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## M.S. in Pure Mathematics

**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**:

- Advanced Calculus I and II (MATH 5043 and 5053)
- Modern Algebra I and II (MATH 5003 and 5013)
- General Topology (MATH 5303)
- Complex Variables (MATH 4283)

**Option II**:

- Advanced Calculus I and II (MATH 5043 and 5053)
- Modern Algebra I and II (MATH 5003 and 5013)
- 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 nine hours of course work selected from the following list:

Combinatorial Mathematics (MATH 4663), Number Theory (MATH 4713), Groups and Representations (MATH 4813), 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), Algebraic Topology I (MATH 6323).

**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 nine 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 32 hours, which may include two hours for a Master's report. If a student elects to write a thesis, the minimum number of hours is reduced to 30. The courses taken on the M.S. degree program must include 21 hours of courses in the mathematical sciences numbered 5000 or above. All the courses for the M.S. degree program must constitute a coherent whole and must be approved by the student's advisory committee.

Creative component, report, or thesis: Each student must complete a creative component, report, or thesis. Under any of these three 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.

## M.S. in Mathematics Education

**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 4713), 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 4513), Linear and Nonlinear Programming (MATH 4553), Combinatorial Mathematics (MATH 4663), 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 4793), Computer Science Migration (CS 4154)**Geometry**: Groups and Representations (MATH 4813), Differential Geometry (MATH 5413), Computer Graphics (CS 4143)**Statistics**: Applied Regression Analysis (STAT 4043), 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.

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 32 hours, which may include two hours for a Master's report. If a student elects to write a thesis, the minimum number of hours is reduced to 30. The courses taken on the M.S. degree program must include at least 21 hours of courses numbered 5000 or above, 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.

Creative component, report, or thesis: Each student must complete a creative component, a report, or a thesis. Under any of these three 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.

## Creative Components, Reports, and Theses

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.

In recognition of the effort involved in preparing a thesis, the requirement for courses taken in graduate school is reduced to 30 hours if the thesis option is elected. These hours include 6 hours of credit for the thesis (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. The required 32 hours of course work includes 2 hours of credit for the report (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.

**Creative Component Option**

A creative component in the Mathematics Department is an individual investigation of a special topic in the mathematical sciences beyond normal course work. This work is done under the direction of a faculty member who determines what work is to be done and whether or not the student has completed it satisfactorily. The director of the creative component need not be a member of the student's advisory committee. A written presentation and a lecture to the Mathematics Department are required. Under this option, no credit for Math 5000 may be included in the required 32 hours.

Work on the creative component should be started 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 a talk on the work at a regional mathematics meeting.

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

Upon approval by the creative component director, a Verification of Completion form and Assessment Questionnaire must be submitted by the end of the graduating semester to the graduate director for inclusion in the student's file.

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

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

- revise as appropriate the student's plan of study
- approve a written detailed qualifying exam syllabus, consisting of research papers and portions of books
- 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.

## Preparation for Research in Mathematics Education

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.

## Dissertation and Dissertation Defense

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.

## Chronology of Doctoral Studies in Mathematics: Steps and Assessment of Progress

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.

## 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.

## Doctoral Candidacy Status: Qualifying Exam and Dissertation Proposal

**Doctoral Candidacy Status**

Candidacy status is an important attainment for doctoral students. Admission to candidacy status must occur at least six months prior to the date of the final dissertation defense. 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.

**Purpose of the Qualifying Exam**

The purpose of the Qualifying Exam is to test students in their area of specialization in order to determine their readiness to write a dissertation in that particular area.

**Schedule and Application Procedures**

The Qualifying Exam should be taken when the student has mastered a significant body of material related to the area of specialization. This should be approximately at the beginning of the dissertation work. The exam is scheduled by the student's advisory committee in consultation with the student. Admission to candidacy status must occur at least six months prior to the date of the final dissertation defense.

