Off-Campus Housing
ROLE OF THE GRADUATE COMMITTEE
This document is meant to supply prospective students
with specific information about the options available to them
for graduate study in mathematics at Oklahoma State University.
Contained within are sections on the four degree
programs:
There are also general descriptions of the Mathematics
Learning Resource Center (MLRC), and the research interests of
the faculty.
Requests for further information and applications
should be directed to: Dr. Amit Ghosh, Director of Graduate Studies, Oklahoma State University, Department of Mathematics , 401 Math Sciences, Stillwater, OK 74078, Phone: 405/744-5688, e-mail: ghosh@math.okstate.edu
Oklahoma State University is a major land grant university
with an enrollment of over 20,000 students. It has a long record
of excellence in teaching and research, especially in the basic
and applied sciences. Its large and diverse student body comes
from every state and 67 foreign countries. Its physical facilities
and libraries are outstanding for both research and instruction.
Admission to the university is selective. The largest college
is the College of Arts and Sciences. The Graduate College has
an enrollment of 3000 students.
Among institutions of its size, Oklahoma State has
perhaps been unique in the emphasis it has given to its concern
for the welfare of individual students. The University has sought
to maintain not only the availability of the superior resources
naturally associated with large universities but also the close
personal contact and its sense of community usually expected only
in smaller institutions.
The University is located in Stillwater, a town of 40,000 and
is within an hour's drive of Tulsa and Oklahoma City. By virtue
of being a college town, Stillwater has many of the cultural
advantages associated with metropolitan areas.
Financial Assistance
Financial assistance is available for teaching and research.
This primarily comes in the form of a teaching assistantship,
although some advanced students receive support from faculty grants.
The stipends for teaching assistantships are increased regularly
and remain very competitive with schools nationwide.
In addition to the teaching assistantships, there are also a
limited number of fellowships available. These are highly
competitive and preference is given to students who plan to
ultimately pursue a doctor's degree. Graduate students in the
Mathematics Department have also been very successful in
receiving university fellowships which usually are awarded
after one or more years of study.
Overview of Master's Programs
The department offers Master's degrees in both Mathematics
and in Applied Mathematics. The Master of Science in Mathematics,
which emphasizes basic work in mathematics, prepares the student
for teaching mathematics at the high school, junior college, or
four year college level as well as for working in industry. The
Applied Mathematics degree requires greater breadth within the
mathematical sciences (including statistics and computer science)
and is intended to prepare students for positions in business,
industry, and government. Both degrees can prepare the student
for doctoral work leading to a career in either mathematical research,
university instruction, or mathematics education. Master's programs
are varied and are planned on an individual basis.
Graduates of the Master's degree programs in mathematics
continue to be highly successful in obtaining diverse professional
positions upon graduation. A few examples of recent graduates
and their initial positions are:
- Michael McClurkan--Bell Laboratories, Chicago
- Joe Swartz--Martin Marietta, Denver
- Sherri Hinds--Oklahoma City Public Schools
- Doug Punke--Arkansas College, Batesville, AR
- Chuck Davison--E-Systems, Dallas
- Charles Matthews--Connecticut College, New London, CT
- Jeff Dimick--Hughes Aircraft, Los Angeles
- Retha Ulbrich--McDonnell Douglas, St. Louis
- William King--NE Oklahoma State Univ., Tahlequah
- Jack Rau-- Rahco Corporation, Oklahoma City
- Bryan Smith--National Security Agency, Washington, D.C.
- Vicky Hite--General Dynamics, Ft. Worth
- Lisa Patterson--Bell Laboratories, New Jersey
A student with a strong interest in some related field outside
mathematics is encouraged during graduate work to develop further
competence in this related area. In addition, students are
encouraged to do exploratory work in other areas of the mathematical
sciences such as computing and statistics. The department's excellent
computing facilities are freely available to all graduate students.
Highlights of a Master's Degree Program
The following highlights of a Master's program are described in
more detail in later sections.
A Master's degree in mathematics requires 30 to 32 semester
hours of courses. In addition, the student must pass the
departmental Master's examination and complete a creative
component, report, or thesis. These requirements can be completed
in two years. During the second semester each student, with the
aid of the graduate director, sets up a Master's committee of
three faculty members. The chairman and the other two members
of this committee advise and oversee the student's progress toward
a degree.
Each Master's student, working individually with a faculty member,
must complete a creative component, report, or thesis. This project,
which provides an excellent opportunity to investigate a topic in an
area of special interest to the student, includes writing a paper
and giving a public oral presentation.
Each Master's student must pass a written comprehensive examination
covering some of the basic concepts in modern mathematics.
The director of the graduate program works closely with new students
to select their courses and to get them off to a good start. Beyond
the required courses considerable variety is possible in elective
courses which may be taken in computer science and statistics as
well as mathematics. Electives are chosen to meet each individual
student's interests and career objectives.
Sample Plans of Study
Although the actual course sequences taken by students are
dependent on their own individual situations, there are fairly
"standard" plans for course work. Samples are as follows:
Master of Science
Degree in Applied Mathematics
First Year
Fall Semester
- Math 4143 - Adv Calculus I
- Math 4513 - Numerical Analysis
- Elective I
Spring Semester
- Math 4153 - Adv Calc II
- Math 5580 - Case Studies in Applied Math
- Math 5023 - Adv Linear Algebra
Second Year
Fall Semester
- Math 5593 - Applied Math II
- Math 4283 - Complex Analysis Elective 4
- Elective 2
- Master's Comprehensive Exams
Spring Semester
- Elective 3
- Elective 4
- Creative Component, Report or Thesis
Master of Science
Degree in Pure Mathematics
First Year
Fall Semester
- Math 4143 - Adv Calculus I
- Math 4613 - Modern Algebra I
- Elective 1
Spring Semester
- Math 4153 - Adv Calc II
- Math 5013 - Modern Algebra II
- Elective 2
Second Year
Fall Semester
- Math 5303 - General Topology
- Math 4283 - Complex Analysis
- Elective 3
- Master's Comprehensive Exams
Spring Semester
- Elective 4
- Elective 5
- Creative Component, Report, or Thesis
Departmental Requirements for the
Master of Science Degrees
The following are the official departmental requirement statements for
the two Master's degrees as approved by the mathematics faculty.
Graduate College requirements, further regulations, procedures,
and details are discussed in the next section.
Departmental Requirements: Master
of Science Degree in Applied Math
(Approved May 1991)
Specific Courses
- Advanced Calculus I and II (Math 4143, Math 4153)
- Advanced Linear Algebra (Math 5023)
- Complex Analysis (Math 4283)
- One Numerical Analysis course, 4000 level or above
- Case Studies in Applied Math (3 hours of Math 5580)
- One of the following: Methods of Applied Math
(Math 5593), or an additional 3 hours of Math 5580
- Four additional courses in Mathematics or
areas related to Applied Mathematics to be selected from the following:
- Intermediate Probability (Math 5113)
- Stochastic Processes (Math 5133)
- Fourier Analysis (Math 5213)
- Partial Differential Equations (Math 5233)
- Ordinary Differential Equations I or II (Math 5243, Math 5253)
- Numerical Analysis for Differential Equations (Math 5543)
- Numerical Analysis for Linear Algebra (Math 5553)
- Automata and Finite State Machines (Math 5653)
- Computability and Decidability (Math 5663)
- Calculus of Variations and Optimal Control (Math 5523)
- Advanced Probability Theory (Math 6123)
- Theory of Partial Differential Equations (Math 6233)
- Topics in Applied Math (Math 6590)
- Theoretical Numerical Analysis (Math 6513)
Courses outside the Mathematics Department must be approved by the
student's advisory committee. Computer Science courses must be beyond
programming courses (COMSC 4113 is considered a programming course).
Courses Taken in Graduate School
The courses taken in graduate school must total at
least 32 hours which may include two hours credit 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 Master's degree
program must include at least 21 hours of mathematics, statistics,
or computer science courses numbered 5000 or above. No more than
6 hours outside the mathematical sciences will count towards the
Master's degree. All the courses on the Master's degree program
must constitute a coherent whole and must be approved by the student's
advisory committee.
Comprehensive Examination
A Master's degree student must pass a comprehensive written
examination on Advanced Calculus, Advanced Linear Algebra,
Numerical Analysis, and Complex Analysis.
Creative Component, Report, or Thesis
Each student must complete either 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 Graduate Catalog contains detailed procedures and requirements applicable
to all Master's degrees.
Departmental Requirements: Master
of Science Degree in Pure Mathematics
(Approved November 1995)
Specific Courses
Option I:
- Advanced Calculus I and II (Math 4143 and 4153)
- Modern Algebra I and II (Math 4613 and 5013)
- General Topology (Math 5303)
- Complex Analysis (Math 4283 or Math 5283)
Option II:
Students interested in pursuing a doctoral degree
have the option of replacing the above courses with three of the
following sequences:
- Real Analysis I & II (Math 5143, Math 5153)
- Complex Analysis I & II (Math 5283, Math 5293)
- Geometric Topology & Algebraic Topology (Math 5313, Math 6323)
- Algebra I & II (Math 5613, Math 5623)
Courses taken as an undergraduate can be used to
satisfy the above requirements. If this is done the Master's degree
program can be more flexible.
Courses Taken in Graduate School
The courses taken in graduate school must total at
least 32 hours which may include two hours credit 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 Master's degree
program must include at least 21 hours of mathematics, statistics,
or computer science courses numbered 5000 or above. No more than
6 hours outside the mathematical sciences will count towards the
Master's degree. All the courses on the Master's degree program
must constitute a coherent whole and must be approved by the student's
advisory committee.
Comprehensive Examination
A Master's degree student must pass a comprehensive
written examination on Advanced Calculus, Modern Algebra, and
General Topology. If a student chooses option II above and if
grades of B or better are received in all three of the sequences
selected, then the student will be exempted from the Master's
Comprehensive Exam.
Creative Component, Report, or Thesis
Each student must complete either 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 Graduate Catalog contains detailed procedures
and requirements applicable to all Master's degrees.
Overview of Doctoral Programs
The Department of Mathematics offers two doctoral
degrees: a PhD and an EdD. The PhD degree is meant to prepare
a mathematician for a career in college instruction, university
research, or industrial research. The PhD 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. The EdD degree program,
sponsored by the Mathematics Department, is in conjunction with
the Department of Educational Administration and Higher Education.
It is designed to train expert college level instructors in mathematics.
