Graduate

To receive a graduate minor in Mathematics, a graduate student must take 12 hours for graduate credit in mathematics courses numbered 4000 or above, and at least 9 of those hours must be in courses numbered 5000 and above. Further, no more than 3 credit hours for the minor may be earned through transfer credit of courses taken at other institutions, with approval of the coordinator of the minor in Mathematics. The student must have been an enrolled graduate student at the other institution at the time the credit was earned.

No course with a grade below C can be used as part of a minor, and the grade point average for all coursework constituting the minor must be at least 3.0.

For more information please contact the math department at (405) 744-5688 or email the graduate director at graddir@mathdept.okstate.edu.

Departmental Requirements for M.S. in Mathematics:
Mathematics Education

The Master of Science degree with specialization in mathematics education requires that the student demonstrate knowledge in certain core areas.

Core course requirements: All candidates for the M.S. degree wirh specialization in mathematics education must earn a grade of A or B in a prescribed 18 hours from the following list of core courses.

Basic areas:

Nine hours total from the following courses, with three hours from courses listed in each of the following areas:

• Analysis: Advanced Calculus I (MATH 5043)
• Algebra/Number Theory: Three hours from any of Modern Algebra I (MATH 5003), Number Theory (MATH 5713*), Introduction to Cryptography (MATH 5753*), Modern Algebra II (MATH 5013), Advanced Linear Algebra (MATH 5023)
• Mathematics Education: Introduction to Research in Mathematics Education (MATH 5913)

Topical areas:

Nine hours total from the following courses, with six hours in one of these areas and three hours in another:

• Discrete Mathematics/Computer Science: Numerical Analysis (MATH 5513*), Linear and Nonlinear Programming (MATH 4553), Combinatorics (MATH 5673*), Numerical Analysis for Differential Equations (MATH 5543), Numerical Analysis for Linear Algebra (MATH 5553), Data Structures and Algorithm Analysis I (CS 4343), Artificial Intelligence I (CS 5723*), Computer Science Migration (CS 4154)
• Geometry:  Geometry and Algorithms in Three-Dimensional Modeling (MATH 5423*), Groups and Representations (MATH 5803*), Differential Geometry (MATH 5413), Computer Graphics (CS 5143*)
• Statistics: Applied Regression Analysis (STAT 5543*), Probability Theory (STAT 5123), Statistical Inference (STAT 5223), Statistics for Experimenters I (STAT 5013), Statistics for Experimenters II (STAT 5023), Sample Survey Designs (STAT 5043), Multivariate Methods (STAT 5063), Experimental Design (STAT 5303)

Note on prerequisites: It is assumed that students will have already completed the equivalent of Introduction to Modern Algebra (MATH 3613), Introduction to Modern Analysis (MATH 4023), Geometry (MATH 4403), and Statistical Methods I (STAT 4013), thereby providing a sound foundation for graduate study. Courses taken as an undergraduate can be used to satisfy the above requirements, as long as they are consistent with the Graduate College requirements.

Course numbers labeled * are cross-listed with an undergraduate section.

Courses outside the Mathematics Department other than those listed above must be approved by the student's advisory committee.

Courses taken in graduate school: The courses taken in graduate school must total at least 33 hours. The courses taken on the M.S. degree program must include at least 21 hours of non-cross-listed courses, of which 20 hours must be from the mathematical sciences (mathematics, statistics, or computer science). No more than six hours outside the mathematical sciences will count towards the M.S. degree. All the courses on the M.S. degree program must constitute a coherent whole and must be approved by the student's advisory committee.

Report or thesis: Each student must complete either a report or a thesis. Students electing to write a report must complete three hours of MATH 5000, and those electing to write a thesis must complete six hours of MATH 5000. Under both of these options, a written document and a public presentation based on this individually directed project is required.

Teaching experience: Any student in this program who is also a Teaching Assistant in the Department of Mathematics is encouraged to work with the Associate Head in designing a broad spectrum of teaching assignments.