**Administration and Evaluation**

The Qualifying Exam is given by the student's advisory committee. The chairman of this committee leads the examination process. The advisory committee also determines the result of the exam. The completed Qualifying Exam Report form should be returned to the graduate director.

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.

**Format and Exam Topics**

Part of the Qualifying Exam must be oral. It will cover material previously outlined to the student in the form of a reading list. This reading list will be prepared by the student's advisory committee and will consist of portions of books and research papers applicable to the student's area of specialization. The reading list will be given to the student at least two months prior to the exam.

**Failure and Re-examination**

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.

**Dissertation Proposal**

After the student has passed the Qualifying Exam and after an outline of the dissertation work has been prepared, the student must formally present the research plans to the advisory committee. A written dissertation proposal should be prepared and distributed to the advisory committee. The committee may require an oral presentation by the student. In any case the student should be present to answer questions. It is the responsibility of the committee to evaluate this proposal and determine whether the research plans will lead to an acceptable dissertation. 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. Upon approval by the advisory committee of the dissertation proposal, the student should inform the graduate director and submit the Admission to Doctoral Candidacy form to the Graduate College.

## Minor Thesis

Students who have passed two comprehensive exams may, with the approval of their advisor, substitute a minor thesis for one of the comprehensive exams.

The minor thesis must be a creative, written work of research or exposition on a topic of mathematical content that is:

- In an area different from an area in which the student has passed a written comprehensive exam.
- On a topic that is not covered completely in any prior coursework.
- On a topic approved by the student's advisory committee.
- Completed in one semester (fall, spring, or summer), from start to finish (to encourage the ability to learn mathematics independently and write a suitable exposition in a timely manner). No extensions will be granted.

After completion of the written minor thesis, the student must pass an oral exam on the subject of the minor thesis. This exam is administered by three faculty members approved by the advisory committee. A grade of pass or fail on the minor thesis will be assigned following this examination. The completed Minor Thesis Report form and Assessment Questionnaire should be returned to the graduate director. A public presentation is encouraged but not required. A student who takes the minor thesis option and does not pass has no further option of a minor thesis.

## Foreign Language Requirement for Doctoral Students

The foreign language requirement for doctoral students depends 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.

**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 of calculator and computer-assisted instruction, which is then documented in their professional development portfolio.

**Pure Mathematics: Foreign Language Reading Proficiency Examination**

Candidates for the Ph.D. degree in pure mathematics must pass a written examination to demonstrate reading knowledge of one foreign language before they take the qualifying examination. 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 completed copy of the report form should be given to the graduate director after the exam is graded.

## Ph.D. in Mathematics Education

**Departmental Requirements for Ph.D. in Mathematics:****Mathematics Education**

The Ph.D. degree with specialization in mathematics education is designed to prepare a student for a career where instruction in mathematics and research in mathematics education are of primary importance. It is especially intended for students with an interest in college teaching of mathematics.

**Credit requirements**: A total of 90 hours above the B.S. degree or 60 hours above the M.S. is required, including 15-24 credit hours for the Ph.D. dissertation.

**Core requirements**: All candidates for the Ph.D. with specialization in mathematics education are required to complete 24 credit hours of core courses. These must include three of the following seven options plus six credit hours from the other courses on this list. A minimum GPA of 3.0 must be maintained in core courses.

- Real Analysis I and II (MATH 5143 and 5153)
- Complex Analysis I and II (MATH 5283 and 5293)
- Algebra I and II (MATH 5613 and 5623)
- Geometric Topology (MATH 5313) and Algebraic Topology I (MATH 6323)
- Numerical Analysis for Differential Equations (MATH 5543) and Finite Element Methods (MATH 5563)
- Partial Differential Equations (MATH 5233) and Ordinary Differential Equations (MATH 5243)
- Probability Theory (STAT 5123) and Statistical Inference (STAT 5223)

**Additional courses**: All candidates are required to complete an additional 12 hours, namely, Introduction to Research in Mathematics Education (MATH 5913), Research in Undergraduate Mathematics Education (MATH 6923), and six hours from the following list: Theoretical Foundations of Inquiry (SCFD 6113), Qualitative Research I (SCFD 6123), Psychology of Learning (EPSY 5463), Statistical Methods in Education (REMS 5953).

