## Requirements and Timetable for Ph.D. in Mathematics: Through the Comprehensive Exams

This document covers the period through the completion of the comprehensive exam requirements. General requirements and a timetable for the next period are available here. For a brief statement of the requirements, look here. A chronology showing steps and assessment of progress is available here.

**1. Entrance Requirements for the Ph.D. Program**

Students entering the Ph.D. program are expected to have the equivalent of an undergraduate degree in mathematics at Oklahoma State University. Students should have completed upper-division courses in abstract algebra and analysis.

Students admitted into the Ph.D. program are placed in one of the following two tracks.

**Track 1** is for students who are prepared to take the core Ph.D. courses. These students are expected to pass three comprehensive exams or two comprehensive exams and a minor thesis within the first two years after starting the program.

**Track 2** is for students who are not prepared to take the core Ph.D. courses. Students who are admitted into this track are expected to complete the two-year course of study described in Section 3 of this document. In the spring of the second academic year after admission, the Graduate Committee will evaluate the student's performance in accordance with the regulations specified in Section 4 of this document. Students who obtain a satisfactory report will be granted a third year to complete all comprehensive exam requirements (see Section 4).

**2. Timetable**

Students will be evaluated annually by the Graduate Committee to determine whether they are making reasonable progress.

In typical cases it is expected that students in Track 1 progress through the program in five years: two years to pass the comprehensive exams, one year to pass the qualifying exam, and two years to complete the dissertation.

In typical cases it is expected that students in Track 2 progress through the program in six years: three years to pass the comprehensive exams, one year to pass the qualifying exam, and two years to complete the dissertation.

The mathematics comprehensive exams are administered in January, May/June, and August. There is no limit on the number of times a student is allowed to take an exam in a given subject in mathematics.

Before completing 28 credit hours, students choose an adviser and an advisory committee. The committee holds a meeting to determine the student's plan of study. After passing the comprehensive exams, students work with their adviser to prepare for the qualifying exam.

**3. Requirements for Tracks**

**Requirements for Track 1**

Students are expected to complete the core courses with a GPA of at least 3.0. These courses and the comprehensive exam requirements should be completed within two years after admission to the program. The Graduate Committee will review the case of a student who fails to do so.

**Requirements for Track 2**

Students in Track 2 must fulfill the following requirements. During the first two years, students must earn a GPA of at least 3.0 each semester in the courses they use to fulfill the requirements stated below. Students who have the required background may substitute a more advanced course for a first-year course with the approval of the Graduate Committee.

**Track 2: First Year**

· Complete the two-semester sequence Advanced Calculus I and II (Math 5043 and 5053).

· In addition,

if planning to work in pure mathematics, the student should complete the two-semester sequence Modern Algebra I and II (Math 5003 and 5013).

if planning to work in applied mathematics, the student should complete Advanced Linear Algebra (Math 5023) and Numerical Analysis for Linear Algebra (Math 5553).

if planning to work in mathematics education, the student should complete two courses from the following list: Modern Algebra I (Math 5003), Modern Algebra II (Math 5013), Advanced Linear Algebra (Math 5023), Numerical Analysis for Linear Algebra (Math 5553).

**Track 2: Summer after First Year**

· Complete one of the following courses: Complex Variables (Math 4283), Fourier Analysis and Wavelets (Math 5213), General Topology (Math 5303).

**Track 2: Second Year**

· Complete two sequences of two-semester courses from a list of three sequences of core courses, as follows.

**For even-numbered academic years:** Complex Analysis I and II (Math 5283 and 5293); Geometric Topology (Math 5313) and Algebraic Topology I (Math 6323); Partial Differential Equations (Math 5233) and Ordinary Differential Equations (Math 5243); Probability Theory (Stat 5123) and Statistical Inference (Stat 5223).

**For odd-numbered academic years:** Real Analysis I and II (Math 5143 and 5153); Numerical Analysis for Differential Equations (Math 5543) and Finite Element Methods (Math 5563); Algebra I and II (Math 5613 and 5623).

· By June of the second year students must have taken at least two comprehensive exams and passed at least one of them.

**4. Further Regulations for Track 2**

Those students who successfully completed all course work specified in Section 3 but did not pass a comprehensive exam are placed in the M.S. program. All students have one semester (the first semester of their third year) to complete that degree, except that students wishing to complete an M.S. in mathematics education have two semesters. If, in addition to completing the M.S. degree, a student passes two comprehensive exams by January of the third year, that student will be re-admitted to the Ph.D. program. Students passing only one comprehensive exam by January will be evaluated by the Graduate Committee.

Those students who completed all of the requirements specified in Section 3 are granted one year to complete the core courses and comprehensive exam requirements, as follows.

**Track 2: Third Year**

· During the third year students should complete the remaining requirements for core courses with a GPA of 3.0.

· By June of the third year students should have passed at least two comprehensive exams.

· By August of the third year students should have fulfilled the comprehensive exam requirements. Students who have passed two comprehensive exams can choose to replace the remaining exam by a minor thesis. The minor thesis should be defended by August of the third year. No extensions will be granted.