The Mathematics Department at Oklahoma State University
has granted over 200 doctoral degrees. Graduates of either doctoral
program 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 long history of the degree programs
has allowed them to develop to a point where they give maximum
benefit to the students. A core of standard courses is required
of all students, allowing students to delay committing themselves
to the EdD or PhD until after they have been in school for over
a year. The faculty at Oklahoma State is highly recognized for
its accomplishments both in pure mathematical research and in
mathematics education. In the past several years two department
members have been named the College of Arts & Sciences outstanding
researchers. Three faculty have received the very prestigious
Sloan Foundation Fellowships. Many of the faculty members have
recently been supported by National Science Foundation research
grants. Others have received grant support for projects in mathematics
education. This kind of activity makes it possible for prospective
doctoral students to choose a specialty from a wide variety of
areas.
Highlights of a Doctoral Degree Program
A doctoral student must complete at least 60 hours
of graduate work beyond a Master's degree. The student must also
pass a written comprehensive exam, pass an oral qualifying exam,
and write a thesis. PhD students are also expected to demonstrate
mathematical reading ability in one foreign language. EdD degree
candidates are not required to take a foreign language exam, but
they must complete a qualifying exam given by the Department of
Educational Administration and Higher 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 thesis. The thesis itself is of integral importance
to both 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 PhD thesis is an original piece of relevant
mathematical research. The EdD thesis, on the other hand, is more
often expository in nature, yet it still must make a significant
contribution to mathematical understanding.
Beginning students concentrate on gaining general
knowledge in the core areas of algebra, topology, complex analysis,
and real analysis. They also take courses on more specific topics
and attend seminars to gain greater understanding of particular
research topics. After the core courses have been completed they
take their comprehensive exams. The next step is to gain specific
knowledge about an area of interest which might lead to a thesis
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 thesis, a qualifying
exam is administrated 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 thesis.
Sample Plans of Study
The actual course sequences taken by a doctoral candidate
will vary greatly depending on the preparation received in their
Master's work. The sample plans of study given are typical of
students entering with a Master's degree similar to that given
at OSU.
PhD in Mathematics
First Year
- Math 5313, Math 6323 Geometric Topology, Algebraic Topology I
- Math 5143, Math 5153 Real Variables I & II
- 6 hours of electives
Second Year
- Math 5613, Math 5623 Algebra I & II
- Math 5283, Math 5293 Complex Variables I & II
- 6 hours of electives
- PhD Comprehensive Exams
Third Year
- 6 to 9 hours of electives each semester; seminars; outside
readings
- Qualifying Exam
- Language Exam
Fourth Year
- 6 to 9 hours each semester consisting primarily of thesis-
related work
- Thesis Proposal
- Thesis Defense
Frequently students take electives, prepare for the
language exam, and work on research during the summers.
EdD in Mathematics
First Year
- Math 4143, Math 4153 Advanced Calculus I & II
- Math 5303, Math 5313 General Topology, Geometric Topology
- 6 hours of electives
Second Year
- Math 5613, Math 5623 Algebra I & II
- Math 5143, Math 5153 Real Variables I & II
- OR Math 5283, Math 5293 Complex Variables I & II
- 6 hours of electives
- EdD Comprehensive Exams
Third Year
- 6 to 9 hours of electives each semester, possibly including education requirements; seminars; outside readings
- Mathematics Qualifying Exam
- Education Qualifying Exam
Fourth Year
- 6 to 9 hours each semester involving primarily thesis-related work
- Thesis Proposal
- Thesis Defense
Frequently students take electives or education courses
in the summer as well as do thesis work.
Departmental Requirements for the
PhD and EdD
Requirements for the PhD in Mathematics
(Approved November 1995)
Credit Requirements
A total of 90 hours above the BS degree is required,
including credit hours for the PhD thesis.
Core Requirements
All candidates for the PhD Degree are required to
complete the following courses:
- MATH 5283, 5293 Complex Variables
- MATH 5143, 5152 Real Variables
- MATH 5613, 5623 Algebra
- MATH 5313, 6323 Topology
In addition to the above courses, every plan of study
must contain at least 12 hours of graduate mathematics courses
chosen from outside the field in which the student is specializing.
Comprehensive Examination
A PhD student must take the comprehensive examination
within one year of residence after completion of the required
course work. The comprehensive examination covers the content
of the four core courses described above.
Qualifying Examination
The student must pass an oral qualifying exam over
the area of specialization for their graduate study. This exam
covers the material on a reading list presented to the student
by their advisory committee. Its purpose is to test the student's
readiness to begin thesis work.
Thesis Proposal
An outline of the proposed thesis research must be
presented to the student's advisory committee for approval. A
written proposal is then filed with the Graduate College.
Foreign Language Requirement
Candidates must pass an examination demonstrating
reading knowledge of one foreign language, usually French, German,
or Russian, before they take the final examination to defend their
thesis. Other languages may be substituted subject to recommendation
of the student's committee and approval of the Graduate Committee.
Thesis
A thesis must be written according to Graduate College
guidelines. The thesis consists of an original research contribution
in Mathematics.
Graduate College Requirements
All requirements listed in the Graduate Catalog must
be satisfied.
Requirements for the EdD in Mathematics
Credit Requirements
A total of 90 hours above the BS degree is required,
including credit hours for the EdD thesis. At least 60 of these
must be in the mathematical sciences.
Core Requirements
1. Mathematics
All candidates for the EdD degree are required to
complete the following courses:
- MATH 4143, 4153 Advanced Calculus I, II
- MATH 4613, 5013 Modern Algebra I, II
- MATH 5303 General Topology
In addition the student must complete at least two
of the following three sequences:
- MATH 5283, 5293 Complex Variables I, II
- MATH 5143, 5153 Real Variables I, II
- MATH 5613, 5623 Algebra I, II
2. Statistics, Computer Science, and Numerical Analysis:
At least 6 graduate hours must be taken in either
statistics, computer science, or numerical analysis. Normally,
this requirement is satisfied by a pair of courses from the following
list:
- STAT 4013, STAT 4023
- STAT 4403, STAT 5043
- STAT 4613, STAT 4213
- COMSC 3333, COMSC 4343
- COMSC 3443, COMSC 4263
- MATH 4513, MATH 4553
- MATH 6513, MATH 5543
- MATH 5553
3. Education
The student must complete at least 15 hours of EAHED courses.
Required courses are:
- EAHED 6753 Development and Organization on Higher Education
- EAHED 6813 Curriculum Development in Higher Education
- EAHED 6230 Critical Issues in Higher Education
- EAHED 6843 The Academic Department
Additional courses may be selected from the following:
- EAHED 5853 Educational Systems, Design and Analysis
- EAHED 6263 Supervision
- EAHED 6683 The Community Junior College
- EAHED 6850 Directed Readings
4. Thesis Work
At least 10 hours of Math 6000 (thesis) are required.
Comprehensive Examination in Mathematics
Before being admitted to candidacy the student must
pass the Comprehensive Examination in the mathematical sciences.
The exam covers the material approximated by the core mathematics
courses and it should be taken within a year of completion of
the core courses.
The student has several options for topics on which to be examined.
In general, the student will be tested on the following topics:
- Complex Variables Math 5283, 5293
- Real Variables Math 5143, 5153
- General Topology Math 5303
- Algebra Math 5613, 5623
- Computer Science/Statistics/Numerical Analysis 6 hour sequence
(selected by student)
Advanced Calculus (Math 4143, 4153) can be substituted
for Complex Variables or Real Variables. If this substitution
is NOT made, then Algebra can be replaced by Modern Algebra I
(Math 4613) and Modern Algebra II (Math 5013).
Qualifying Examinations
The Qualifying Examination is required by the Graduate
College. The examination consists of two parts, one administered
by the Department of Educational Administration and Higher Education
and one administered by the Department of Mathematics.
Thesis Proposal
An outline of the proposed thesis research must be
presented to the student's advisory committee for approval. A
written proposal is then filed with the Graduate College.
Foreign Language Requirement
None
Thesis
A thesis must be written according to Graduate College
guidelines. The thesis consists of an original or expository research
contribution to mathematics or mathematics education.
Graduate College Requirements
All requirements listed in the Graduate Catalog must
be satisfied.
The Mathematics Learning Resource Center (MLRC) is
a combination microcomputer, video, and tutorial laboratory which
supplements undergraduate mathematics instruction. It is located
on the lower level of South Murray Hall (down Monroe from the
math building and across the street from Theta Pond). It is under
the direction of Catherine Costanza and is managed on a day to
day basis by highly qualified and talented undergraduate staff.
Resources available in the MLRC include:
- A lab of 36 microcomputers arranged in a classroom
configuration and connected with a local area network.
Software for the computers includes:
- A lab with 10 VCR/TV stations and one of the
largest collections of high-quality mathematics videotapes anywhere.
Topics range from arithmetic through algebra, trigonometry and
calculus to differential equations.
- Undergraduate tutors are available to tutor
students from Beginning Algebra through Linear Algebra level classes.
Students may stop in any time the MLRC is open, no appointment
is necessary.
Math Faculty
In this section an attempt is made to describe some
of the many diverse interests of the faculty in the Department
of Mathematics at Oklahoma State University. A list is given of
the faculty for 1996-97, along with their degrees and institutions
where these degrees were granted. Following this list is a breakdown
of the research programs into several areas. Such a classification
is difficult to make as many faculty have interests in many areas.
However, the information should give a feel for some of the work
that is being conducted by department faculty.
Faculty List (1996-97)
- Alan Adolphson, PhD, Princeton 1974
- Doug Aichele, EdD, Missouri-Columbia 1969
- Dale Alspach, PhD, Ohio State 1976
- Dennis Bertholf, PhD, New Mexico State 1968
- Birne Binegar, PhD, UCLA 1982
- Hermann Burchard, PhD, Purdue 1968
- J.T. Chang, PhD, Harvard 1985
- James Choike, PhD, Wayne State 1970
- James Cogdell, PhD, Yale 1981
- J. Brian Conrey, PhD, Michigan 1980
- Bruce Crauder, PhD, Columbia 1981
- Edward Dunne, PhD, Harvard 1984
- Benny Evans, PhD, Michigan 1971
- Amit Ghosh, PhD, Nottingham 1981
- William Jaco, PhD, Wisconsin 1968
- Sheldon Katz, PhD, Princeton 1980
- Marvin Keener, PhD, Missouri-Columbia 1970
- Weiping Li, PhD, Michigan 1992
- Lisa Mantini, PhD, Harvard 1983
- Mark McConnell, PhD, Brown 1987
- Robert Myers, PhD, Rice 1977
- Alan Noell, PhD, Princeton 1983
- Wayne Powell, PhD, Tulane 1978
- Zhenbo Qin, PhD, Columbia 1990
- David Ullrich, PhD, Wisconsin 1981
- Dave Witte, PhD, Chicago 1985
- John Wolfe, PhD, Berkeley 1971
- David Wright, PhD, Harvard 1982
- Akihiko Yukie, PhD, Harvard 1986
- Roger Zierau, PhD, Berkeley 1985
Faculty Research Interests
Algebra
Universal algebra is the study of different classes
of algebras and the properties that are either common to them
or that make these classes special. Classes of algebras are identified
as to the structures that can be constructed within them, maintaining
all the properties of the class. Such classes are often characterized
in terms of equations or implications involving the operations
standard to all algebras in the class. Most of the research in
universal algebra at OSU has been done by Wayne Powell, who works
primarily with classes of algebras carrying an inherent order
structure. This work has also been funded by the National Science
Foundation.