Guidance about selecting further courses on research in education is available here.

Comprehensive exams: A Ph.D. student in mathematics education must select three of the areas from the core requirements listed above and for each must pass a comprehensive exam covering material in that area. The mathematics comprehensive exams are administered in January, May/June, and August. See the separate document covering timetables and requirements. A student who elects to take the exam over the statistics sequence must notify the Department of Statistics and take the exam when that department offers exams, which may not coincide with the time when mathematics exams are given. The exam in statistics is governed by that department's rules. Students who have passed two comprehensive exams may, with the approval of the student's advisor, substitute a minor thesis (as described below) for one of the comprehensive exams.

Minor thesis: The minor thesis must be a creative, written work of research or exposition on a topic of mathematical content. Further requirements are given in a separate document.

Language requirement: There is no foreign language requirement; 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 (see below).

**Professional development portfolio**: Students in mathematics education must prepare a professional development portfolio documenting professional activities in mathematics and mathematics education undertaken while a graduate student. This portfolio should contain a record of actual activities completed for future inclusion on the student's curriculum vitae. Required components of the professional development plan include active participation in the mathematics education seminar; attending and presenting at other workshops and conferences; attaining broad teaching experience in courses at different levels and with different modes of instruction, including the use of technology; documenting teaching quality with course syllabi and exams given, course evaluations, and letters of recommendation; and participating in a curriculum development project.

**Curriculum development project**: Every mathematics education candidate must participate in a curriculum development project under the supervision of a member of the faculty. A proposal for the curriculum development project should be developed within six months of passing the comprehensive exams and must be approved by the student's advisory committee.

Qualifying exam: The student must pass an oral qualifying exam over the area of specialization for the Ph.D. dissertation. This exam covers material on a reading list presented to the student by the advisory committee. Its purpose is to test the student's readiness to begin dissertation work.

Dissertation proposal: An outline of the proposed dissertation research must be presented to the student's advisory committee for approval.

Dissertation: A dissertation must be written according to Graduate College guidelines. The dissertation consists of an original research contribution in mathematics education. It must be prepared according to the style required of doctoral dissertations and defended.

Graduate College requirements: All requirements listed in the university catalog must be satisfied.

## Ph.D. in Pure Mathematics

**Departmental Requirements for Ph.D. in Mathematics:****Pure Mathematics**

The Ph.D. degree with emphasis in pure mathematics is intended to prepare a student for a career in university and industrial research and college instruction. Recipients of the Ph.D degree in pure mathematics are expected to have significant breadth across the core areas of mathematics as well as skills to undertake independent and original research in a particular area.

**Credit requirements:** A total of 90 hours above the B.S. degree or 60 hours above the M.S. is required, including 15-24 credit hours for the Ph.D. dissertation.

**Core requirements:** All candidates for the Ph.D. in pure mathematics are required to complete 24 hours of core courses from the following list. A minimum GPA of 3.0 must be maintained in core courses.

- Real Analysis I and II (MATH 5143 and 5153)
- Complex Analysis I and II (MATH 5283 and 5293)
- Algebra I and II (MATH 5613 and 5623)
- Geometric Topology (MATH 5313) and Algebraic Topology I (MATH 6323)

**Additional courses:** In addition to the core course requirements, every plan of study must contain at least 12 hours of graduate courses in the mathematical sciences (mathematics, statistics, or computer science).

Comprehensive exams: A Ph.D. student in pure mathematics must select three of the four areas from the core requirements listed above and for each must pass a comprehensive exam covering material in that area. The mathematics comprehensive exams are administered in January, May/June, and August. See the separate document covering timetables and requirements. Students who have passed two comprehensive exams may, with the approval of the student's advisor, substitute a minor thesis (as described below) for one of the comprehensive exams.

