of subjects:


Degree requirements/COURSEWORK
The course requirements for the Ph.D. degree consist of at least seven sequences (each sequence contains two consecutive courses on a subject) numbered 6000 or above, or their equivalent, approved by the student’s supervisory committee. Exceptions must be approved on an individual basis by the Graduate Committee upon the recommendation by the student’s supervisory committee.
The following is a list of departmental requirements, in addition to the requirements of the Graduate School, for candidates seeking a Ph.D. degree in mathematics.
 At least 42 credit hours numbered 6000 or above
 At least 14 credit hours of the 42 credit hours should be courses numbered 78007970 (topics courses, seminars, and thesis research).
 Six written qualifying examinations
 An oral qualifying examination
 Two semesters of teaching
 The final oral examination
More details can be found in the Graduate Bulletin.
WRITTEN QUALIFYING EXAMINATIONS
The written qualifying examinations are given twice a year, in January and August, just before the start of the Spring and Fall semesters. A Ph.D. candidate is required to pass six written qualifying examinations chosen from the following set of subjects (corresponding course numbers are included in parenthesis):
 6010 Linear Models
 6040 Mathematical Probability I
 6070 Mathematical Statistics
 6210 Real Analysis
 6220 Complex Analysis
 6310 Algebra I
 6320 Algebra II
 6410 Ordinary Differential Equations
 6420 Partial Differential Equations
 6510 Differentiable Manifolds
 6520 Algebraic Topology
 6610 Analysis of Numerical Methods I
 6620 Analysis of Numerical Methods II
 6710 Applied Linear Operators and Spectral Methods
 6720 Applied Complex Variables and Asymptotic Methods
Each exam lasts two hours and is written at a firstyear graduate level. Entering
students are recommended to take the 6000level course corresponding to a particular
exam and use the course materials to prepare for the exams. Students with particularly
strong backgrounds can choose to take the exams without taking the courses. Copies
of past exams from the last ten years can be obtained by contacting the Graduate Coordinator.
ORAL QUALIFYING EXAMINATION
This exam is conducted by the student’s supervisory committee and it can take one of the following two formats: a general exam to measure the student’s overall mathematical maturity and breadth, or a presentation of the proposed dissertation project. The exam also evaluates the student’s skill at chalkboard exposition and verbal exchange.
TEACHING REQUIREMENT
Each Ph.D. candidate is required to teach a minimum of two courses or equivalent tutorials, or supervise laboratory sessions.
FINAL ORAL EXAMINATION
This examination consists of a public thesis defense that summarizes the candidate's thesis work.
ADMISSION REQUIREMENTS
Admission to graduate status in the Ph.D. program requires that students hold a Bachelor's degree in Mathematics, or its equivalent, with a grade point average of at least 3.0 and that they show promise of success in graduate work. Qualified applicants typically possess a Bachelor's or Master's degree in mathematics. Students should be prepared to take the courses that directly lead to qualifying exams.
GRE Exams
While GRE general and mathematics subject test scores are not required for graduate
admission application, we understand that some applicants may prefer to have test
scores to be included in the evaluation. In this case you may submit the test scores,
especially the mathematics subject test score if you are interested in pure mathematics
areas, and we will take them into consideration. On the other hand, the omission of
GRE test scores will not adversely impact your application.
English Tests
All applicants must meet the University of Utah's minimum requirements for English
proficiency, click here.
Additionally, successful applicants for Teaching Assistantships must be proficient
in their spoken and listening English skills. Those skills are usually reflected in
the submitted TOEFL scores (or equivalent). In most cases, for those subsections of
the TOEFL, we look for scores of at least about 20, and optimally, of at least about
23.
FILLING OUT THE APPLICATION
For instructions on filling in the Graduate Mathematics Application Form:
Questions?