One of the more classical areas of interest in algebra
at OSU is abelian group theory. This area has its roots in the
foundations of algebra. Group theory has split into several different
fields. One of these fields, abelian groups, has been developed
as completely as almost any other area of modern mathematics.
A number of applications have arisen in homological algebra as
well as other areas.
Dennis Bertholf is the faculty member with the primary
expertise in abelian group theory.
Research Interests in Algebra
Dennis Bertholf: Interests are in the areas of Abelian
p-Groups and Homological Algebra
Wayne Powell: Main research interest is in universal algebra with
a special interest in ordered algebraic structures. These structures
arise naturally from functional analysis and classical group theory and
have been studied extensively during the last four decades. Particular
work is with finding descriptions of the universal objects such as free
algebras and free products of algebras and with considering universal
embedding properties that relate to these objects. Research on these
topics has only become wide-spread in the past ten years. The techniques
involved in this work are a combination of those from pure group
theory, universal algebra, and ordered group theory.
David Witte: He is also interested in applications of group theory to
problems in graph theory.
Algebraic Geometry
Algebraic geometry is the study of polynomial equations
and their graphs, which are called algebraic varieties. Classification
of algebraic varieties, the geometry of special algebraic varieties
and the description of mappings of algebraic varieties are important
problems of current research interest. Algebraic geometry is closely
related to some areas in differential geometry and topology, commutative
algebra, and number theory. In addition to continuing faculty
members Bruce Crauder, Sheldon Katz, and Zhenbo Qin, the department
has had a number of visitors working in algebraic geometry. The
National Science Foundation as well as the National Security Agency
have provided funding for OSU research in algebraic geometry.
Research Interests in Algebraic Geometry
Bruce Crauder: Main interest
is the study of three-dimensional algebraic varieties, particularly
questions about birational geometry, and degenerations of surfaces.
One secondary interest is the geometry of resolutions of some
three-dimensional singularities. Recent collaboration is with
S. Katz on a project involving higher dimensional Cremona
transformation-the birational geometry of projective spaces.
Sheldon Katz: Main research interest is algebraic geometry,
focusing on the classification of algebraic varieties (the solution
set of a finite collection of polynomial equations in several variables),
as well as the converse problem of recovering the equations from the
variety. Often techniques of projective geometry (both classical and
modern), deformation theory (i.e., perturbing the equations), and Hodge
theory are used. Also, some interest lies in applications of algebraic
geometry to computer modeling as well as to superstring theory
in physics.
Zhenbo Qin: My research field is algebraic geometry, which is the
study of spaces called varieties. These are generalizations of the
Riemann sphere in complex analysis with one variable. The subject
has a close relation with algebra.
Analysis
Workers in mathematical analysis at OSU conduct research
in a variety of areas. There are groups in functional analysis
and in complex/harmonic analysis, as well as workers in the areas
of approximation theory, differential equations, numerical analysis,
and probability theory, among others. In this brief introduction
only activity in Banach space theory and complex/harmonic analysis
are described in any detail; the statements of research interests
in the next section provide information on all areas represented.
There are active research programs under way in both
the infinite dimensional and local theory of Banach spaces. In
the infinite dimensional theory the main focus is the problem
of classification of complemented subspaces of classical Banach
spaces such as LP and C(K). In local theory highly geometric
investigation of convex bodies is under way. Of particular
interest is the classification of projection bodies and sections of
bodies which arise naturally in classical spaces.
The Banach space theory group regularly sponsors
visits from other experts in this area of research and participates
in joint seminars with researchers at the University of Texas
and Texas A&M University. Research in Banach space theory
at Oklahoma State has been regularly supported by the National
Science Foundation.
In complex/harmonic analysis there is activity in
the areas of boundary values of holomorphic functions and geometric
properties of pseudoconvex domains. With regard to boundary values,
there has been work on H, BMOA, and the Bloch space (among others)
in the disc and the ball. In the study of pseudoconvexity, the
focus of attention has been convexity properties, considered in
terms of function algebras and holomorphic mappings.
Research Interests in Analysis
Dale Alspach: Main interest is in the geometry of infinite dimensional
Banach spaces. Of particular interest is the nature of complemented
subspaces of the classical Banach spaces which arise in various parts
of analysis. Recently this has led to some problems in harmonic analysis
concerning the complementation of certain translation invariant subspaces
of L1 and H1 of locally compact abelian groups.
Hermann Burchard: Interested in approximation theory, numerical analysis,
spline functions of one or more variables, optimization, and solution of
ordinary and partial differential equations.
James Choike: Interests in analysis include: complex variables,
function theory, boundary behavior of analytic functions.
Marvin Keener: Interests lie primarily in the qualitative theory
of ordinary differential equations. More specifically, the study of
distribution of zeros and asymptotic behavior associated with solutions
of linear differential equations. The problems originate with the study
of the calculus of variations and the generalization of those concepts
to other settings. Also studies are made of the stability of nonlinear
systems with a particular emphasis on bifurcation theory.
Alan Noell: Interested in Several Complex Variables in general
and in convexity properties of pseudoconvex domains in particular. Much
of the work relates to peak sets and boundary interpolation sets. Also
work is done on constructions of proper holomorphic maps to convex
domains.
David Ullrich: Harmonic analysis: Fourier series (especially random
Fourier series and lacunary series - these are certain non-random
Fourier series which emulate random Fourier series in various ways),
Hardy spaces, boundary behavior of harmonic/analytic function in one
and several variables, Besov spaces and related topics. Recently: Of
course the distribution of a partial sum of a (complex) lacunary series
is not actually "smooth" - it is concentrated on a curve.
But if you look at the distribution at a large enough scale it
appears smooth, and even normal. Now suppose we are looking at
one of these things from a fair distance and we begin to zoom
in on it. At what point does the distribution begin to look irregular?
This question is not very well-defined; it might be regarded as
the motivation behind a few specific questions I've been studying
concerning such things as recurrence of lacunary series or the
geometric means of such series. (It is not hard to see that under
appropriate hypotheses the partial sums must be "almost recurrent"
(at almost every point of the circle) in that they must return
to any disc of radius 10 infinitely often. The problem is to replace
10 by here - as of recently I can do this for the real part.)
John Wolfe: A wide-ranging general interest in analysis including
general functional analysis, Banach space theory, theory of continuous
function spaces, and approximation theory. Research work has generally
been confined to Banach space theory.
David Wright: Interested in the theory of Riemann surfaces,
where work is done on the structure of Teichmuller space.
Lie Groups and Representation Theory
OSU has an active group of mathematicians working
on Lie groups and their representations. This is a very interesting
and active area of research at this time. Lie Theory has connections
with many branches of mathematics as well as physics. The faculty
here is mainly concerned with representation theory of semi-simple
Lie groups. A Lie group is (usually) a closed subgroup of the
group of n x n invertible matrices, for example, the group of
orthogonal matrices or the Lorentz group (those matrices which
preserve the space-time metric). Lie groups arise very naturally
as groups acting in interesting ways on geometric systems, for
example as groups of transformations preserving a Riemannian metric
or preserving a system of differential equations. A representation
of a Lie group G is a continuous homomorphism from G into the
space of continuous linear operators on a topological vector space
(often infinite dimensional). In a very broad sense the underlying
problems in representation theory are to "decompose"
(large) representations into their irreducible constituents and
to understand in great detail the irreducible ones. The former
is often called noncommutative harmonic analysis as it is the
analog for a noncommutative group G of Fourier analysis for the
groups R (or the circle group). The latter involves classification
and construction of irreducible representations as well as determining
certain of its properties (such as unitarity).
Numerous techniques have been very useful in representation
theory and many relationships between different fields of mathematics
have resulted. The various techniques include ideal theory for
noncommutative rings, algebraic and differential geometry (including
D-modules and complex manifolds) and functional analysis. Here
at OSU we are mostly interested in geometric techniques. See the
more detailed descriptions below.
Many faculty members at OSU who work in other areas
of mathematics use Lie Theory in their research. For example Jim
Cogdell, a number theorist, studies automorphic forms. This is
a subject which uses Lie group techniques to obtain results in
number theory. Besides number theory, there are strong connections
with topology, algebraic geometry, differential equations, and
mathematical physics. Lie groups also provide many excellent and
concrete examples of powerful theorems in various fields of mathematics
(especially geometry and topology). For these reasons we encourage
students (especially PhD students) learn some Lie theory, even
if they choose to specialize in a different area. Special topics
courses are often offered and there is an active weekly seminar
in Lie groups. Also, there are many opportunities for Master's
students to complete an interesting creative component in this
subject.
Research Interests in Lie Groups and Representation Theory
Faculty working in the theory of Lie groups at OSU
are:
Birne Binegar
J. T. Chang
Edward Dunne
Lisa Mantini
David Witte
Roger Zierau
Edward Dunne: My research interests lie in the following
three broad categories, listed in order: Representations of Semi-
simple Lie Groups, Complex Geometry, and Mathematical Physics. The
principal part of my research is to try to find geometric
constructions of infinite-dimensional representations of semi-simple
Lie groups. The paradigm for this approach is Schmid's thesis. The
type of geometry that I do depends heavily on group theory. For
instance, I like to look at structures or differential objects that
are invariant with respect to some group action. The physics that I
know is mostly twistor theory, which is a way of using complex integral
geometry to understand some of the differential equations of particle
physics and general relativity. Here again, I emphasize the parts of
twistor theory where groups play a major role.
David Witte: Main research interest is in algebraic aspects
of the study of Lie groups. Arithmetic groups are a particular
emphasis. For example, it is known that many arithmetic groups have
essentially no normal subgroups, and he is interested in extending this
by showing that there are no "almost normal" subgroups, either
(and also no normal sub-semigroups). He is also interested in
understanding how these algebraic properties are reflected in the
actions of the groups. For example, it should be the case that most
arithmetic groups are too complicated to be able to act on a one-
dimensional space such as the real line.