Other requirements: The university catalog contains detailed procedures and requirements applicable to all Master's degrees.

Doctoral students in Mathematics Education must conduct research in Mathematics Education. Research in education, however, is by nature quite different from research in Mathematics. In education, there are several different theoretical viewpoints and research paradigms that govern the conduct of educational studies. Articles in Mathematics Education typically begin by stating the author’s research framework or theoretical paradigm. Students conducting such research might learn about the theoretical paradigms on which social research is based in one of the following:

• SOC 5243, Social Research Design
• SCFD 6113, Theoretical Foundations of Inquiry

Educational research can be either quantitative, that is, based on analyzing numerical data, or qualitative, that is, based on an analysis of data involving more words than numbers, such as answers to interview questions, observations of classroom situations, etc. Both methods, along with studies that explicitly mix the methods, are conducted in educational research, and students doing educational research should have a foundation in both modes of inquiry.

Training in qualitative research methods might be undertaken in the following courses:

• SOC 5273, Qualitative Research Methods
• SCFD 6123, Qualitative Research I
• SCFD 6193, Qualitative Research II

The following course emphasizes mixed methods but also helps compare and contrast the two research styles and helps students understand the research paradigms:

• CIED 5730, Conducting Mixed Methods Research

Training in quantitative methods can come from courses in Sociology or courses in REMS (in the College of Education), but the Mathematics Department encourages Mathematics students to take advantage of the rigorous foundation and more thorough treatment provided by graduate courses in Statistics. The foundational applied sequence, covering analysis of experimental data, is

• STAT 5023, Statistics for Experimenters II (STAT 5013 or 4023 is a prerequisite)
• STAT 5303, Experimental Design

To go along with these classes, it would be helpful for the student to have computational experience with large statistical data sets:

• STAT 5091, SAS Programming (or STAT 4091)

Many educational studies involve surveys and construction of questionnaires. The following course could be very helpful:

• STAT 5043, Sample Survey Designs

These courses are very good starting points, but they tend to deal with a single varying quantity. Advanced quantitative studies in education might perform statistical analysis on multivariate quantities instead, or on data that are not normally distributed. These research methodologies are taught in:

• STAT 5063, Multivariate Methods
• STAT 5073, Categorical Data Analysis
• STAT 5033, Nonparametric Methods

The Graduate Advisor in Statistics will usually be able to help graduate students in Mathematics with questions of placement in Statistics courses.

As a final note, we remark that the theoretical Probability sequence in Statistics is currently allowed as one of the core course sequences on a Mathematics Education Ph.D. plan of study:

• STAT 5123, Probability Theory
• STAT 5223, Statistical Inference

These courses serve as a valuable theoretical foundation to all future study or future teaching in Probability and Statistics but do not explicitly cover the data analysis techniques for quantitative educational research beyond those contained in STAT 5013.

The Graduate College at OSU

Graduate College Homepage

The Graduate College is a great resource for information about:

*ITA and TELP tests

*GSSI Tuition Waivers

* The current academic calendar and submission deadlines

This portion of the Master's degree program is designed to demonstrate that the student has reached a level of mathematical maturity beyond that of successfully taking courses and examinations. The student should exhibit such qualities as creativity and good judgment, as well as independence, clarity, depth, and breadth of thought.

Master's Thesis Option

A Master's thesis in the Department of Mathematics is a substantial written work in the mathematical sciences in which the student makes an original research contribution to the subject which they are investigating. The thesis topic is determined by the student in consultation with the student's advisor. A public oral defense of the thesis is required after its completion. The committee must submit the thesis defense form to the Graduate College and should give a copy to the Mathematics Department's graduate director along with the Assessment Questionnaire for Theses.

Those electing to write a thesis must complete six hours of MATH 5000.

Work on the thesis should begin as soon as possible after the student has completed a substantial portion of their required course work. The student is encouraged (but not required) to present the thesis at a regional mathematics meeting.

