The Ph.D. Program in the Department of Mathematics enjoys an excellent reputation in a diversified set of subjects:

algebraic geometry commutative algebra differential geometry geometric topology group and representation theory number theory

materials and fluids mathematical biology mathematical finance numerical analysis partial differential equations probability and statistics

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 7800-7970 (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:

• 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 first-year graduate level. Entering students are recommended to take the 6000-level 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 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

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For instructions on filling in the Graduate Mathematics Application Form:

apply here

 

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 6000-level sequence consisting of two one-semester courses
• Four additional one-semester courses at the 5000- or 6000-level

FOR THE MASTER'S DEGREE IN APPLIED MATHEMATICS:

• MATH 5210 - Introduction to Real Analysis 4 Credit(s) and
• one 6000-level course

  OR

• two 6000-level 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 6000-level 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 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:

Apply here

 

 

The Master of Statistics (M-Stat) 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.

 

• 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

 

• 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:

apply here