Number Theory
Beginning in the early eighties, the Department of
Mathematics at Oklahoma State University adopted the approach
of recruiting tightly knit groups of research mathematicians all
at once, rather than one mathematician at a time. The first success
in this venture is a group of six young number theorists, eagerly
bent first and foremost on refining and promoting their craft.
Already they have established a thriving program of research,
including a regular seminar series featuring lectures of both
a research and expository nature by the resident number theorists,
as well as frequent lectures by distinguished young and senior
number theorists from around the country.
In 1984, members of this research group organized an
international conference in Stillwater on analytic number theory,
attracting many mathematicians of the highest possible caliber
(conference proceedings: Birkhauser, Progress in Mathematics,
vol. 70). All six members of the groups have received continuous
NSF support. Three have received Sloan fellowships. Members of
this group have played key roles in securing two recent NSF computer
equipment grants for our department. Number theory is famed not
just for the beauty of its theorems, but for the enormous wealth
and variety of techniques involved in discovering and proving
these theorems. Number theory has drawn on and inspired developments
in complex analysis, harmonic analysis, representation theory,
and algebraic geometry. In line with our focus on research groups
with a unity of research efforts, our department has recently
hired core groups of young algebraic geometers and representation
theorists. In addition, there are active researchers in harmonic
analysis and pure algebra. There is ample opportunity at Oklahoma
State University to gain the broad understanding of modern mathematics
necessary to pursue research in number theory.
Research Interests in Number Theory
Our faculty is prepared to offer courses in algebraic
number theory, class field theory, analytic number theory, the
arithmetic of elliptic curves as well as other arithmetic algebraic
varieties, p-adic analysis, automorphic and modular forms, discrete
subgroups of algebraic groups, computational number theory, as
well as many other subfields of number theory.
Alan Adolphson: Main interest is the study of L-functions
of algebraic varieties over finite fields, using cohomological
techniques. Most recent work has been on exponential sums, using
both p-adic and l-adic cohomologies. Also interested in studying
the variation of cohomology within a family of varieties, which
involves among other things the classical Fuchs-Picard differential
equation.
James Cogdell: Research interest is centered on automorphic
representations and L-functions. Presently at work on a book (with
Piatetski-Shapiro) on L-functions for automorphic representations of
GL(n). Current research projects are the extension of Hecke's converse
theorem to GL(n) and applications of this converse theorem to liftings
of automorphic forms and indirectly to class field theory. This also
involves the study of Rankin-Selberg theory of L-functions for classical
groups. Also interested in application of theta liftings to arithmetic.
Brian Conrey: Main interest is in the classical problems
of analytic number theory. Most work involves the Riemann zeta function
(or more general zeta of L-functions) and pertains to mean-values or
to the distribution of zeros. Also interested in methods from the theory
of automorphic forms, especially in connection with the above problems.
Amit Ghosh: Main interest is in analytic number theory. More
precisely, it is in analyzing L-functions (of number fields, automorphic
forms, etc.) to see the arithmetic they contain. All this work contains
in one form or another the interplay between arithmetic and harmonic
analysis. Most published work revolves around the distribution of zeros
of the Riemann zeta function. Current work involves automorphic
L-functions.
David Wright: Main research interest is the relation between
algebraic number theory and algebraic groups. First work proved
theorems on the distribution of cubic extensions of number fields
using the theory of equivalence of binary cubic forms. Now involved
in a general project together with A. Yukie using "zeta
functions" associated with representations of algebraic groups
to prove theorems about algebraic number fields. Secondary interest
is in the theory of Riemann surfaces, where work has been done on the
structure of Teichmuller space.
Akihiko Yukie: General interest is the theory of algebraic
groups over algebraic number fields, especially from the point of
view of geometric invariant theory. Presently occupied with
generalizing Shintani's zeta functions. These are functions
associated with representations of reductive groups over number
fields; however, they are not the automorphic L-functions occurring
in Langlands' theory. The main reason for studying this subject
is to determine the distribution of equivalence classes orbits
under the action of the group. This in turn may be used to prove
the existence of certain rational orbits with given geometric
properties.
Topology
There is a very strong group of topologists at OSU.
There is normally an active topology seminar with good graduate
student participation. The topology research at OSU is concentrated
in the area of low dimensional manifolds. There is good reason
to study such objects. The universe we live in is normally thought
of by physicists as a four dimensional manifold.
Three and four dimensional manifolds are unique in
many surprising ways. The biggest recent surprise was the proof
by Donaldson that four dimensional Euclidean space was more than
one differentiable structure. In all other dimensions, there is
only one such structure. This is particularly striking when one
considers the fact that we live in a four dimensional manifold.
One of the most difficult problems in topology is to determine
when things are different and when they are the same. There are
natural group invariants associated with manifolds. Perhaps the
single most interesting problem in low dimensional topology is
to determine to what extent group invariants characterize a manifold.
It is for example not known if the three sphere is characterized
by its group variants. This is the classical Poincare conjecture.
It is known to be true in every dimension except three. It was
thought for many years that three dimensional manifolds were generally
lacking geometric structure. Mathematicians were wrong in a big
way. In the seventies Thurston showed that most (perhaps all)
compact three manifolds are in fact very rich in geometric structure.
Even more surprisingly the natural geometry for the most common
three manifolds is not Euclidean, but rather hyperbolic. (There
are infinitely many lines through a given point parallel to a
given line.) The existence of this structure has allowed problems
that seemed untouchable ten years ago to be attacked and solved.
The classical Smith conjecture that circles left fixed by group
actions on the three sphere must be unknotted is now the Smith
theorem. It is a very exciting time in low dimensional topology.
The Poincare conjecture is no longer thought to be unreachable,
and Thurston's structure theorems may even lead to a classification
scheme for all compact three manifolds. Mathematicians at OSU
are heavily involved in studying these problems and will be a
part of their final solutions.
Research Interests in Topology
Benny Evans: Main research interest is in low dimensional
topology and work that involves a regular use of group theory. Research
centers around describing three-dimensional manifolds.
William Jaco: Research area is low-dimensional topology.
Most of the investigations involve 3-manifolds and combinatorial
group theory.
Mark McConnell: Main interest in the topology of locally symmetric
spaces, an area where many parts of mathematics are used together.
A locally symmetric space is made from a semisimple Lie group G
(or rather from its quotient G/K by a compact subgroup) by taking
the quotient by a descrete subgroup of G. So the space contains
Lie-theoretic information (from the discrete subgroup), and the
geometry of the space is beautiful for its own sake. The work has
applications in number theory, automorphic forms, algebraic geometry,
and analysis.
Robert Myers: My main area of research is the topology of 3-dimensional
manifolds. Most of my work has been about the structure and class-
ification of compact 3-manifolds, group actions on these spaces, and their
knot theory. In recent years I have been concerned with non-compact
3-manifolds, attempting to discover to what extent classical theorems
about compact 3-manifolds generalize to the non-compact case and
also which non-compact 3-manifolds can be covering spaces of compact
3-manifolds. The main tools used in my research are the fundamental
group and covering spaces, piecewise-linear and differential topology,
algebraic topology, combinatorial group theory, and hyperbolic
geometry. A secondary interest of mine is geometric group theory,
which uses methods from geometry, topology, and automata theory
to work on problems in group theory.
Weiping Li: Research interests on low dimensional topology.
Most of the investigations involve 3-manifolds, Casson invariants
and Floer homology. Most of the methods used are from gauge theory,
nonlinear analysis on infinite dimensional manifolds, symplectic
topology and dynamical systems.
Introduction
Mathematics education is a primary activity of the
Department of Mathematics at Oklahoma State University. In the
broad overall view, mathematics education encompasses pure and
applied mathematical research, mathematics teaching at the Baccalaureate,
the Master's, and the Doctorate level, the development of mathematics
curriculum, the use of the latest that technology has to offer
to promote and enhance mathematics learning, pre-service and in-service
programs for mathematics teachers at all levels, and the development
of programs to increase the awareness and importance of mathematics
among students in their early formative school years. The Department
of Mathematics at OSU has been and is currently very active in
all of these areas of mathematics education.
The Mathematics Department has established an outstanding
record of federally funded projects of national importance and
impact in mathematics related to student and teacher development.
During recent years leadership has come from our department with
the administration and implementation of seven major student/teacher
development projects funded from federal sources. Project objectives
include producing a catalog of industrial problems to be used
as instructional materials for use in a college/university mathematics
classroom, mathematics career awareness materials for high school
students, applied mathematics learning modules for both the high
school and college/university mathematics student, designing and
implementing a new teacher preparation program for middle school
teachers of mathematics, and researching whether teleconference
instruction can help the entry year teacher of high school mathematics
become better at problem solving and at the teaching of problem
solving. These projects, taken collectively, illustrate the commitment
and energy of the department to improving the learning and teaching
of mathematics. Many of these projects are currently in progress.
The total federal funding or these collective projects exceeds
$3,000,000.
Highlights of departmental activities in mathematics
education follow.
Development of Mathematics Curriculum
The Department of Mathematics has an outstanding
record of accomplishments in the area of the development of mathematics
curriculum. The record and the tradition began with the National
Science Foundation (NSF) funded project to the OSU Department
of Mathematics to develop instructional materials for applied
mathematics utilizing actual industrial case-studies of applied
mathematics. The case studies in applied mathematics lead to further
funded projects in curriculum materials development in applied
mathematics. The Teaching Experiential Applied Mathematics (TEAM)
project, funded by the U.S. Department of Education and sponsored
by The Mathematical Association of America (MAA), developed written
material, video, and microcomputer software on industrial applied
mathematics for use by other college mathematics instructors as
classroom materials on applied mathematics. The Application in
Mathematics (AIM) project, again funded by NSF and sponsored by
the MAA, carried the OSU model of applied mathematics, with materials
similar to TEAM, to the secondary school classroom. The TEAM and
the AIM materials are currently in use in college and high school
classrooms across the United States.
Mathematics Awareness Programs
The Mathematics Department has long recognized the
value of presenting to students early in their school years while
their academic choices still lay ahead of them. The importance
of mathematics is a key to career choices in adulthood. OSU addressed
this need with the NSF-funded Mathematics at Work in Society (MAWIS)
project. MAWIS is a career and mathematics awareness package,
consisting of written and video materials which are targeted for
students of grades 8 and above. The MAWIS project was conceived
and developed by faculty of the OSU Department of Mathematics
for the MAA. MAWIS materials were disseminated by the MAA nationwide.
