Graduate Programs

The Mathematics Department offers three graduate programs: Master of Science (MS), Master of Arts (MA), and a doctoral program (PhD).

Students who plan to obtain a doctorate in Mathematics should apply to the PhD program. Once enrolled in the PhD program, students may, but are not required, to earn an MA along the way. Below is a typical PhD schedule.

The MS program is offered for students who want to pursue studies in Mathematics beyond the undergraduate level, but who do not plan to obtain a doctorate in Mathematics.

Typical PhD schedule

• Become English Language Qualified (concerns International Students only).
• Take and pass the Qualifying Examinations.
• During the first few years, students should be taking 3 courses per semester.

• Get a Ph.D. Advisor and form a Ph.D. Committee. Have an Advisory Conference with your Ph.D. Committee.
• Pass the Foreign Language Proficiency Examination (traditional Ph.D. students) or IRB training (RUME students).
• Take and pass the General Examination.

• Thesis Research.
• Write up, defend, and submit thesis.

Program Requirements

Table of Contents

• Entrance Requirements
• Requirements for Graduate Teaching Assistants
• Graduation Requirements for the PhD Program
• Graduation Requirements for the MA Program
• Graduation Requirements for the MS Program
• The Qualifying Examination
• The General Examination
• Advisement, Enrollment and Academic Progress
• The Departmental Teaching Certificate
• Language Qualification
• Reporting Requirements
• Probationary Status

In the rules below,

• M denotes a Math Department rule.
• G denotes a Graduate College rule.
• U denotes a University rule.

Entrance Requirements

Below we outline the entrance requirements for our various degree programs. Students coming from smaller programs might not meet all the entrance requirements and in this instance the department can consider a provisional acceptance when reviewing your application. If you have questions, please contact the Graduate Director.

• G To enter any graduate program, students must have a baccalaureate degree or equivalent from a regionally accredited college or university. See the Graduate College Bulletin for general requirements.
• M To be admitted to the MA or the PhD program, a student must have completed at least two 3-hour senior level courses in abstract algebra, analysis or topology.
• M To be admitted to the MS program, a student must have completed, at a minimum, coursework in the following areas:
  • Differential Equations (MATH 3113 or MATH 3413 or equivalent).
  • Linear Algebra (MATH 3333 or equivalent).
  • Modern Algebra (MATH 4323 or MATH 4383 or equivalent).
  • Introductory Mathematical Analysis (MATH 4433 or equivalent).
  • Introductory Probability/Statistics (MATH 4733 or MATH 4743 or equivalent).
  In the case of a student who has taken some or all of these courses at other universities, the Graduate Committee will determine whether the student's courses are acceptable substitutes for the courses listed above. Students lacking one or more of the above requirements may be admitted on a provisional basis. In this case, they are expected to remedy any deficiencies in their first semester of study. For coursework taken to remedy deficiencies, at most three hours of credit can be applied toward the student's degree program.
• U All applicants for whom English is a second language must present evidence of proficiency in the English language. You need a TOEFL score of at least 79, an IELTS score of at least 6.5, or a PTE score of at least 60. For more details, see here.

Requirements for Graduate Teaching Assistants

• M Before the start of the Fall semester, the Mathematics Department has an orientation for new graduate students. Among other things, students are given information about professional conduct of GTAs and initial training for their role as a TA in the Math Department. Graduate students are expected to be in Norman by August 1 to begin departmental and university orientations.
• U Incoming or returning students who will be Graduate Teaching Assistants at OU for the first time are required to attend the New Graduate Teaching Assistant Orientation offered by the Graduate College. Eligibility for tuition waiver depends on completion of this orientation.
• G General requirements, expectations, and procedures for GTAs are laid out in the Graduate College Bulletin.

Graduation Requirements for the PhD Program

• M Students in the PhD program may choose Research in Undergraduate Mathematics Education (RUME) as a research area; this is known as the RUME Option of the PhD program. All other research areas fall under the Traditional Option of the PhD program.
• In order to graduate with a PhD degree, a student in the PhD program must satisfy all of the following:
  • G Students must satisfy the general graduation requirements for the doctoral degree as stated in the Graduate College Bulletin. In particular, the total number of hours, combining both formal courses and hours of research, will be at least 90 post-baccalaureate hours.
  • M Students must satisfy the Math Hours Requirement, as follows. They must complete 12 hours at the 5,000 or 6,000 level in one of the major areas of mathematics, or in the area of RUME. They must also complete at least 18 hours of coursework in mathematics at the 5,000 level or above. This coursework must include a sequence of two 3-hour courses at the 5,000 or 6,000 level outside of the student's major research area.
  • M Students must pass the Qualifying Examination. Only after this examination has been passed may the student form an Advisory Committee according to the rules of the Graduate College.
  • M Students choosing the Traditional Option must demonstrate reading proficiency in a foreign language or proficiency in a programming language as determined by the student's Advisory Committee. Students choosing the RUME Option must undergo IRB training. This requirement must be satisfied before the General Examination takes place.
  • G Students must pass the General Examination.
  • G Students must write, defend and submit a dissertation.