Minor thesis: The minor thesis must be a creative, written work of research or exposition on a topic of mathematical content. Further requirements are given in a separate document.

Language requirement: Candidates for the Ph.D. in pure mathematics must pass an examination demonstrating reading knowledge of one foreign language, usually French, German, or Russian, before they take the qualifying exam. Other languages may be substituted subject to the recommendation of the student's committee and the approval of the Graduate Committee, including a working ability with a computer language or symbolic computation meeting the satisfaction of the student's committee.

Qualifying exam: The student must pass an oral qualifying exam over the area of specialization for the Ph.D. dissertation. This exam covers material on a reading list presented to the student by the advisory committee. Its purpose is to test the student's readiness to begin dissertation work.

Dissertation proposal: An outline of the proposed dissertation research must be presented to the student's advisory committee for approval.

Dissertation: A dissertation must be written according to Graduate College guidelines. The dissertation consists of an original research contribution in pure or applied mathematics. It must be prepared according to the style required of doctoral dissertations and defended.

Graduate College requirements: All requirements listed in the university catalog must be satisfied.

## Comprehensive Exams for the Doctoral Program

**Comprehensive exam requirements**

Each Ph.D. student must select three of the areas listed in the core requirements for that student's specialization (applied mathematics, pure mathematics, or mathematics education) and for each must pass a comprehensive exam covering material in that area. The mathematics comprehensive exams are administered in January, May/June, and August. (The exam in Statistics, one option in mathematics education, is administered through the Department of Statistics and is governed by that department's rules.) See the separate document covering timetables and requirements. Students who have passed two comprehensive exams may, with the approval of the student's advisor, substitute a minor thesis for one of the comprehensive exams.

**Archive of Comprehensive Exams**

An archive of comprehensive exams is available here.

**Syllabi for comprehensive exams**

Ordinary Differential Equations

Partial Differential Equations

Some of the exams administered in 2000 and earlier are available here.

## Ph.D. in Applied Mathematics

**Departmental Requirements for Ph.D. in Mathematics:****Applied Mathematics**

The Ph.D. degree with emphasis in applied mathematics is intended to prepare a student for a variety of careers in industry, in government research laboratories, and in university research and teaching. Application of mathematics is an important skill to be cultivated by students based on an ability to discern occurrences of mathematical structures in the human environment.

**Credit requirements**: A total of 90 hours above the B.S. degree or 60 hours above the M.S. is required, including 15-24 credit hours for the Ph.D. dissertation.

**Core requirements**: All candidates for the Ph.D. in applied mathematics are required to complete 24 credit hours of core courses. These must include three of the following four options plus six credit hours from the approved electives given below. A minimum GPA of 3.0 must be maintained in core courses.

- Real Analysis I and II (MATH 5143 and 5153)
- Complex Analysis I and II (MATH 5283 and 5293)
- Numerical Analysis for Differential Equations (MATH 5543) and Finite Element Methods (MATH 5563)
- Partial Differential Equations (MATH 5233) and Ordinary Differential Equations (MATH 5243)

**Electives:** Any of the courses in the above four options, MATH 5133, MATH 5213, MATH 5303, MATH 5580, MATH 5593, MATH 5613, MATH 5623.

**Additional courses**: In addition to the core course requirements, every plan of study must contain at least 12 hours of graduate courses in the mathematical sciences (mathematics, statistics, or computer science).

**Comprehensive exams:** A Ph.D. student in applied mathematics must select three of the four areas from the core requirements listed above and for each must pass a comprehensive exam covering material in that area. The mathematics comprehensive exams are administered in January, May/June, and August. See the separate document covering timetables and requirements. Students who have passed two comprehensive exams may, with the approval of the student's advisor, substitute a minor thesis (as described below) for one of the comprehensive exams.