On the statewide scene the Mathematics Department
has been the leader in instituting the Early Placement Evaluation
in Mathematics (EPEM). This is a mathematics evaluation program
designed to inform high school juniors about their present level
of mathematics skills in terms of college requirements, to provide
information regarding mathematics requirements for degree programs
at Oklahoma institutions for higher education, and to increase
the awareness of the importance of mathematics learning in high
school for success in college. The EPEM program provides each
student tested with a personalized report containing his/her college
mathematics placement level, a list of mathematics competencies
and deficiencies, and recommendations on how to prepare mathematically
for college during their senior year of high school.
Pre-service and In-service Preparation Programs
The Department of Mathematics is an active partner
with the Department of Curriculum and Instruction of the College
of Education in the design, development, and implementation of
pre-service and in-service programs for teachers of mathematics
at the secondary and middle school level. The OSU Department of
Mathematics is currently involved through faculty participation
and resources in the development of a four-year undergraduate
academic program for the preparation of students for middle school
(grades 5 - 9) mathematics teaching. This project, entitled "The
DIRECT Middle School Mathematics and Science Project," is
a five-year project funded by the NSF. It is one of only nine
such projects funded by NSF.
In-service programs for mathematics teachers offered
by the Mathematics Department have included workshops and seminars
by our faculty on a multitude of topics usually in response to
requests by schools and their teachers. A strength of OSU is its
teleconferencing facility, the Educational Telecommunications
Center. The Department of Mathematics produces an impressive and
wide variety of in-service and enrichment presentations from this
state-of-the-art telecommunications facility. Just a sample of
the topics presented include: teaching problem solving, a mathematical
perspective on the Electoral College System, topics in probability
and statistics, mathematics preparation for the college bound,
and others. The NSF-funded project "Teleconferencing Instruction
in Problem Solving" (TIPS) is another example of in-service
outreach programming by the Mathematics Department via
telecommunications.
Technology in Mathematics Instruction
The Mathematics Department has designed and developed
a model facility for mathematics learning for students at OSU.
This facility is called the Mathematics Learning Resource Center
(MLRC). It includes a microcomputer lab, a video review lab, and
a tutoring lab staffed by qualified undergraduate mathematics
majors. The Department's faculty have developed an extensive library
of microcomputer software and video review cassettes which offer
to OSU students individualized instruction on any topic of mathematics
from arithmetic, algebra, trig to calculus, and all the way up
through linear algebra and differential equations. The MLRC is
a learning center where students who need help on a topic of mathematics
can get it on a drop-in basis at their choice of a microcomputer
work station, a TV monitor, or with the aid of an experienced
mathematics tutor.
The MLRC also serves as a research lab for faculty
in the area of mathematics education enabling them to develop,
test, and implement the latest in microcomputer technology to
mathematics instruction. Telecommunications technology and its
role in mathematics learning is another area of current departmental
activity. The Department is presently working with the OSU College
of Arts and Sciences in testing the feasibility of delivering
teleconference instruction via satellite of needed mathematics
courses to high schools across the nation. PreCalculus and Advanced
Placement Calculus are being offered primarily to rural schools
desiring to present a college level calculus course to their college-
bound students.
Cooperation with Department of
Curriculum and Instruction
The Mathematics Department enjoys close ties of professional
cooperation with the Department of Curriculum and Instruction
in the College of Education. Both departments are active partners
on the DIRECT Middle School Mathematics and Science Project, the
TIPS Project, and the EdD Degree program. In addition, the departments
have marshaled their expertise to conduct in-service workshops
and seminars as well as teleconferences on problem solving and
other enrichment topics in mathematics for teachers and students.
This climate of cooperation fosters interactions over a multitude
of mathematics education issues that result in action in the form
of successful proposal ideas for federal funds.
Faculty Working in Mathematics Education
A number of the faculty in the Mathematics Department
have been involved in one or more of the mathematics education
projects in recent years. They are as follows:
Jeanne Agnew (Emeritus)
Doug Aichele
Dennis Bertholf
James Choike
Benny Evans
John Jobe (Emeritus)
Marvin Keener
Ignacy Kotlarski (Emeritus)
Wayne Powell
John Wolfe
Doug Aichele: I am interested in the issues of school
mathematics (i.e., school mathematics curriculum, instruction,
learning, and assessment) and the professional development of
teachers of mathematics (i.e., pre-service preparation and
continuing education). I have a particular interest in school
geometry (i.e., curriculum, instruction, learning, and assessment)
and the appropriate use of technology applied to it.
Overview of Master's Programs
The department offers Master's degrees in both Mathematics
and in Applied Mathematics. The Master of Science in Mathematics,
which emphasizes basic work in mathematics, prepares the student
for teaching mathematics at the high school, junior college, or
four year college level as well as for working in industry. The
Applied Mathematics degree requires greater breadth within the
mathematical sciences (including statistics and computer science)
and is intended to prepare students for positions in business,
industry, and government. Both degrees can prepare the student
for doctoral work leading to a career in either mathematical research,
university instruction, or mathematics education. Master's programs
are varied and are planned on an individual basis. Graduates of
the Master's degree programs in mathematics continue to be highly
successful in obtaining diverse professional positions upon graduation.
A few examples of recent graduates and their initial positions
are:
- Michael McClurkan Bell Laboratories, Chicago
- Joe Swartz Martin Marietta, Denver
- Sherri Hinds Oklahoma City Public Schools
- Doug Punke Arkansas College, Batesville, AR
- Chuck Davison E-Systems, Dallas
- Charles Matthews PhD student, OSU
- Jeff Dimick Hughes Aircraft, Los Angeles
- Retha Ulbrich McDonnell Douglas, St. Louis
- William King NE Oklahoma State University, Tahlequah
- Jack Rau Rahco Corporation, Oklahoma City
- Bryan Smith National Security Agency, Washington, D.C.
- Vicky Hite General Dynamics, Ft. Worth
- Lisa Patterson Bell Laboratories, New Jersey
A student with a strong interest in some related
field outside mathematics is encouraged during graduate work to
develop further competence in this related area. In addition,
students are encouraged to do exploratory work in other areas
of the mathematical sciences such as computing and statistics.
The department's excellent computing facilities are freely available
to all graduate students.
Companies employing OSU graduate students in the
past few summers include Telex (Tulsa), American Fidelity Assurance
(Oklahoma City), Texas Instruments (Dallas), McDonnell Douglas
(St. Louis), Eyring Research (Provo, Utah), Hughes Aircraft (Los
Angeles), Ammann & Whitney Consulting Engineers (New York
City), BDM Corporation (Washington, D. C.), Federal Aviation
Administration (Oklahoma City) and Oak Ridge National Research
Laboratories (Oak Ridge, TN).
Highlights of a Master's Degree Program
The following highlights of a Master's program are
described in more detail in later sections.
A Master's degree in mathematics requires 30 to 32
semester hours of courses. In addition, the student must pass
the departmental Master's examination and complete a creative
component, report, or thesis. These requirements can be completed
in two years.
During the second semester each student, with the
aid of the graduate director, sets up a Master's committee of
three faculty members. The chairman and the other two members
of this committee advise and oversee the student's progress toward
a degree.
Each Master's student, working individually with
a faculty member, must complete a creative component, report,
or thesis. This project, which provides an excellent opportunity
to investigate a topic in an area of special interest to the student,
includes writing a paper and giving a public oral presentation.
Each Master's student must pass a comprehensive examination
covering some of the basic concepts in modern mathematics.
The director of the graduate program works closely
with new students to select their courses and to get them off
to a good start. Beyond the required courses considerable variety
is possible in elective courses which may be taken in computer
science and statistics as well as mathematics. 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. Samples are as follows:
Master of Science Degree in Applied Math
First Year
Fall Semester
- Math 4143 - Adv Calculus I
- Math 4513 - Numerical Analysis
- Elective 1
Spring Semester
- Math 4153 - Adv Calc II
- Math 5583 - Applied Math
- Math 5023 - Adv Linear Algebra
Second Year
Fall Semester
- Math 5593 - Applied Math II
- Math 4283 - Complex Analysis
- Elective 2
- Master's Comprehensive Exams
Spring Semester
- Math II Elective 3
- Elective 4
- Creative Component, Report, or Thesis
First Year
Fall Semester
- Math 4143 - Adv Calculus I
- Math 4613 - Modern Algebra I
- Elective 1
Spring Semester
- Math 4153 - Adv Calc II
- Math 5013 - Modern Algebra II
- Elective 2
Second Year
Fall Semester
- Math 5303 - General Topology
- Math 4283 - Complex Analysis
- Elective 3
- Master's Comprehensive Exams
Spring Semester
- Elective 4
- Elective 5
- Creative Component, Report, or Thesis
Departmental Requirements for the
Master of Science Degree
The following are the official departmental requirement
statements for the two Master's degrees as approved by the mathematics
faculty. Graduate College requirements, further regulations, procedures,
and details are discussed in the next section.
Departmental Requirements for the Master of Science Degree in Applied Mathematics
(Approved May 1991)
Specific Courses
- Advanced Calculus I and II (Math 4143, Math 4153)
- Advanced Linear Algebra (Math 5023)
- Complex Analysis (Math 4283)
- One Numerical Analysis course, 4000 level or above
- Case Studies in Applied Math (3 hours of Math 5580)
- One of the following: Methods of Applied Math (Math 5593)
or an additional 3 hours of Math 5580
- Four additional courses in Mathematics or areas related
to Applied Mathematics. The Mathematics courses must come from
the following:
- Intermediate Probability (Math 5113)
- Stochastic Processes (Math 5133)
- Fourier Analysis (Math 5213)
- Partial Differential Equations (Math 5233)
- Ordinary Differential Equations I or II (Math 5243,
Math 5253)
- Numerical Analysis for Differential Equations (Math 5543)
- Numerical Analysis for Linear Algebra (Math 5553)
- Automata and Finite State Machines (Math 5653)
- Computability and Decidability (Math 5663)
- Calculus of Variations and Optimal Control (Math 5523)
- Advanced Probability Theory (Math 6123)
- Theory of Partial Differential Equations (Math 6233)
- Topics in Applied Math (Math 6590)
- Theoretical Numerical Analysis (Math 6513)
Courses outside the Mathematics Department must be
approved by the student's advisory committee. Computer Science
courses must be beyond programming courses (COMSC 4113 is considered
a programming course).
Courses Taken in Graduate School
The courses taken in graduate school must total at
least 32 hours which may include two hours credit 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 Master's degree
program must include at least 21 hours of mathematics, statistics,
or computer science courses numbered 5000 or above. No more than
6 hours outside the mathematical sciences will count towards the
Master's degree. All the courses on the Master's degree program
must constitute a coherent whole and must be approved by the student's
advisory committee.
Comprehensive Examination
A Master's degree student must pass a comprehensive
written examination on Advanced Calculus, Advanced Linear Algebra,
Numerical Analysis, and Complex Analysis.