Graduation Requirements for the MA Program

• M The MA program is a non-thesis program.
• In order to graduate with an MA degree, a student in the MA program must satisfy all of the following:
  • G Students must satisfy the general graduation requirements for the master's degree as stated in the Graduate College Bulletin. In particular, at least 32 hours of graduate coursework are required.
  • M Students must complete at least five of the six core courses:
    • Abstract Algebra I and II (MATH 5353 and MATH 5363).
    • Real Analysis I and II (MATH 5453 and MATH 5463).
    • Topology I and II (MATH 5853 and MATH 5863).
    If not all of the three year-long sequences above are taken, then the student may substitute another sequence approved by the Graduate Director.
  • G Students must take and pass a Comprehensive Examination based on the content of the core sequences (Algebra, Analysis, and Topology). The Comprehensive Exam is an oral or written exam administered by a committee of at least three faculty members.
• G Students enrolled in the PhD program may earn an MA degree by adding the MA program and either
  • satisfy the above requirements for the MA degree, or
  • pass the PhD General Examination.
  See Graduate College Bulletin for additional details. In particular, students must file the Admission to Candidacy form in the semester before taking the Comprehensive Examination; deadlines can be found on the Grad College website.
• M At the time of filing the Admission to Candidacy form, students must inform the Graduate Director of their intent to earn the MA degree.

Graduation Requirements for the MS Program

• M The MS program is a non-thesis program.
• In order to graduate with an MS degree, a student in the MS program must satisfy all of the following:
  • G Students must satisfy the general graduation requirements for the master's degree as stated in the Graduate College Bulletin. In particular, at least 32 hours of graduate coursework are required.
  • M No course below the 4000 level may be applied to the MS degree. A maximum of 12 hours of 4000-level coursework may be applied to the MS degree, and this total may not include more than 9 hours of 4000-level mathematics courses. No more than 9 hours of coursework outside the Mathematics Department may be applied to the MS degree.
  • M Students must complete coursework in the following areas. A single course cannot be used to fulfill two different requirements.
    • Statistics: One 3-hour course beyond the introductory level (MATH 5743 and MATH 4753 are admissible).
    • Numerical Analysis or Computer Science: One 3-hour course.
    • Mathematical Models: This requirement consists of the course MATH 5103.
    • Abstract Mathematics: Two 3-hour courses.
    • Applied Mathematics: Two 3-hour courses.
    • Outside Courses: Two 3-hour courses taken outside the Mathematics Department that use some mathematics at the level of Calculus or higher.
  • G Students must take and pass a Comprehensive Examination according to the rules laid out in the Graduate College Bulletin.
  • M The dates of the exam will be determined by the MS Adviser in consultation with the students involved. Students must inform the MS Adviser that they intent to take the Comprehensive Examination in the semester prior to the one in which they take the exam.
• M The structure of the Comprehensive Examination is as follows:
  • The Comprehensive Examination will consist of five written exams based on five mathematics courses from the student's degree program. No courses from outside the Mathematics Department can be used. Each exam will be two hours long.
  • The choice of the five exam courses is made by the student but is subject to the approval of the Graduate Committee.
  • The selection of the five exam courses must conform to the following guidelines:
    • At least three of the courses must be at the 5000 level or higher.
    • At least one course must be an abstract mathematics course.
    • At least one course must be in either probability/statistics or numerical analysis.

The Qualifying Examination

• M The Qualifying Examination consists of three qualifying exams in Algebra, Analysis and Topology, and a Complex Analysis requirement.
• M The qualifying exams in Algebra, Analysis and Topology are based on the three core sequences:
  • Abstract Algebra I and II (MATH 5353 and MATH 5363).
  • Real Analysis I and II (MATH 5453 and MATH 5463).
  • Topology I and II (MATH 5853 and MATH 5863).
  These are written exams. They are offered each August and each January in the weeks before classes start (in the case of January, the week before; in the case of August, two weeks before).
• M The qualifying exams in Algebra, Analysis and Topology are written and graded by qualifying exam committees, one for each of the three areas. The qualifying exam committee responsible for the August n and January n+1 exams consists of the teachers on record for the corresponding qualifying courses that started in fall n-2, fall n-1 and fall n.
• M Each qualifying exam will be graded on a scale of A-level pass, B-level pass, or fail. To pass the qualifying exams, each student must receive either three A-level passes or two A-level passes and one B-level pass on the three exams.
• M After the qualifying exams have been graded, the grading committees will make a recommendation to the Graduate Committee on the outcomes. The Graduate Committee will meet and make the final decisions.
• M Students who in their first year are not placed into one of the introductory courses - Introduction to Abstract Algebra I and II (MATH 4323, MATH 4333) and Introduction to Analysis (MATH 4433, MATH 4443/5443) - must pass the three qualifying exams (as described above) within 2.5 years of entering the program. Students who in their first year are placed into one of the introductory courses must pass the three qualifying exams within 3.5 years.
• M Students are encouraged to attempt the qualifying exams as soon as they are able. Newly arriving students may attempt the qualifying exams before the start of their first semester.
• M To complete the Complex Analysis requirement, students must pass the course Complex Analysis I (MATH 5423) with a grade of B or higher, or pass an exam at an equivalent level based on the content of the course. This requirement must be met before taking the General Exam.