**Minor thesis**: The minor thesis must be a creative, written work of research or exposition on a topic of mathematical content. Further requirements are given in a separate document.

**Language requirement**: The student's advisory committee must be satisfied that the student has a strong working ability with a computer language or symbolic computation.

**Qualifying exam:** The student must pass an oral qualifying exam over the area of specialization for the Ph.D. dissertation. This exam covers material on a reading list presented to the student by the advisory committee. Its purpose is to test the student's readiness to begin dissertation work.

**Dissertation proposal**: An outline of the proposed dissertation research must be presented to the student's advisory committee for approval.

**Dissertation:** A dissertation must be written according to Graduate College guidelines. The dissertation consists of an original research contribution in applied mathematics. It must be prepared according to the style required of doctoral dissertations and defended.

**Graduate College requirements**: All requirements listed in the university catalog must be satisfied.

## Financial Aid for Graduate Study

Financial assistance is available for teaching and research. This primarily comes in the form of a teaching assistantship, but some advanced students receive support from faculty grants. A teaching assistantship includes a waiver of both resident and non-resident tuition for eligible credit hours during the academic year. The total of tuition waivers is limited to the number of hours in the degree program. (Students who held an assistantship in the immediate, preceding spring semester, who completed their entire assignments satisfactorily, and who are enrolled in at least 2 credit hours of eligible courses during the summer terms immediately following the qualifying spring appointment may receive a tuition waiver for those eligible credit hours even if they are not employed as graduate assistants during the summer terms.) Currently stipends for the academic year range from$14,940 to $17,334. Stipend enhancements are available for outstanding applicants. Stipends for summer support are available for some teaching assistants. A teaching assistantship also includes health insurance.

For full consideration, international students applying for a teaching assistantship should take the speaking section when they take the internet-based TOEFL (iBT).

Duties of teaching assistants vary. Students without teaching experience are not assigned direct teaching duties during the first semester. Instead, they receive training in being a teaching assistant. More advanced students may have reduced teaching loads.

In addition to the teaching assistantships, there are also fellowships available. Preference is given to students who plan ultimately to pursue a doctor's degree. Graduate students in the Department of Mathematics have also been very successful in receiving university fellowships, which usually are awarded after one or more years of study.

Each year the department gives a number of monetary awards for outstanding academic achievement and for excellent teaching.

If you have received a graduate assistant non-resident tuition waiver, your graduate spouse is eligible for a waiver of non-resident tuition. The spouse will need to complete the Spousal Graduate Tuition Waiver Form and return it to the Office of the Registrar at the beginning of each semester to receive the waiver. More information is available here.

## Applying for Graduate Study in Mathematics

In order to apply to one of our graduate programs, a student must fill out the Graduate College's CollegeNET online application form. This is accessible via the following URL: https://app.it.okstate.edu/gradcollege/

In order to complete this online application a student should prepare beforehand the following documents in pdf form so that they can be uploaded into the online application form:

- a Personal Statement (a short essay about your long and short range goals and how you think our graduate program would help you meet these goals).
- a current Curriculum Vita (resume). It would be especially helpful if you include in your Vita a list of the mathematics courses you have taken and the associated textbooks used in those courses.
- copies most recent transcripts (unofficial copies will do so long as they are complete)

Besides basic biographical data, the following information will be needed to complete the application form

- the names and email addresses of three references (typically former instructors or supervisors)
- GRE test soores (if available)
- TOEFL or IELS socres (required of all international students coming from countries with English is not the native language).

The application process is not completed until the $50 application fee is paid.

Applications are accepted at any time; however, for full consideration, applications for the Fall semester should be received by March 1 of the preceding Spring, and applications for the Spring semester should be received by October 1 of the preceding Fall semester.

More information about about the Graduate College's requirements and application process can be found on their website http://gradcollege.okstate.edu

Interested students can also correspond directly with our Graduate Director via the following email address: graddir@math.okstate.edu.