Fernando Guevara Vasquez, Director of Graduate Studies fguevara@math.utah.edu
Paula Tooman, Graduate Program Coordinator tooman@math.utah.edu
Master of Arts (M.A.) and Master of Science (M.S.) in Mathematics
DEGREE REQUIREMENTS/COURSEWORK
The M.A. and M.S. degree requirements are identical except that the M.A. degree requires an additional language proficiency. The following is a list of departmental requirements for candidates seeking a M.S. or M.A. degree in mathematics.
Minimum Degree Hours: 30
FOR THE MASTER'S DEGREE IN PURE MATHEMATICS:
 MATH 5210  Introduction to Real Analysis 4 Credit(s)
 MATH 5310  Introduction to Modern Algebra I 3 Credit(s)
 MATH 5320  Introduction to Modern Algebra II 3 Credit(s)
 One 6000level sequence consisting of two onesemester courses
 Four additional onesemester courses at the 5000 or 6000level
FOR THE MASTER'S DEGREE IN APPLIED MATHEMATICS:
 MATH 5210  Introduction to Real Analysis 4 Credit(s) and
 one 6000level course
OR
 two 6000level courses
WRITTEN QUALIFYING EXAMINATIONS
The written qualifying examinations are given twice a year, in January and August, just before the spring or the fall semester starts. A candidate can fulfill the graduation requirements by passing four written qualifying examinations, chosen from the following set of subjects (corresponding course numbers included in parentheses):
 6010 Linear Models
 6040 Mathematical Probability I
 6070 Mathematical Statistics
 6210 Real Analysis
 6220 Complex Analysis
 6310 Algebra I
 6320 Algebra II
 6410 Ordinary Differential Equations
 6420 Partial Differential Equations
 6510 Differentiable Manifolds
 6520 Algebraic Topology
 6610 Analysis of Numerical Methods I
 6620 Analysis of Numerical Methods II
 6710 Applied Linear Operators and Spectral Methods
 6720 Applied Complex Variables and Asymptotic Methods
Each exam lasts three hours and is written at a first year graduate level. Entering
students are required to take the 6000level course corresponding to a particular
exam and use the course materials to prepare for the exams. Copies of past exams are
posted (as PDF files) on the Graduate Program homepage (see Qualifying Examinations).
ORAL COMPREHENSIVE EXAMINATION AND ADDITIONAL REQUIREMENTS
An oral comprehensive exam can be chosen as an option to fulfill the Master’s degree requirements. This exam is conducted by the student’s supervisory committee. In case a candidate chooses the option of oral comprehensive exam, the student must complete nine (9) additional credits of a Masters Project, which can be one of the following:
ADMISSION REQUIREMENTS
Admission to graduate status in the Master's program requires that students hold a Bachelor's degree in Mathematics, or its equivalent, with a grade point average of at least 3.0 and that they show promise of success in graduate work. The prerequisites for the various programs vary. Master of Arts / Master of Science degrees, qualified applicants typically possess a Bachelor's or Master's degree in mathematics. Students should be prepared to take the courses that directly lead to qualifying exams.
GRE Exams
While GRE general and mathematics subject test scores are not required for graduate
admission application, we understand that some applicants may prefer to have test
scores to be included in the evaluation. In this case you may submit the test scores,
especially the mathematics subject test score if you are interested in pure mathematics
areas, and we will take them into consideration. On the other hand, the omission of
GRE test scores will not adversely impact your application.
English Tests
All applicants must meet the University of Utah's minimum requirements for English
proficiency, click here.
Additionally, successful applicants for Teaching Assistantships must be proficient
in their spoken and listening English skills. Those skills are usually reflected in
the submitted TOEFL scores (or equivalent). In most cases, for those subsections of
the TOEFL, we look for scores of at least about 20, and optimally, of at least about
23.
FILLING OUT THE APPLICATION
For instructions on filling in the Graduate Mathematics Application Form:
Questions?