Creative Component, Report, or Thesis
Each student must complete either 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 Graduate Catalog contains detailed procedures
and requirements applicable to all Master's degrees.
Departmental Requirements for the Master of Science Degree in Mathematics
(Approved May, 1991)
Specific Courses
Option I:
- Advanced Calculus I and II (Math 4143 and 4153)
- Modern Algebra I and II (Math 4613 and 5013)
- General Topology (Math 5303)
- Complex Analysis (Math 4283 or Math 5283)
Option II:
Students interested in pursuing a doctor's degree
have the option of replacing the above courses with three of the
following sequences:
- Real Analysis I & II (Math 5143, Math 5153)
- Complex Analysis I & II (Math 5283, Math 5293)
- General Topology & Geometric Topology (Math 5303, Math 5313)
- Algebra I & II (Math 5613, Math 5623)
Courses taken as an undergraduate can be used to satisfy the above
requirements. If this is done the Master's degree program can be more
flexible.
Courses Taken in Graduate School
The courses taken in graduate school must total at
least 32 hours which may include two hours credit 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 Master's degree
program must include at least 21 hours of mathematics, statistics,
or computer science courses numbered 5000 or above. No more than
6 hours outside the mathematical sciences will count towards the
Master's degree. All the courses on the Master's degree program
must constitute a coherent whole and must be approved by the student's
advisory committee.
Comprehensive Examination
A Master's degree student must pass a comprehensive
written examination on Advanced Calculus, Modern Algebra, and
General Topology. If a student chooses option II above and if
grades of B or better are received in all three of the sequences
selected, then the student will be exempted from the Master's
Comprehensive Exam.
Creative Component, Report, or Thesis
Each student must complete either 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 Graduate Catalog contains detailed procedures and
requirements applicable to all Master's degrees.
General Requirements, Regulations
and Procedures for Master's Degrees
These requirements apply to both Applied Mathematics
and Mathematics Master's degrees. The Graduate Catalog contains
further information on many of these requirements.
Total credit hours
There are three plans by which the Master of Science
degrees may be earned.
- Plan I requires a thesis and completion of at
least 30 hours; 6 of these hours (under Math 5000) must be for
the thesis work.
- Plan II requires a report and completion of at
least 32 credit hours; the report (Math 5000) may be counted as
2 of these hours.
- Plan III requires a creative component and completion
of at least 32 credit hours. (Math 5000 may not be counted under
this option.)
Students, with the concurrence of their advisors, may choose
among these three plans.
Master's Committee
During the second semester, each student, with the
aid of the graduate director, must set up a Master's committee
of three faculty members. The chairman and other two members of
this committee advise and oversee the student's progress toward
the degree.
Plan of Study
The plan of study is a statement of how the student
intends to fulfill the requirements for the degree; in particular
it lists those courses which the student has taken or plans to
take and wishes to count for this purpose. A preliminary plan
of study must be filed with the Graduate College before enrollment
for the 17th graduate credit hour. The plan of study
may be changed as the student progresses. A final, accurate plan
of study must be filed with the Graduate College by the end of
the second week of the session in which the degree is to be conferred.
The student should prepare the plan of study in consultation with
the advisor and committee, who must approve all versions before
filing. Plan of study forms are available from the Mathematics
Department office.
The Master's Comprehensive Exam
A comprehensive written examination is required for
each of the two degrees. See section 7.1 for details.
Public Presentation and Written Exposition of the Creative Component
A public presentation to fellow graduate students
and faculty on the work done for the creative component is required
for a student following Plan III. A written exposition on this
is also required. See section 3.2 for a further discussion on
this creative component.
Final Examination Over
Master's Report or Thesis
A student following Plan I or Plan II must take a
final oral examination defending the thesis or report after it
has been filed with the Graduate College and distributed to the
advisory committee. See the Thesis Writing Manual: A Guide for
Oklahoma State University Graduate Students which is available
from the Graduate College office for specifications for reports
and theses submitted to the graduate college.
Minimum Grade Requirements
An average of "B" (3.0) in all courses on the plan of study and in research
and thesis (Math 5000) is required. A course with a grade below
"C" cannot be used as part of the minimum number of
hours required for the degree.
The Graduate Catalog lists regulations governing academic probation for failure
to maintain a cumulative grade point average of 3.0.
Graduate Credit Courses
Only courses numbered 5000 or above and courses numbered
3000 and 4000 that are identified by an asterisk in the Graduate
Catalog may be used on a plan of study. Some other exceptions
are noted in the Departmental Policy Statements (Sections 2.1
and 2.2).
Transfer of Graduate Credits
A maximum of nine credits can be accepted as transfer
credits toward a Master's degree. See the Graduate Catalog for
details.
Residence Requirements
Students following Plan I must complete at least 21 hours in residence; those following
Plan II or Plan III must complete at least 23 hours in residence.
See the Graduate Catalog for details and exceptions to this
requirement.
Time Limit and Continuous Enrollment
Students are expected to complete the requirements
for the Master's degree within four years after filing the plan
of study. The Graduate Committee will decide whether or not courses
taken over four years prior to the anticipated date of the degree
will be counted. A student must maintain continuous enrollment
during the entire research phase of the program.
Timetable - Master of Science Degrees
After a student has been admitted to the Graduate College at
Oklahoma State University for the purpose of receiving a Master of Science
degree in Mathematics or Applied Mathematics the following procedures are
to be followed.
- The student consults with the Graduate Director to seek
advice on initial enrollment and on activities of graduate
students. The director will serve as temporary advisor until
a committee is formed.
- An advisory committee is formed to monitor the student's
progress throughout the degree program. This committee is
selected by the student in consultation with the Graduate
Director usually during the second semester of study. One
member of the committee will serve as advisor and is
principally responsible for advising the student.
- The student together with the advisory committee creates a
plan of study which lists the courses that are to be taken.
At the same time a preliminary decision is made as to whether
the thesis, report, or creative component option will be
exercised. These decisions are tentative and are usually made
in the second semester of study. The plan of study must be
updated during the semester prior to graduation.
- The Master's Comprehensive Exams are taken as soon after
completion of the appropriate courses as is possible. These
exams are offered three times a year, in the week preceding
each semester.
- The student conducts the independent study component of
the degree program, whether this be a thesis, report, or
creative component. This is usually done after the student
has completed the core course work and passed the Master's
Comprehensive Exams.
- A formal defense or presentation must be made of a thesis
or report. Application for this defense must be filed with
the Graduate College in advance. The defense should come as
soon after completion of the thesis or report as is possible.
- A thesis or report must be typed according to Graduate
College guidelines and must be submitted before specific
dates. The rules for preparation of the thesis or report
can be attained from the Graduate College.
- A Verification of Completion form must be filed with the
Graduate College certifying the completion of the thesis,
report, or creative component.
- At the time of enrollment for the final semester of study,
an Application for Diploma must be filed with the
Graduate College.
- For those choosing the thesis option, a binding fee must
be paid in the Bursar's Office and the certification form
must be turned into the Graduate College. The form is
attained from the Graduate College after the thesis has
been formally accepted by that office.
- If the student plans to attend commencement, arrangements
must be made for cap and gown at the Student Union
Bookstore.
Creative Components, Reports and Theses
(Approved May, 1988)
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. 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 may include
up to 6 hours 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 their thesis at a regional mathematics meeting. Copies
of Master's theses are on display in the Mathematics Department
lounge.
Technical style and format specifications for the
thesis are found in the Thesis Writing Manual: A Guide for Oklahoma
State University Graduate Students, which is available from the
Graduate College.
The student must submit three copies of the thesis
and six copies of the thesis abstract to the Graduate College
by the due date announced annually in the "Graduate College
Calendar" in the OSU Catalog.
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. A public oral presentation of the report is required.
The student is encouraged (but not required) to present their
report at a regional mathematics meeting. The required 32 hours
of course work may include up to 2 hours of credit for the report
(Math 5000).
Technical style and format specifications for the
report are found in the Thesis Writing Manual: A Guide for Oklahoma
State University Graduate Students, which is available from the
Graduate College.
The student must submit to the Graduate College one
copy of the report, with six copies of the report abstract. The
report must be bound in a pressboard cover as described in the
Thesis Writing Manual: A Guide for Oklahoma State University Graduate
Students. One copy of the report must also be submitted to the
Mathematics Department's Graduate Program 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. 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 their work at a regional
mathematics meeting. Copies of creative components are on display
in the mathematics department lounge.
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.
The student must submit one copy of the written portion
to each of the Director of the Graduate Program, the director
of the creative component and the student's advisor.
Upon approval by the creative component director,
a Verification of Completion form must be submitted to the Graduate
College.
Overview of Doctoral Programs
The Department of Mathematics offers two doctoral
degrees: a PhD and an EdD. The PhD degree is meant to prepare
a mathematician for a career in college instruction, university
research, or industrial research. The PhD 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. The EdD degree program,
sponsored by the Mathematics Department, is in conjunction with
the Department of Educational Administration and Higher Education.
It is designed to train expert college level instructors in mathematics.
The Mathematics Department at Oklahoma State University
has historically been a leader in doctoral education. The department
has granted over 200 doctoral degrees. Graduates of either doctoral
program 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 long history of the degree programs
has allowed them to develop to a point where they give maximum
benefit to the students. A core of standard courses is required
of all students, allowing students to delay committing themselves
to the EdD or PhD until after they have been in school for over
a year.
The faculty at Oklahoma State is highly recognized
for its accomplishments both in pure mathematical research and
in mathematics education. In the past several years two department
members have been named the College of Arts & Sciences outstanding
researchers. Three faculty have received the very prestigious
Sloan Foundation Fellowships. Many of the faculty members have
recently been supported by National Science Foundation research
grants. Others have received grant support for projects in mathematics
education. This kind of activity makes it possible for prospective
doctoral students to choose a specialty from a wide variety of
areas.
Highlights of a Doctoral Degree Program
A doctoral student must complete at least 60 hours
of graduate work beyond a Master's degree. The student must also
pass a written comprehensive exam, pass an oral qualifying exam,
and write a thesis. PhD students are also expected to demonstrate
mathematical reading ability in one foreign language. EdD degree
candidates are not required to take a foreign language exam, but
they must complete a qualifying exam given by the Department of
Educational Administration and Higher Education.
The comprehensive exams are meant to test students
on breadth in mathematics. They cover material from several general
areas as outlined on specific syllabi (see Section 7.8). The qualifying
exam determines the student's readiness to write a thesis. The
thesis itself is of integral importance to both 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
PhD thesis is an original piece of relevant mathematical research.