## Information for Prospective Graduate Students

- Departmental and Graduate College application forms
- Information about financial aid
- List of mathematics courses from the catalog
- Employment in the Mathematical Sciences
- Career Information on the AMS site
- AMS Employment Services
- Careers in Applied Mathematics and Computational Sciences
- DW Simpson Actuary Jobs

For more information send an email to graddir@mathdept.okstate.edu

## Pure Mathematics

**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 4283)

**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 nine hours of course work selected from the following list:

Combinatorial Mathematics (MATH 4663), Number Theory (MATH 4713), Groups and Representations (MATH 4813), 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), Algebraic Topology I (MATH 6323).

**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 nine 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 32 hours, which may include two hours for a Master's report. If a student elects to write a thesis, the minimum number of hours is reduced to 30. The courses taken on the M.S. degree program must include 21 hours of courses in the mathematical sciences numbered 5000 or above. All the courses for the M.S. degree program must constitute a coherent whole and must be approved by the student's advisory committee.

Creative component, report, or thesis: Each student must complete a creative component, report, or thesis. Under any of these three 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.

## Mathematics Education

**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 4713), 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 4513), Linear and Nonlinear Programming (MATH 4553), Combinatorial Mathematics (MATH 4663), 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 4793), Computer Science Migration (CS 4154)**Geometry:**Groups and Representations (MATH 4813), Differential Geometry (MATH 5413), Computer Graphics (CS 4143)**Statistics:**Applied Regression Analysis (STAT 4043), 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.

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 32 hours, which may include two hours for a Master's report. If a student elects to write a thesis, the minimum number of hours is reduced to 30. The courses taken on the M.S. degree program must include at least 21 hours of courses numbered 5000 or above, 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.

Creative component, report, or thesis: Each student must complete a creative component, a report, or a thesis. Under any of these three 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.

## M.S. in Computational and Applied Mathematics

**Departmental Requirements for M.S. in Mathematics:****Computational and Applied Mathematics**

The Master of Science degree in computational and applied mathematics requires that the student demonstrate knowledge in certain core areas.

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

**1. Basic mathematics (3 hours)** One of Advanced Calculus I (MATH 5043) or Advanced Linear Algebra (MATH 5023)

**2. Numerical analysis (3 hours)** Numerical Analysis for Differential Equations (MATH 5543) or Numerical Analysis for Linear Algebra (MATH 5553)

**3. Applied analysis (12 hours)** Twelve hours from the following list: Intermediate Differential Equations (MATH 4233), Numerical Analysis (MATH 4513), Linear and Nonlinear Programming (MATH 4553), Fourier Analysis and Wavelets (MATH 5213), Partial Differential Equations (MATH 5233), Ordinary Differential Equations (MATH 5243), Advanced Ordinary Differential Equations (MATH 5253), Numerical Analysis for Differential Equations (MATH 5543), Numerical Analysis for Linear Algebra (MATH 5553), Finite Element Methods (MATH 5563), Case Studies in Applied Mathematics (MATH 5580), Methods in Applied Mathematics (MATH 5593)

**Industrial experience:** All students must either earn three hours credit under requirement 3 above for MATH 5580 or have industrial experience. The requirement of industrial experience is satisfied by a summer internship or full-time employment in a mathematical context for at least six months in either industry or business.

**Electives:** All candidates for the M.S. degree in computational and applied mathematics must choose six additional hours from the following list of elective courses:

Introduction to Partial Differential Equations (MATH 4263), Complex Variables (MATH 4283), Mathematical Interest Theory (MATH 4453), Combinatorial Mathematics (MATH 4663), Groups and Representations (MATH 4813), Advanced Linear Algebra (MATH 5023), Advanced Calculus I (MATH 5043), Advanced Calculus II (MATH 5053), Real Analysis I (MATH 5143), Real Analysis II (MATH 5153), Fourier Analysis and Wavelets (MATH 5213), Complex Analysis I (MATH 5283), Complex Analysis II (MATH 5293), General Topology (MATH 5303), Numerical Analysis for Differential Equations (MATH 5543), Numerical Analysis for Linear Algebra (MATH 5553).