The thesis must conform to the guidelines for thesis preparation established by the Graduate College. The student must submit the thesis, thesis abstract, and signed approval page to the Graduate College by the due date. One copy of the thesis must also be submitted to the Mathematics Department's graduate director. Copies of Master's theses are on display in the Mathematics Department lounge.

Master's Report Option

A Master's report in the Department of Mathematics is a substantial written expository work on a topic in the mathematical sciences determined by the student in consultation with the student's advisor. Those electing to write a report must complete three hours of MATH 5000.

A public oral presentation of the report is required. The student is encouraged (but not required) to present the report at a regional mathematics meeting.

The written portion of the report must be typed. However, the technical style and form specifications are determined by the director of the report. One copy of the written report must be submitted to the Mathematics Department's graduate director. Copies of reports are on display in the Mathematics Department lounge.

Upon approval of the written report by the committee, the Formal Report Approval form must be submitted to the Graduate College by the end of the graduating semester. A copy of this form along with the Assessment Questionnaire for Formal Reports should be given to the graduate director.

The doctoral dissertation should present, in a self-contained manner, the results of research which makes a new and original contribution to knowledge in mathematics or, for students specializing in mathematics education, in mathematics education. The results should have the quality of work publishable in peer-reviewed journals.

The student must take a final oral exam defending the dissertation. The advisory committee acts as the exam committee. As the date for the exam approaches, the student should periodically provide drafts of the dissertation to the committee. The student must provide a final draft of the dissertation to members of the advisory committee at least three weeks before the dissertation defense.

The dissertation presentation should be announced on the department's bulletin board and electronically. The presentation is open to all faculty members and graduate students in the Department of Mathematics, all members of the OSU Graduate Faculty, and anyone else who obtains the permission of the committee.

The dissertation defense begins with a formal lecture by the student on the results of the dissertation. Questions by all those present are allowed. After the public portion of the defense is completed, the advisory committee may question the student further. Then the student shall be excused, and the committee shall determine the result of the exam on the basis of the oral defense. The committee must submit the dissertation defense form to the Graduate College and should give a copy to the graduate coordinator. The student is responsible for bringing the Dissertation Assessment Questionnaire to the defense for the committee to complete.

In decisions resulting from a vote of the advisory committee (e.g., qualifying exam, dissertation proposal, dissertation defense, approving a dissertation), a pass requires that the advisor vote in the affirmative and that no more than one member of the committee dissent.

If the student fails this exam, the advisory committee shall determine whether and under what conditions a second exam may be taken. If the student fails to meet the conditions imposed by the advisory committee, or fails a second exam, then the Graduate Committee may dismiss the student from the program. Appeals to such dismissal must be filed in writing with the Graduate Committee within 10 working days of the dismissal.

If the student passes this exam, the advisory committee shall determine whether to approve the dissertation itself and what revisions are necessary before the dissertation can be submitted to the Graduate College. The dissertation must conform to the guidelines for dissertation preparation established by the Graduate College. The student must make any changes in the dissertation required by the committee and by the Graduate College and submit the dissertation in final form signed by the committee to the Graduate College.

The student's successful defense of the dissertation and submission of the dissertation in acceptable form complete the doctoral program.

Departmental Requirements for M.S. in Mathematics:
Pure Mathematics

The Master of Science degree in pure mathematics requires that the student demonstrate knowledge in certain core areas. There are two options. Both options require a student to earn a grade of A or B in 18 hours of core courses.

Core courses:

Option I:

1. Advanced Calculus I and II (MATH 5043 and 5053)
2. Modern Algebra I and II (MATH 5003 and 5013)
3. General Topology (MATH 5303)
4. Complex Variables (MATH 5273*)

Option II:

1. Advanced Calculus I and II (MATH 5043 and 5053)
2. Modern Algebra I and II (MATH 5003 and 5013)
3. Six hours from the following list: Real Analysis I and II (MATH 5143 and 5153), Complex Analysis I and II (MATH 5283 and 5293), Geometric Topology (MATH 5313) and Algebraic Topology I (MATH 6323), Algebra I and II (MATH 5613 and 5623).