The General Examination

The General Examination is governed by the rules laid out in the Graduate College Bulletin.

• G The General Examination consists of a written part and an oral part. Both parts have to be taken in the same semester. The written part has to be successfully completed before the oral part takes place.
• M The written part consists of one or more 3-hour written exams, each based on a 5,000 or 6,000 level sequence in the student's research area. The student's Advisory Committee determines the number of written exams. The Advisory Committee determines the specific sequences the student will be examined on. A sequence need not necessarily consist of parts I and II of the same course; it may consist of a one-semester course combined with a reading course, or it may consist of two reading courses. A sequence must consist of the equivalent of 6 credit hours. Transfer credit is admissible as material for the written exam.
• G The student must pass the written part before proceeding to the oral part. The Advisory Committee determines whether the written part has been completed successfully. If the student fails the written part, the entire General Examination counts as failed.
• M Before proceeding to the oral part, the student is required to give a seminar presentation in an appropriate venue, usually one of the departmental area seminars, based on a research paper selected by the student's Advisory Committee. The seminar presentation may take place in the same semester as the General Examination, or in an earlier semester.
• M The oral part for the Traditional Option consists of an oral exam that covers two 5,000 or 6,000 level sequences, including any sequence used in the written part. The oral exam also covers the student's seminar presentation.
• M The oral part for the RUME Option consists of an oral exam the scope of which is determined by the student's Advisory Committee. In addition, the student must present a prospectus for the dissertation or a review of a paper submitted for publication to a research journal.
• G A doctoral student who enters the graduate program with a bachelor's degree is expected to pass the General Examination within five years of the student's first enrollment in a graduate course applied to the doctoral degree. A doctoral student who enters the graduate program with a master's degree is expected to pass the General Examination within four years of the student's first enrollment in a graduate course applied to the doctoral degree.

Advisement, Enrollment and Academic Progress

• Program and course advisement:
  • M Each fall and spring semester each graduate student should meet with his/her adviser to determine courses to enroll in for the following semester.
  • M Doctoral students who have formed their Advisory Committee should consult their dissertation adviser. The Graduate Director serves as adviser for doctoral students who do not yet have a dissertation adviser, and for all MA students. The Graduate Liaison for MS students serves as adviser for all students seeking the MS degree.
• Enrollment requirements:
  • G All enrollments must be approved by the student's adviser (the dissertation adviser in the case of PhD students who have formed their Advisory Committee, in all other cases the Graduate Director).
  • G Graduate Teaching Assistants are required to take at least five credit hours per semester. The expected standard, however, is at least six credit hours per semester.
  • G The maximum enrollment is 16 hours per regular semester.
• Academic standards:
  • M After initial enrollment, a graduate student is expected to maintain academic standards set by the department and to make reasonable progress towards the degree sought. These standards include enrollment requirements, grade requirements, taking appropriate courses and number of hours, and meeting degree requirements in a timely manner.
  • M The Graduate Director is responsible for monitoring the student's academic performance and progress toward the desired degree. In the case of a student who has formed a PhD Advisory Committee, the student's PhD adviser is responsible for monitoring the student's academic performance and progress and reporting these to the Graduate Director.
  • M Concerns about matters of academic performance and progress will be discussed at the request of the Graduate Director. In addition, discussions concerning progress and performance may be initiated by graduate students by making an appointment with the Graduate Director.
• Satisfactory progress:
  • M All appointments as a Graduate Teaching Assistant are contingent on satisfactory academic progress. Unless in exceptional circumstances, this is interpreted to mean completing at least six hours of work per semester with at least a B average over all work taken.
  • M Students must take the specific courses required for their degree in a timely manner.
  • M Students must prepare for and take required examinations at a pace acceptable to the Graduate Committee and the Graduate Director.
  • M In addition, doctoral students are required
    • to form an Advisory Committee and have its first meeting at the earliest feasible time, and
    • to make reasonable progress in dissertation research. These elements of satisfactory progress will be determined by the dissertation adviser. They will be monitored under the supervision of the Graduate Director.