**Alternative course selections:**

· A course chosen to satisfy a core requirement in one area cannot be used to satisfy a core requirement in another area. A course chosen to satisfy the elective requirement cannot be used to satisfy a core requirement and vice-versa.

· Courses taken as an undergraduate can be used to satisfy the above requirements, as long as they are consistent with the Graduate College requirements.

· Courses outside the Department of Mathematics must be approved by student's advisory committee. Computer science courses must be beyond programming courses. (The course Techniques of Computer Science for Science and Engineering, CS 4113, is considered a programming course.)

· Any of the 18 hours of core courses may be replaced by a higher level course for which it is a prerequisite. Any such change requires consent from the Graduate Committee.

· Substitutions for any of the six 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 32 hours, which may include two hours for a Master's report. If a student elects to write a thesis, the minimum number of hours is reduced to 30. The courses taken on the M.S. degree program must include 21 hours of courses numbered 5000 or above. All the courses for the M.S. degree program must constitute a coherent whole and must be approved by the student's advisory committee.

Creative component, report, or thesis: Each student must complete a creative component, report, or thesis. Under any of these three 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.

## Mathematics Masters Program

Highlights of the Masters Program

The following highlights of a Master's program are described in more detail in the sections on Departmental Requirements for the Master's Degree, with specializations in Computational and Applied Mathematics, Mathematics Education, and Pure Mathematics. A Master's degree in mathematics has three main requirements.

- 30 to 32 semester hours of courses (depending on whether or not a thesis is written).
- Passing 18 hours of core course work with a grade of either A or B
- Completion of a creative component, report, or thesis

The program is designed so these requirements most often can be completed in two years. A student beginning graduate study in mathematics is expected to have had, as an undergraduate, at least 18 semester hours in mathematics beyond elementary integral calculus including courses in differential equations, linear algebra, introductory analysis and modern algebra. The latter two courses should include elements of logic and practice in writing rigorous arguments. An applicant whose preparation is deficient may be admitted to the program, if otherwise qualified, but will be required to correct the deficiency, increasing somewhat the time required to complete work for the degree. Prospective graduate students are advised to take at least introductory courses in related fields such as physics, statistics, and computer science. The graduate director works closely with new students to help them select their courses and to get them off to a good start. The 18 hours of core course work varies dependent upon the student's choice of a Master's Degree in Computational and Applied Mathematics, Mathematics Education or Pure Mathematics. Beyond the required courses considerable variety is possible in elective courses. These may be taken in computer science and statistics as well as mathematics. For the applied specialization, courses may be taken in a discipline outside of the mathematical sciences. Electives are chosen to meet each individual student's interests and career objectives. Although the actual course sequences taken by students are dependent on their own individual situations, there are fairly "standard" plans for course work. Sample plans of study for each specialization are given below along with the Departmental Requirements for the various specializations (Computational and Applied Mathematics, Mathematics Education, Pure Mathematics). During the second semester of study each student, with the aid of the Graduate Director, sets up a Master's Committee of three faculty members and develops a Plan of Study, which is filed with the Graduate College. The chairman and the other two members of this committee advise and oversee the student's progress toward a degree.

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

## Highlights of the Doctoral (Ph.D.) Program

The following highlights of a doctoral program are described in more detail in the sections on departmental requirements for the Ph.D. degree, with specializations in Applied Mathematics, Pure Mathematics and Mathematics Education. For general requirements and a timetable, look here. A chronology showing steps and assessment of progress is available here.

A doctoral degree in mathematics has several main requirements.