Elective courses: Students working towards the M.S. degree in pure mathematics should complete 12 hours of course work selected from the following list:

Geometry and Algorithms in Three-Dimensional Modeling (MATH 5423*), Combinatorics (MATH 5673*), Number Theory (MATH 5713*), Introduction to Cryptography (MATH 5753*), Groups and Representations (MATH 5803*), Advanced Linear Algebra (MATH 5023), Fourier Analysis and Wavelets (MATH 5213), Partial Differential Equations (MATH 5233), Ordinary Differential Equations (MATH 5243), General Topology (MATH 5303), Geometric Topology (MATH 5313), Numerical Analysis for Differential Equations (MATH 5543), Numerical Analysis for Linear Algebra (MATH 5553), Algebra I (MATH 5613), Algebra II (MATH 5623), Seminar and Practicum in the Teaching of College Mathematics (MATH 5903), Algebraic Topology I (MATH 6323).

Course numbers labeled * are cross-listed with an undergraduate section.

Alternative course selections:

· Courses taken as an undergraduate can be used to satisfy requirements for core and elective courses as long as they are consistent with the Graduate College requirements.

· Substitutions for any of the 12 hours of electives requires consent from the Graduate Committee. In no case may more than nine hours outside the mathematical sciences (mathematics, statistics, or computer science) be counted toward the M.S. degree.

Courses taken in graduate school: The courses taken in graduate school must total 33 hours. The courses taken on the M.S. degree program must include 21 hours of non-cross-listed courses in the mathematical sciences. All the courses for the M.S. degree program must constitute a coherent whole and must be approved by the student's advisory committee.

Report or thesis: Each student must complete either a report or a thesis. Students electing to write a report must complete three hours of MATH 5000. Those electing to write a thesis must complete six hours of MATH 5000; three of those hours may be counted toward the 12 hours of electives. Under both of these options, a written document and a public presentation based on this individually directed project is required.

Other requirements: The university catalog contains detailed procedures applicable to all Master's degrees.

This document covers the period after the completion of the comprehensive exam requirements. General requirements and a timetable for the preceding period are available here.

1. Doctoral Candidacy Status

Candidacy status is an important attainment for doctoral students. The condition for granting candidacy status by the Graduate College is the approval of a dissertation proposal by the student's advisory committee. The Department of Mathematics requires in addition that the student pass a qualifying exam before approval of the dissertation proposal. Students are expected to attain candidacy status within two years of completing the comprehensive exam requirements. The advisory committee plays a key role in guiding students through this process.

2. Composition of the Advisory Committee

The doctoral advisory committee shall consist of at least four members of the OSU Graduate Faculty. Roles of the committee members are: chair, advisor, expert member, and outside member.

The chair must hold an OSU faculty appointment. Normally the chair is a faculty member in the department. The chair's duties include convening meetings of the advisory committee as appropriate and ensuring compliance with policies, procedures, and requirements. If the chair is not the advisor, s/he should serve as a liaison with the advisor with regard to progress in fulfillment of the degree requirements.

The advisor's primary duty is to mentor the student in regard to the conduct of research that is original and publishable. The advisor must be a member of the Graduate Faculty but need not hold an OSU faculty appointment.

The outside member of the committee serves as a representative of the Graduate College and ensures a high level of integrity in the procedures used by the committee to review and evaluate students.

The other members of the committee should be experts in research areas closely related to the work to be conducted by the student.

In decisions resulting from a vote of the advisory committee (e.g., qualifying exam, dissertation proposal, dissertation defense, approving a dissertation), a pass requires that the advisor vote in the affirmative and that no more than one member of the committee dissent.  

3. Forming the Advisory Committee

Students are encouraged to begin looking for an advisor before completing the comprehensive exam requirements. The dissertation advisor will usually suggest which individuals should be asked to serve on the advisory committee and will guide the student after the completion of the comprehensive exam requirements.