Fernando Guevara Vasquez, Director of Graduate Studies fguevara@math.utah.edu
Paula Tooman, Graduate Program Coordinator tooman@math.utah.edu
Master of Statistics (Mathematics)
The Master of Statistics (MStat) program is administered by the University Statistics Committee and applications should be made through the Graduate Admissions Office. Upon admission by the University Statistics Committee, the student is also admitted to the Mathematics Department Master's program. The degree of Master of Statistics (Mathematics) is awarded by the Mathematics Department.
Degree requirements/coursework
 MATH 5010  Introduction to Probability 3 Credit(s)
 MATH 5080  Statistical Inference I 3 Credit(s)
 MATH 5090  Statistical Inference II 3 Credit(s)
 MATH 6010  Linear Models 3 Credit(s)
 MATH 6020  Multilinear Models 3 Credit(s)
 MATH 6070  Mathematical Statistics 3 Credit(s)
 MATH 6960  Special Projects 1  6 Credit(s) (Masters Project)
 Electives approved by the supervisory committee, 12 credits
 Final project approved by supervisory committee
ADMISSION REQUIREMENTS
 Bachelor’s Degree in Mathematics, or equivalent
 MATH 3070, 3080, or equivalent
FILLING OUT THE APPLICATION
For instructions on filling in the Graduate Mathematics Application Form:
Questions?
Thomas Albert, Associate Professor  alberts@math.utah.edu
Paula Tooman, Graduate Program Coordinator tooman@math.utah.edu
MASTER OF SCIENCE (M.S.) IN MATHEMATICS TEACHING
APPLICATIONS FOR 20192021 ARE NOW CLOSED
The Department of Mathematics at the University of Utah offers a general Master of Science degree as well as some specialized master’s degrees. One such degree is the Master of Science (M.S.) in Mathematics Teaching (also known as Mathematics Teaching M.S.), a twoyear program primarily addressed to inservice secondary teachers of mathematics.
The main goal of the Master of Science in Mathematics Teaching program is to extend and enrich secondary teachers' understanding of mathematics and to help teachers acquire a deeper and broader mathematics background.
The program is structured to best meet the needs of Utah’s secondary teachers of mathematics. Coursework is designed to extend teachers’ mathematical knowledge for teaching at the secondary level. Courses are offered at times that fit working educators’ schedules, with a majority of courses offered over the two summer semesters of the program, and other courses offered once a week during evening hours in the fall and spring semesters.
The student is admitted to the Master of Science in Mathematics Teaching program upon admission by the Mathematics Education Committee. The degree is awarded by the Mathematics Department.
Tuitions are significantly reduced to make the program more accessible, and we are pleased to be able to offer this program to practicing Utah teachers for $150 per credit hour.
ADMISSION REQUIREMENTS
1. Licensed teachers with a level 4 endorsement (level 3 teachers will be considered, but may need additional course work).
2. Completion of the Praxis 5161 Mathematics (post2012) or Praxis 0061 (pre2012) Math Content Knowledge Exam. A score of at least 165 (5161) or 143 (0061) is required.
3. At least two years of teaching experience as of the application deadline. Applicants must be recommended by two professional educators who can judge their performance.
4. Satisfy University requirements for Graduate School admissions.
The Mathematics Education Committee may advise candidates to take additional courses to ensure readiness for the required course work in the program.
PLANNED SCHEDULE FOR 2019 COHORT
The Master of Science in Mathematics Teaching program requires a total of 39 credit hours: 30 are core courses, and the remaining 9 credits are to be electives with at least 6 from the disciplinespecific mathematics courses at the 5000 level or above. This meets the requirements for the Master of Science degree set by the Graduate School at the University of Utah. In addition, candidates must take and pass two midprogram exams and submit and defend a final program project. The program for the current cohort is structured as follows:
FIRST ACADEMIC YEAR
SECOND ACADEMIC YEAR
Questions?
Aaron Bertram, Associate Chair / Professor  bertram@utah.edu
Paula Tooman, Graduate Program Coordinator tooman@math.utah.edu
• Master of Statistics
Ph.D. and Master Programs
M.S. Mathematics Teaching