The Departmental Teaching Certificate

• M The department offers all graduate students the possibility of earning an Endorsement in Preparation for Teaching Undergraduate Mathematics (the “Teaching Certificate”). This program is separate and independent of the RUME option of the PhD program.
• M The requirements for the Teaching Certificate are as follows:
  • The student must have taught at least one mathematics course at OU.
  • The student must have completed at least six hours of graduate credit coursework focused on the teaching and learning of undergraduate mathematics.
• M The courses MATH 5253, MATH 5263 and MATH 5950 (RUME seminar) may be used to satisfy the hours requirement. A maximum of three hours of MATH 5950 may be used. Other courses require the approval of the Graduate Committee.
• M Graduate students who complete the endorsement will obtain a certificate that verifies that the awardee has expressed special interest in teaching mathematics courses at the undergraduate level, has taught college mathematics courses, and has completed at least six semester hours of coursework focused on the teaching and learning of undergraduate mathematics.

Language Certification

By state law, graduate students whose native language is not English need to be language certified before holding any instructional position at OU that requires contact with students. This certification is administered through the English Training and Certification Services (ETCS).

• G There are three levels of language certification: A, B and C. Level A means the student is fully language qualified. For all levels there is an oral/aural requirement and a written requirement. The precise requirements are listed here. These requirements can be satisfied by passing a SPEAK test, a TEACH test, and a WRITTEN test administered by the ETCS.
• M The Mathematics Department expects all graduate students to be fully language qualified by the end of their second year. Students who do not meet this deadline are required to
  • attempt the relevant ETCS administered tests every semester until they are fully qualified, and
  • participate in all departmentally sponsored activities designed to improve language and teaching skills.
  Students past their second year who are not fully language qualified and who do not satisfy these requirements will automatically go on probationary status.
• M Each fall and spring semester the ETCS offers a free, non-credit Spoken English Class. International students wishing to take this class must notify the Graduate Director at least one month before the beginning of classes. The Graduate Director will nominate students for the Spoken English Class as soon as possible to increase the likelihood of acceptance.
• M Any student who has not passed the SPEAK test and the TEACH test, at least at the support level, by the end of their first year will be required to enroll in the ETCS Spoken English Class in the fall semester of their second year. They will also be required to take tests every semester until they are fully language qualified.
• M Students must inform the Assistant to the Graduate Director of any attempts made at an ETCS administered test, and of the outcome of the test. The Graduate Director will monitor each student's progress and discuss a plan of action with students who fail to get qualified in a timely manner.
• M The Mathematics Department pays for the student's first attempt at each of the SPEAK, TEACH and WRITTEN test. The student is responsible for the costs of each subsequent ETCS test. However, the department reimburses the student for the cost of a test if the student passes it at the instruct level.

Reporting Requirements

• M Students must keep the Graduate Director informed, in a timely manner, of all plans for taking qualifying, comprehensive or general exams, plans for graduation, and plans for termination or change of program.
• M All of a student's communication with the Graduate College must be done through the Assistant to the Graduate Director. Students must provide a copy of all forms and written communication with the Graduate College. The Assistant to the Graduate Director keeps records of each student's progress, and keeps on file all forms, communication and paperwork related to the student's graduate studies.
• M International students must inform the Assistant to the Graduate Director of any attempts made at a test administered through the English Training and Certification Services (ETCS), and of the outcome of the test.

Probationary Status

This section is about probationary status imposed by the Mathematics Department (not the Graduate College or the University).

• M Students will be placed on probationary status in the following circumstances:
  • International students past their fourth semester who are not fully language qualified, and who have failed to actively engage in trying to get qualified.
  • Students must take an appropriate course load each semester as determined by the Graduate Committee. Students who underenroll for two consecutive semesters will be removed from the graduate program.
  • Other severe circumstances as determined by the Graduate Committee. Such could include serious violations of academic standards or neglect of teaching assistant duties.
• M Students on probationary status are not eligible for any of the following:
  • Departmental travel support.
  • Summer teaching assistantships.
  • Departmental awards.
  The Graduate Committee has the authority to overwrite these rules in individual cases.
• M Students on probationary status will be monitored and are subject to review by the Graduate Committee. If the situation leading to probationary status has been remedied, the probationary status will be lifted. Otherwise the Graduate Committee may or may not extend the probationary period. If the committee finds no compelling reason to recommend an extension of the probationary period, the student's assistantship may be terminated.
• M Students will be notified in writing when they are placed on probationary status, for what reason this action was taken, what are the possible consequences, and what actions they must take for the probationary status to be lifted.