Within one semester of fulfilling the comprehensive exam requirements, students should complete the departmental Advisory Committee form (available here) and give it to the graduate coordinator. (Students should also complete and submit the Graduate College's Committee Change Request form as appropriate.)  

4. First Conference of the Committee: Qualifying Exam Preparation

The advisory committee and the student shall hold a conference in preparation for the qualifying exam, which covers the area of the student's research specialization. The advisor should prepare for the conference a draft syllabus for the exam. During the conference, the advisory committee shall 

1. revise as appropriate the student's plan of study
2. approve a written detailed qualifying exam syllabus, consisting of research papers and portions of books
3. set a date for the qualifying exam. 

The syllabus shall be given to the student at least two months prior to the qualifying exam. A copy of the revised plan of study and the qualifying exam syllabus should be given to the graduate coordinator shortly after the meeting. The revised plan of study must be submitted to the Graduate College. 

5. Qualifying Exam

The purpose of the qualifying exam is to test the student in the area of specialization in order to determine readiness to write a dissertation in that area. The exam should be taken when the student has mastered a significant body of material related to the area of specialization. Before taking this exam the student must have an approved plan of study on file.

The exam is conducted by the advisory committee and must be based on the syllabus agreed to by the advisory committee. Part of the exam must be oral. Normally the chair of the committee leads the examination process. After the committee determines the result of the exam, it should record the result using the departmental Qualifying Exam Report form (available here) and give that form to the graduate coordinator.

If the student fails this exam the advisory committee shall notify the student of the conditions under which a second exam may be taken. If the student fails to meet the conditions imposed by the advisory committee, or if s/he fails the second exam, then the Graduate Committee may dismiss the student from the program. Appeals to such dismissal must be filed in writing with the Graduate Committee within 10 working days of the dismissal.  

6. Second Conference of the Advisory Committee: Dissertation Proposal

After the student passes the qualifying exam, the advisory committee shall meet to consider for approval a dissertation proposal prepared by the student. This meeting may be held in conjunction with the qualifying exam. The committee should ensure that the research topic undertaken is appropriate to satisfy the degree requirements.

The committee may require an oral presentation by the student. In any case the student should be present to answer questions.

The committee should discuss the extent to which the student will be permitted to use in the dissertation results of papers published (or to be published) with others. The dissertation proposal should identify any portions of the research project that are planned as joint work with others.  

7. Admission to Candidacy

Upon approval of the dissertation proposal the committee must file a doctoral candidacy form with the Graduate College. A copy of this form should be given to the graduate coordinator. Admission to candidacy status must occur at least six months prior to the date of the final dissertation defense.

8. Language Exam Requirement

Foreign language requirements for doctoral students depend on the area of specialization.

Applied Mathematics

The advisory committee of a student in applied mathematics must be satisfied that the student has a strong working ability with a computer language or symbolic computation. A statement to this effect should be approved by the committee and given to the graduate coordinator.

Mathematics Education

There is no foreign language requirement for the Ph.D degree with specialization in mathematics education; however, it is expected that students in mathematics education exhibit a strong working ability in calculator and computer-assisted instruction, which is then documented in their professional development portfolio.

Pure Mathematics

Candidates for the Ph.D degree in pure mathematics must pass a written exam to demonstrate reading knowledge of a foreign language. This exam should be passed before the student takes the qualifying exam. Usually the language is French, German, or Russian. Other options, including demonstrating a working ability with a computer language or symbolic computation, may be substituted subject to the recommendation of the student's advisory committee and the approval of the Graduate Committee.

The language exam consists of the translation into English, with dictionary allowed, of a suitable passage from a mathematics paper or book in the language. The passage is to be about 300 words in length excluding any symbolic expressions, and the exam period is one hour.

Language exams are scheduled by the Graduate Committee at the request of the student. A form for reporting the results on the exam is available here. A completed copy of the report form should be given to the graduate coordinator after the exam is graded. 

