The PhD degree is a research degree and is granted only as a consequence of original research presented in the form of a formal dissertation.
No specified course plan nor any particular number of credit hours is given as a partial requirement of the degree. It is the student's responsibility to be informed of the current regulations as set forth in the Graduate Studies Bulletin and the Bulletin of the College of Natural Sciences and Mathematics. This includes a residency requirement of enrollment in 9 semester-credit-hours each in two consecutive long semesters, and a completion of at least 24 semester-credit-hours in the PhD program (Among the 24 hours, at least 12 hours must be regular graduate math course credit hours). Other basic requirements must be met as follows:
- The student is required to pass a preliminary examination. The Preliminary Examination consists of three 3-hours written exams for three topics chosen from three distinct groups. Click here to see more details on the Preliminary Examination.
- The student must complete a minimum of one full year of continuous, fulltime residence after obtaining a Master's degree in mathematics or the equivalent. Currently, registration for nine semester hours' work, each semester for two consecutive semesters implies fulltime residence.
- All supported PhD students who have passed preliminary exam should take at least 2 regular math graduate courses. However, if his/her PhD advisor agrees (to have more time to do research), the student can take only 1 regular math graduate course. In that case, the student has to indicate "the agreement" in the "Any additional information" of the Course Selection Form. Additional form or signature is not required.
- As a primary requirement for the degree, the student must produce, under the guidance of a faculty advisor, original, independent research in mathematics in the form of a formal dissertation. The results should be of a sufficiently scholarly nature to be considered publishable in the mathematical literature.
- The student must defend the dissertation in a final examination before a reading committee which shall consist of at least four members; three of whom, including the faculty advisor, shall be from the Mathematics Department, and one from outside the Mathematics Department. This committee must be approved by the Chairman of the Mathematics Department and the Dean of the College and the names of the committee members must be on file in the Office of the Dean at least one semester prior to graduation. Copies of the dissertation must be in the hands of the committee at least three weeks prior to the scheduled date of the final examination. One copy of the dissertation is to be placed (at departmental expense) in the Mathematics Department office at the time it is distributed to the committee. The dissertation committee will not be assigned until the language and preliminary examinations have been passed.
- The student must complete twelve hours of Doctoral Dissertation (MATH 8399). The University requires that a student who registers for Doctoral Dissertation be enrolled for dissertation courses continuously (Fall and Spring) up to and including the semester in which the dissertation is accepted by the University.
- PLEASE NOTE: The Coordinating Board has put a uniform cap on doctoral hours at Texas institutions. All resident doctoral students admitted (starting Fall 1993 and after) will be transferred to non-resident tuition status as of the semester following the one in which they exceed the 99 doctoral hours limit.
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Since teaching skill is important for PhD students, the department develops a program to improve students' teaching skill.
- For any PhD student before finishing the PhD degree, the department may arrange him/her to teach regular courses. In this case, some senior professors will be mentors to improve the student's teaching skill.
- 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.
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Background and Purpose
The Preliminary Exam is the final step in assessing that the student has the ability and appropriate mathematical background to undertake a program of supervised research and study leading to the Mathematics PhD. Any student taking the Preliminary Examination will already have the equivalent of a Master's degree in mathematics. Students who have completed their MS degree in mathematics at UH may often be ready to take the Preliminary Examination without further course study.
Three-hour written examinations in each of the five core topics will be offered twice a year, after the Spring semester and before the Fall semester.
The questions in the examination will emphasize problem solving skills and mathematical ability as opposed to rote memorization.
Timing
The Preliminary Examinations are offered twice
a year in the week before classes start in August
and
January.
Students who receive support from the Department of Mathematics will be expected to pass the Preliminary Examination according to the rules below. For non-supported students, the University rules apply.
A student graduating from the UH Masters program will have to pass all three core topic examinations before beginning their second year in the PhD program.
An external student who is admitted directly into the UH PhD program must pass two of the three core topic examinations before the beginning of their second year. The third examination must be passed before the beginning of their third year.
Administration of the Exam
A student shall choose three subtopics from three distinct core topics (see below). For each chosen subtopic, the student cannot fail twice. The overall maximum number of attempts is six, summed over all the core topics. This limit of six is in effect even if the student changes their field.
Examination topics
A student must pass three written examinations, chosen from among the five core topics.
Read Syllabus, schedule, and sample examinations to have some idea about preparing for the examinations.
The decision on the exact topics to be examined is the responsibility of each group, working in consultation with the Graduate Studies Committee.
The following is a list of five core topics.
MATH 6302;6303: Modern Algebra
MATH 6342;7350: Topology/Geometry
MATH 6320;6321: Theory of Functions of a Real Variable
MATH 6322;6323: Theory of functions of a Complex Variable
MATH 6324;6325: Differential Equations
MATH 6326;6327: Partial Differential Equations
MATH 6382;6383: Probability Models and Mathematical Statistics
MATH 6366;6367: Optimization and Variational Methods
MATH 6370;6371: Numerical Analysis
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