Doctor of Philosophy in Mathematics (PhD)
Requirements Outline
The PhD degree is a research degree and the principal requirement is that a student writes an original research thesis (also referred to as their doctoral dissertation). The thesis is produced using research conducted under the supervision of a faculty member, and it is examined by a committee of three departmental faculty and an outside expert.
To qualify to write a thesis, a PhD candidate in Mathematics must first satisfy our Candidacy Requirements. After this, they must choose an advisor from the Mathematics Department faculty. The candidate's thesis is developed and written with the guidance of this advisor, who will later chair the thesis defense committee.
Although doctoral research does not officially begin until after candidacy requirements are met, it is strongly recommended that PhD students discuss possible research opportunities with faculty members soon after they enter the program. Entering students should also outline an appropriate sequence of courses to learn the essential material for pursuing their research interests, in whatever subfield of mathematics they intend to work in.
Our program is designed so that most students should be able to complete it in at most 4 years. The department does not support graduate students as Teaching Assistants for more than five academic years.
PhD Degree Requirements
The requirements that must be satisfied for a student to receive a PhD include:
 The student must satisfy the Candidacy Requirements before the end of their second year in the program.
 The candidate must complete 54 hours of coursework (some of which may be graded on an S/U basis), and they most obtain a grade of B or better in at least 24 semester credit hours of courses in the Mathematics PhD program. Students should take doctoral research classes MATH 8x98 (where “x” is the number of credit hours) while conducting thesis research. Students must register for the course MATH 8x99 “Doctoral Dissertation” in the semester when they intend to graduate.
 Starting from their 3rd year in the program, the candidate must complete an Annual Performance Review (APR) each year. The APR evaluates research progress of the candidate. The APR is conducted in oral or written form by a committee consisting of at least two faculty members of the Mathematics Department. The APR committee is chaired by the candidate’s advisor. After the APR the advisor must complete the APR Report form and email it to the Director of Graduate Studies. Candidates failing the APR are subject to termination from the PhD program.
 The candidate must be in residence, and take 9 semester credit hours of courses, in two consecutive long semesters, Fall followed by Spring. Alternatively, the candidate must be in residence and take a full load in consecutive Spring, Summer, and Fall terms.
 The candidate must write a doctoral dissertation with the guidance of an advisor who is a regular faculty member of the Mathematics Department.
 The candidate must defend their dissertation in a public examination by a thesis committee consisting of at least 4 members, three of whom are faculty members in the Mathematics Department and at least one of whom is outside of the UH Mathematics Department.
 A copy of the dissertation, approved by all the members of the thesis committee is transmitted to, and approved by, the office of the Dean of the College of Natural Science and Mathematics.
Candidacy Requirements
Note: Students admitted to our PhD program before Fall 2024 are subject to our old candidacy requirements, which can be found here.
To qualify for PhD candidacy, before the end of their 2nd year in the PhD program, students must complete at least 2 of the following two semester course sequences, with grades of B or higher, and pass the corresponding preliminary examinations:
 Math 6320, 6321 Functions of a Real Variable
 Math 6370, 6371 Numerical Analysis
 Math 6382, 6383 Probability and Statistics
 Math 6302, 6303 Modern Algebra
The maximum total number of attempts at prelim exams is 4.
Preliminary examinations are threehour written examinations. The questions in the examination emphasize problem solving skills and mathematical ability as opposed to memorization. Preliminary examinations are usually offered twice a year: at the end of the Fall and Spring semesters.
Review information for the preliminary written examinations:
Functions of a Real Variable


Numerical Analysis


Probability and Statistics

Syllabus  Sample problems  
Modern Algebra

Syllabus

Sample problems

Teaching Opportunities for Ph.D. Students
Since teaching is extremely important for PhD students, the department has a program to enhance students' teaching skills. PhD students, prior to finishing the PhD degree, may be allowed to teach regular courses. In this case, some senior professors will be mentors/advisors to help assist students with this task. If any student is interested in this program, the student should make request to the Director of Graduate Studies by the end of the fall semester about one and half year before graduation.
As a condition, a student should have experiences of teaching Calculus recitation class with reasonable teaching evaluation. For an international student, by Texas law, the student must pass the English SPEAK test or its equivalence.
All PhD applicants who submit their complete application before the appropriate deadline are automatically considered for Teaching Assistantship. Please contact the Director for Instructional Support and Coordination for more information about course selection requests.