9. Dissertation

A doctoral dissertation is required. It should present, in a self-contained manner, the results of research which makes a new and original contribution to knowledge in mathematics or, for students specializing in mathematics education, in mathematics education. The results should have the quality of work publishable in peer-reviewed journals. 

10. Dissertation Defense and Approval

The student must take a final oral exam defending the dissertation. The advisory committee acts as the exam committee. As the date for the exam approaches, the student should periodically provide drafts of the dissertation to the committee. The student must provide a final draft of the dissertation to members of the advisory committee at least three weeks before the dissertation defense.

The dissertation presentation should be announced on the department's bulletin board and electronically. The presentation is open to all faculty members and graduate students in the Department of Mathematics, all members of the OSU Graduate Faculty, and anyone else who obtains the permission of the committee.

The dissertation defense begins with a formal lecture by the student on the results of the dissertation. Questions by all those present are allowed. After the public portion of the defense is completed, the advisory committee may question the student further. Then the student shall be excused, and the committee shall determine the result of the exam on the basis of the oral defense. The committee must submit the dissertation defense form to the Graduate College and should give a copy to the graduate coordinator.

If the student fails this exam, the advisory committee shall determine whether and under what conditions a second exam may be taken. If the student fails to meet the conditions imposed by the advisory committee, or fails a second exam, then the Graduate Committee may dismiss the student from the program. Appeals to such dismissal must be filed in writing with the Graduate Committee within 10 working days of the dismissal.

If the student passes this exam, the advisory committee shall determine whether to approve the dissertation itself and what revisions are necessary before the dissertation can be submitted to the Graduate College. The dissertation must conform to the guidelines for dissertation preparation established by the Graduate College. The student must make any changes in the dissertation required by the committee and by the Graduate College and submit the dissertation in final form signed by the committee to the Graduate College.

The student's successful defense of the dissertation and submission of the dissertation in acceptable form complete the doctoral program. 

11. Time Limits

Students making reasonable academic progress and fulfilling their assigned duties in an acceptable manner are normally supported for six years.

Doctoral students making reasonable academic progress and fulfilling their assigned duties in an acceptable manner are normally supported for six years. The following list shows the steps involved and indicates how progress is measured. For further details, see the timetable here.

• Initially the student is assigned the graduate coordinator as advisor. The student periodically meets with the advisor for approval of course registration and discussion of short-term goals.
• The Graduate Committee periodically evaluates the overall performance of all graduate students.
• The student submits a plan of study to the Graduate College prior to the end of the third semester of enrollment in the doctoral program.
• As the student completes the core courses, s/he begins taking the comprehensive exams.
• The student completes the comprehensive exam requirements within two years of arrival, if in Track 1 (three years, if in Track 2).
• As the student completes the comprehensive exam requirements, s/he selects an advisor in the intended area of research. In conjunction with the advisor, the student should finalize the choice of an advisory committee within one semester of fulfilling the comprehensive exam requirements.
• The student fulfills the foreign language requirement appropriate to the specialization.
• The advisory committee holds the first advisory conference, in preparation for the qualifying exam. The syllabus for the exam is given to the student at least two months prior to the exam.
• The student passes the qualifying exam.
• The advisory committee holds the second advisory conference, to evaluate the dissertation proposal prepared by the student. This meeting may be held in conjunction with the qualifying exam. Students are expected to have an approved dissertation proposal within two years of completing the comprehensive exam requirements.
• The advisory committee meets periodically to assess the student's progress on research for the dissertation.
• As the date for the dissertation defense approaches, the student should periodically provide drafts of the dissertation to the committee. Three weeks prior to the defense, the student gives copies of the dissertation to each member of the advisory committee. At least a week prior to the dissertation defense, the presentation is announced on the department's bulletin board and electronically.
• The student passes an oral exam defending the dissertation.
• The student makes any changes in the dissertation required by the committee and by the Graduate College, then s/he submits the dissertation in final form signed by the committee to the Graduate College.