The EdD thesis, on the other hand, is more often expository in
nature, yet it still must make a significant contribution to mathematical
understanding.
Beginning students concentrate on gaining general
knowledge in the core areas of algebra, topology, complex analysis,
and real analysis. They also take courses on more specific topics
and attend seminars to gain greater understanding of particular
research topics. After the core courses have been completed they
take their comprehensive exams. The next step is to gain specific
knowledge about an area of interest which might lead to a thesis
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 thesis, a qualifying
exam is administrated 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 thesis.
Sample Plans of Study
The actual course sequences taken by a doctoral candidate
will vary greatly depending on the preparation received in their
Master's work. The sample plans of study given are typical of
students entering with a Master's degree similar to that given
at OSU.
PhD in Mathematics
First Year
- Math 5313, Math 6323 Geometric Topology, Algebraic Topology I
- Math 5143, Math 5153 Real Variables I & II
- 6 hours of electives
Second Year
- Math 5613, Math 5623 Algebra I & II
- Math 5283, Math 5293 Complex Variables I & II
- 6 hours of electives
- PhD Comprehensive Exams
Third Year
- 6 to 9 hours of electives each semester
- seminars; outside readings
- Qualifying Exam
- Language Exam
Fourth Year
- 6 to 9 hours each semester consisting primarily of thesis-
related work
- Thesis Proposal
- Thesis Defense
Frequently students take electives, prepare for the
language exam, and work on research during the summers.
EdD in Mathematics
First Year
- Math 4143, Math 4153 Advanced Calculus I & II
- Math 5303, Math 5313 General Topology, Geometric Topology
Second Year
- Math 5613, Math 5623 Algebra I & II
- Math 5143, Math 5153 Real Variables I & II
- OR Math 5283, Math 5293 Complex Variables I & II
- 6 hours of electives
- EdD Comprehensive Exams
Third Year
- 6 to 9 hours of electives each semester, possibly
including education requirements
- seminars; outside readings
- Mathematics Qualifying Exam
- Education Qualifying Exam
Fourth Year
- 6 to 9 hours each semester involving primarily
thesis-related work
- Thesis Proposal
- Thesis Defense
Frequently students take electives or education courses
in the summers as well as do thesis work.
Departmental Requirements for the
PhD and EdD
The subsequent pages list the official departmental
statements (as approved by the faculty) on the requirements for
the PhD and EdD. Further requirements and descriptions are found
in Sections 6 & 7.
Requirements for the PhD in Mathematics
(Approved May 1988)
Credit Requirements
A total of 90 hours above the BS degree is required,
including credit hours for the PhD thesis.
Core Requirements
All candidates for the PhD Degree are required to
complete the following courses:
- MATH 5283, 5293 Complex Variables
- MATH 5143, 5152 Real Variables
- MATH 5613, 5623 Algebra
- MATH 5313, 6323 Topology
In addition to the above courses, every plan of study
must contain at least 12 hours of graduate mathematics courses
chosen from outside the field in which the student is specializing.
Comprehensive Examination
A PhD student must take the comprehensive examination
within one year of residence after completion of the required
course work. The comprehensive examination covers the content
of the four core courses described in
Qualifying Examination
The student must pass an oral qualifying exam over
the area of specialization for their graduate study. This exam
covers the material on a reading list presented to the student
by their advisory committee. Its purpose is to test the student's
readiness to begin thesis work.
Thesis Proposal
An outline of the proposed thesis research must be
presented to the student's advisory committee for approval. A
written proposal is then filed with the Graduate College.
Foreign Language Requirement
Candidates must pass an examination demonstrating
reading knowledge of one foreign language, usually French, German,
or Russian, before they take the final examination to defend their
thesis. Other languages may be substituted subject to recommendation
of the student's committee and approval of the Graduate Committee.
Thesis
A thesis must be written according to Graduate College
guidelines. The thesis consists of an original research contribution
in Mathematics.
Graduate College Requirements
All requirements listed in the Graduate Catalog must
be satisfied.
Requirements for the EdD in Mathematics
Credit Requirements
A total of 90 hours above the BS degree is required,
including credit hours for the EdD thesis. At least 60 of these
must be in the mathematical sciences.
Core Requirements
1. Mathematics:
All candidates for the EdD degree are required to
complete the following courses:
- MATH 4143, 4153 Advanced Calculus I, II
- MATH 4613, 5013 Modern Algebra I, II
- MATH 5303 General Topology
In addition the student must complete at least two
of the following three sequences:
- MATH 5283, 5293 Complex Variables I, II
- MATH 5143, 5153 Real Variables I, II
- MATH 5613, 5623 Algebra I, II
2. Statistics, Computer Science, and Numerical Analysis:
At least 6 graduate hours must be taken in either statistics,
computer science, or numerical analysis. Normally, this requirement
is satisfied by a pair of courses from the following list:
- STAT 4013, STAT 4023
- STAT 4403, STAT 5043
- STAT 4613, STAT 4213
- COMSC 3333, COMSC 4343
- COMSC 3443, COMSC 4263
- MATH 4513, MATH 4553
- MATH 6513, MATH 5543
- MATH 5553
3. Education
The student must complete at least 15 hours of EAHED
courses. Required courses are:
- EAHED 6753 Development and Organization on Higher Education
- EAHED 6813 Curriculum Development in Higher Education
- EAHED 6230 Critical Issues in Higher Education
- EAHED 6843 The Academic Department
Additional courses may be selected from the following:
- EAHED 5853 Educational Systems, Design and Analysis
- EAHED 6263 Supervision
- EAHED 6683 The Community Junior College
- EAHED 6850 Directed Readings
4. Thesis Work
At least 10 hours of Math 6000 (thesis) are required.
Comprehensive Examination in Mathematics
Before being admitted to candidacy the student must
pass the Comprehensive Examination in the mathematical sciences.
The exam covers the material approximated by the core mathematics
courses and it should be taken within one year upon completion
of the required coursework. A description of the examination is
found in Section 7.1 of the Graduate Student Manual.
The student has several options for topics on which
to be examined. In general, the exam will have the student tested
on:
- Complex Variables Math 5283, 5293
- Real Variables Math 5143, 5153
- General Topology Math 5303
- Algebra Math 5613, 5623
- Computer Science/Statistics/Numerical Analysis 6 hour sequence selected by the student
Advanced Calculus (Math 4143, 4153) can be substituted
for Complex Variables or Real Variables. If this substitution
is NOT made, then Algebra can be replaced by Modern Algebra I
(Math 4613) and Modern Algebra II (Math 5013).
Qualifying Examinations
The Qualifying Examination is required by the Graduate
College. The examination consists of two parts, one administered
by the Department of Educational Administration and Higher Education
and one administered by the Department of Mathematics.
Thesis Proposal
An outline of the proposed thesis research must be
presented to the student's advisory committee for approval. A
written proposal is then filed with the Graduate College.
Foreign Language Requirement
None
Thesis
A thesis must be written according to Graduate College
guidelines. The thesis consists of an original or expository research
contribution to mathematics or mathematics education.
Graduate College Requirements
All requirements listed in the Graduate Catalog must
be satisfied.
General Requirements for the PhD
Total Credit Hours
The student must complete at least 90 credit hours
beyond the bachelor's degree or at least 60 credit hours beyond
the Master's degree. Courses at the 5000 level or above should
make up at least 75 percent of those listed on the plan of study
and must include 15 hours (Math 6000) for the doctoral thesis.
Notice of Intention
Before taking additional courses after completing
the requirements for a Master's degree, a student must file a
Notice of Intention with the Graduate College to become a candidate
for the PhD degree. It should be filed prior to mid-semester of
the first semester of enrollment beyond the Master's degree, or
prior to the second summer of enrollment for those who enroll
only during summer terms.
Residence Requirements
At least 30 credit hours must be taken in residence.
All credit accepted toward the PhD Degree beyond the Master's
degree must be on the plan of study and be approved by the advisory
committee. One academic year of the last two must be spent in
continuous residence. With prior approval by the advisory committee
and the Dean of the Graduate College, the student may do research
for the degree in absentia; research conducted while not in residence
must be under the supervision of the major advisor and the advisory
committee.
Plan of Study
The plan of study is a statement of how the student
intends to fulfill the requirements for the degree; it lists all
those courses which the student has taken or plans to take and
wishes to count for this purpose. The plan of study must be approved
by the student's advisory committee and submitted to the Graduate
College prior to the pre-enrollment date during the second full
semester of enrollment beyond the Master's degree. Any changes
in the plan of study must be approved by the advisory committee
and the Dean of the Graduate College. A final, accurate plan of
study must be filed at the beginning of the session in which the
degree is to be conferred.
Comprehensive Examination
A written comprehensive examination is taken as soon
as possible after the completion of the appropriate courses. See
Section 7.1 for specifics on this examination.
Qualifying Examination
The student must pass an oral qualifying examination
which covers the area of the student's graduate study. It must
be passed not less than six months before the degree is granted.
Before taking this examination the student must have an approved
plan of study on file in the Graduate College and have the approval
of the advisory committee and the Dean of the Graduate College.
If the student fails this examination the examining committee
will notify the student of the conditions under which a second
examination may be taken; a second examination cannot be taken
for four months. If the student fails the second examination,
then no other examination can be given without the approval of
the Graduate College.
Admission to Candidacy
The student must be admitted to candidacy for the
PhD Degree at least six months before the degree is conferred.
Before being admitted to candidacy the student must have passed
the qualifying examination and have an approved plan of study
and thesis outline on file in the Graduate College.
Thesis
A doctoral thesis is required. It should present
the results of research which makes a new and original contribution
to mathematical knowledge. See the Thesis Writing Manual: A Guide
for Oklahoma State University Graduate Students for details on
the preparation and submission of the thesis.
Final Examination
After a final draft version of the dissertation has
been filed with the Graduate College and distributed to the advisory
committee, the student must take a final oral examination defending
the dissertation. Permission for this examination must be requested
from the Dean of the Graduate College. Following satisfactory
completion of this examination the candidate will 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. If the student fails to pass
this examination, the advisory committee will determine whether
and under what conditions a second exam may be taken; a second
exam may not be given earlier than four months after a failure.
If the student fails a second exam, no other examination may be
given without the approval of the Graduate College.
Time limit and continuous enrollment
Students are expected to complete the requirements
for the PhD degree within six years after filing the Notice of
Intention. Otherwise a new program of study must be arranged with
the advisory committee and filed with the graduate college. If
all requirements for the degree are not completed within four
years after taking the qualifying examination a second qualifying
exam must be passed. A student must maintain continuous enrollment
during the entire research phase of the program.