- 90 hours of course work beyond a Bachelor's degree or 60 hours of course work beyond the Master's degree
- 24 hours of core course work (core courses vary with degree specialization)
- Passing written comprehensive exams in three areas or in two areas with a minor thesis
- Completing a language requirement (varies with degree specialization)
- Passing a qualifying exam
- Writing a dissertation

The Department of Mathematics offers three Ph.D. specializations (Applied Mathematics, Pure Mathematics and Specialization in Mathematics Education). The Ph.D. degree is meant to prepare a mathematician for a career in college instruction, university research, or industrial research. The Ph.D. degree is the highest earned degree and consequently its recipients are expected to have significant breadth in mathematical knowledge, as well as research skills in a particular area. In order to prepare students for positions where instructional duties and research in mathematics education are of primary importance the Department offers a Ph.D. with specialization in Mathematics Education.

The Mathematics Department at Oklahoma State University has granted over 200 doctoral degrees. Graduates of the doctoral programs have been highly successful in academic and industrial careers. Most of these graduates have become professors at colleges or universities, and some have gone on to distinguished careers in academic administration. Others have chosen to pursue research careers with either industrial or government concerns.

The Department is exceptionally well equipped to provide doctoral education. The degree program has been designed to give maximum benefit to the students. A core of courses is required in each of the various specializations. The selection of core courses has sufficient overlap so as not to delay students who wish some time before committing themselves to any particular one of the Ph.D. specializations. The faculty at Oklahoma State is highly recognized for its accomplishments both in research and in mathematics education.

The comprehensive exams are meant to test students on breadth in mathematics. They cover material from several general areas. The qualifying exam determines the student's readiness to write a dissertation. The dissertation itself is of integral importance to all doctoral degrees. It is the culmination of a major research project and exhibits the student's expertise in a very specific field of study. The Ph.D. dissertation is an original piece of significant mathematical research or research in mathematics education.

Beginning students in Applied Mathematics concentrate on gaining general knowledge in the core areas of complex analysis, real analysis, differential equations and numerical and computational mathematics. Those in Pure Mathematics concentrate on complex analysis, real analysis, algebra and topology. Students in Mathematics Education are required to take courses in at least three of the 6 above areas, or two of the above and statistics. As students progress, they take more specific topics courses and attend seminars to gain greater understanding of particular research areas. The actual course sequences taken by a doctoral candidate will vary greatly depending on the preparation received in their Master's work. After the core courses have been completed students take their comprehensive exams. Students have the option of taking two comprehensive exams and completing a minor thesis. The next step is to gain specific knowledge about an area of interest which might lead to a dissertation topic. Under the direction of a faculty member, the doctoral student will continue with topics courses, work on outside readings, and become actively involved in seminars. When the student has gained the background to begin serious research for a dissertation, a qualifying exam is administered by his/her advisory committee. This exam determines if the student is ready to conduct the necessary research. Upon completion of the qualifying exam, the student devotes a major portion of his/her time to research for a dissertation.

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

## Degree Programs

The Graduate Program in the Department of Mathematics at Oklahoma State University offers two degree programs: a Master of Science (M.S.) and a Doctor of Philosophy (Ph.D.).

The Master of Science (M.S.) degree in Mathematics has three options and prepares students for high school or college teaching, careers in business or industry, and doctoral study in mathematics or other fields. The Computational and Applied Mathematics option requires greater breadth within the mathematical sciences and provides experiences in solving actual industrial problems in the course Case Studies in Applied Mathematics. The Mathematics Education option emphasizes scope in mathematics and broad teaching experience.The Pure Mathematics option emphasizes course work in core areas of mathematics and gives excellent preparation for future study in a doctoral program.

The Doctor of Philosophy (Ph.D.) degree has three options. Options in Pure Mathematics and Applied Mathematics prepare students for careers in university research and instruction or industrial research. The former emphasizes university research and instruction while the latter emphasizes research in industry. The Mathematics Education option provides excellent training for a career in college teaching of mathematics.

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