General Requirements for the EdD
Total Credit Hours
The student must complete at least 90 credit
hours beyond the bachelor's degree or at least 60 credit hours
beyond the Master's degree. Courses at the 5000 level or above
should make up at least 75 percent of those listed on the plan
of study and must include 10 hours (Math 6000) for the doctoral
thesis. A minimum of 60 hours beyond the bachelor's degree must
be in the mathematical sciences.
Notice of Intention
Before taking additional courses after completing
the requirements for a Master's degree, a student must file a
Notice of Intention with the Graduate College to become a candidate
for the EdD degree. It should be filed prior to mid-semester of
the first semester of enrollment beyond the Master's degree, or
prior to enrollment beyond 30 credit hours of course work above
the bachelor's degree.
Residence Requirements
At least 30 credit hours must be taken in residence.
One academic year of the last two must be spent in continuous
residence. The residence requirement can be met by two semesters
of full-time graduate study. Any other method of meeting the residence
requirement must be approved by the student's advisory committee
and the Dean of the Graduate College.
Plan of Study
The plan of study is a statement of how the student
intends to fulfill the requirements for the degree. It lists all
those courses which the student has taken or plans to take and
wishes to count for this purpose. The plan of study must be approved
by the student's advisory committee and submitted to the Graduate
College prior to the pre-enrollment date during the second full
semester of enrollment beyond the Master's degree. Any changes
in the plan of study must be approved by the advisory committee
and the Dean of the Graduate College. A final, accurate plan of
study must be filed at the beginning of the session in which the
degree is to be conferred.
Comprehensive Examination
A written comprehensive examination is taken
as soon as possible after the completion of the appropriate courses.
See Section 7.1 for specifics on this examination.
Qualifying Examination
The student must pass a qualifying examination
which covers both the mathematical sciences and education. Before
taking this examination the student must complete the main areas
in the plan of study, have filed an approved outline for the dissertation
with the Graduate College and the Mathematics Department, and
have received permission from the advisory committee and the Dean
of the Graduate College. This examination must be passed at least
6 months before the degree is granted. If the student fails this
examination the Graduate Committee will notify the student of
the conditions under which a second examination may be taken.
A second examination cannot be taken for four months. If the student
fails the second examination, then no other examination can be
given without the approval of the Graduate College.
Admission to Candidacy
The student must be admitted to candidacy for
the PhD Degree at least six months before the degree is conferred.
Before being admitted to candidacy the students must have passed
the qualifying examination and have an approved plan of study
and thesis outline on file in the Graduate College.
Dissertation
A doctoral thesis is required. This is customarily
an expository thesis in mathematics which makes a contribution
to the literature or, less frequently, a thesis setting forth
the results of some experimental work in educational research.
See section 7.5 for details on the preparation and submission
of the dissertation.
Final Examination
After the final draft of the dissertation has
been filed with the Graduate College and distributed to the advisory
committee, the student must take the final oral examination defending
the dissertation. Following satisfactory completion of this examination
the candidate will 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.
If the student fails to pass this examination the advisory committee
will determine whether and under what conditions a second exam
may be taken. A second exam may not be given earlier than four
months after a failure. If the student fails a second no other
examination may be given without the approval of the Graduate
College.
Time Limit and Continuous Enrollment
Students are expected to complete the requirements
for the EdD degree within six years after the Notice of Intention.
Otherwise, a new program of study must be arranged with the advisory
committee and filed with the graduate college. If all requirements
for the degree are not completed within four years after taking
the qualifying examination a second qualifying exam must be passed.
A student must maintain continuous enrollment during the entire
research phase of the program.
Timetable - PhD
After a student has been admitted to the Graduate
College at Oklahoma State University for the purpose of receiving
a Doctor of Philosophy degree in Mathematics, the following procedures
are to be followed.
- Before taking additional courses and after completing
the requirements for a Master's degree, the student
should file with the Graduate College a Notice of
Intention form to become a candidate for the degree.
The Notice of Intention must be filed prior to mid-
semester of the first semester of graduate enrollment
beyond the Master's degree or prior to the second summer
of enrollment of those who enroll only during summer terms.
- The dean of the Graduate College will designate a member
of the Graduate Faculty to serve as temporary advisor
to the student. The temporary advisor will arrange the
collection of information about the student and assist
in the early selection of courses.
- An advisory committee is formed to monitor the student's
progress throughout the degree program. The student
should consult this committee frequently and keep them
informed on the progress of his or her work.
- When the student is notified that an advisory committee
has been formed, the student should arrange a conference
with the committee to discuss preparation of the student
for graduate study and to make plans for future study.
- A plan of study is filed with the Graduate College listing
the courses the student must take.
- The student must take the doctoral comprehensive exams as
soon as possible after completing the appropriate courses.
- The student must complete the foreign language exam.
- The student must take the qualifying examination. In case
of failure, a second examination may be given at least
four months after a failure.
- The student is admitted to candidacy after having passed
the qualifying examination and having an approved plan
of study and thesis outline filed in the Graduate College.
- A thesis proposal is presented to the student's advisory
committee.
- The student completes the thesis after the thesis subject
is approved by the advisory committee.
- A formal defense must be made of a thesis. Application for
this defense must be filed with the Graduate College in
advance. The defense should come as soon after completion
of the thesis as possible.
- A thesis must be typed according to Graduate College
guidelines and must be submitted before specific dates.
These rules can be obtained from the Graduate College.
- An application for diploma form must be filed with the
Graduate College early in the student's last semester.
- Graduation fees should be paid through the Graduate
College.
- A cap and gown can be obtained through the Student Union
Bookstore by students who wish to attend commencement.
Timetable - EdD
After a student has been admitted to the Graduate College at
Oklahoma State University for the purpose of receiving a Doctor
of Education Degree with emphasis in Mathematics, the following
procedures are to be followed.
- Before taking additional courses and after completing
the requirements for a Master's degree, the student
should file in the Graduate College a Notice of Intention
form to become a candidate for the degree. The Notice of
Intention must be filed prior to mid-semester of the first
semester of graduate enrollment beyond the Master's degree
or prior to enrollment beyond 30 credit hours of course
work above the Master's degree.
- The dean of the Graduate College will designate a member of the
Graduate Faculty to serve as temporary advisor to the
student. The temporary advisor will arrange the collection of
information about the student and assist them in the early
selection of courses.
- An advisory committee is formed to monitor the student's
progress throughout the degree program.
- When the student is notified that an advisory committee
has been formed, the student should arrange a conference
with the committee to discuss preparation of the student
for graduate study and to make plans for future study.
The student must see that the chairman has transcripts of
previous work and other information that will be needed in
the conference.
- A plan of study is filed with the Graduate College listing
the courses the student must take.
- The student takes the mathematics doctoral comprehensive
exams as soon as possible after completion of the appropriate
courses.
- After completing the main areas in the plan of study and
obtaining the approval of the advisory committee and the
dean of the Graduate College, the student takes the
qualifying examination. Part of this exam is administered by
the Mathematics Department and part by the College of
Education. In case of failure, a second examination may be
given but no sooner than four months after the first exam.
- The student is admitted to candidacy after having passed
the qualifying examination and having an approved plan of
study and thesis outline filed in the Graduate College.
- A thesis proposal is presented to the student's advisory
committee.
- The student completes the dissertation (doctoral thesis)
after the thesis subject is approved by the advisory
committee.
- A formal defense must be made of a thesis. Application for
this defense must be filed with the Graduate College in
advance. The defense should come as soon after completion
of the thesis as possible.
- A thesis must be typed according to Graduate College
guidelines and must be submitted before specific dates.
These rules can be obtained from the Graduate College.
- An application for diploma form must be filed with the
Graduate College early in the student's last semester.
- Graduation fees should be paid through the Graduate
College.
- A cap and gown can be obtained through the Student Union
Bookstore by students who wish to attend commencement.
An important part of a student's graduate degree program is found
in the general examinations. Both Master's degreesm require a
written comprehensive exam. Master's theses and reports
must be defended formally. The EdD and PhD degrees require
a written comprehensive exam in mathematics as well as an
oral qualifying exam, a thesis proposal presentation, and a
thesis defense. EdD candidates must also pass a written
qualifying exam in education. PhD candidates must pass a
language exam.
Doctoral and Master's Comprehensive Exams
(Approved April 1992)
Purpose
The purpose of the comprehensive exams given by the
Mathematics Department is to determine whether the student has
mastered the concepts which the department feels are minimal
prerequisites for an advanced degree.
Schedule and Application Procedure
Exams are offered the week prior to the first week of classes
for the fall semester, spring semester, and summer term. Exact
dates and times are announced at least one month before the exams
are given.
Students wishing to take an exam should obtain an application
form from the departmental secretary and return the completed
form to the Graduate Committee.
A student who applies for an exam is expected to take it and
will be considered to have failed the exam if it is not taken.
Preparation and Administration
Exams cover several areas of mathematics. The exam for each
area is prepared, at the request of the Graduate Committee,
by a member of the faculty. The exams are then administered
by the Graduate Committee.
The Grading Procedure
Master's Exams:
Students are expected to exhibit competence in all of the
areas in which they are tested. After a student has taken
an exam, each part is graded "Pass or "Fail" by its
preparer. (Note: Advanced Calculus I & II make up a single
part of the exam as do Modern Algebra I & II.)
The Graduate Committee reviews the results of the
Comprehensive Examinations and makes the final decision as to
whether or not the student has passed each part of the exam.
Upon request, the Chair of the Graduate Committee will
discuss with the students their performance on the exams.
PhD and EdD Exams:
A student is expected to exhibit competence in a majority
of the areas covered on the exam. After a student has
taken an exam, each part is graded "Pass," "Marginal,"
or "Fail" by its preparer. For grading purposes, Advanced
Calculus and Modern Algebra are each considered as single
parts of an exam.
The Graduate Committee then reviews the results of the
examinations and determines whether the student has passed
the exam. Normally a student will pass an exam if at least 50%
"Pass" marks and no marks of "Fail" are received on the
different portions of the exams. If students fail an exam
for the first time with at least 50% "Pass" marks and have
only one "Fail" mark, then they will be re-examined
only on that part of the exam they failed. Students taking only
one part of an exam on their second try are assured of passing
the exams if they receive a "Pass" on that exam part.
It is the policy of the Graduate Committee to report exam scores
as pass-fail only. The Graduate Committee will discuss exam
performance in general terms with each student, if he/she wishes.
Exam Formats
The Master's Exam is given in two sessions with a rest day
in between. The first exam session is three hours and the
second exam session is two hours in length. A typical format
for these sessions is as follows:
Format for Pure Mathematics Option
Session One
- Advanced Calculus I and II (2 hours)
- General Topology (1 hour)
