Department of Mathematics and Statistics

Program of Study

The curriculum for the Master of Arts in Mathematics has been carefully constructed in order to provide students with a solid foundation in the basic tools and methodologies of their field of choice. But special attention is also given to individual differences. Beyond the basic requirements, students---with the assistance of their advisors---can design a tailor-made program, which not only meets their specific needs and interests but is also geared toward their career goals. Throughout the program, students can be assured of continuing and effective mentoring through close contact with their advisors and professors. They will also profit by the stimulation of studying with other highly motivated and intellectually gifted students in small classes.

Degree Requirements

A total of 30 credit hours is required for the Master of Arts in Mathematics. The base requirement includes 14 credit hours in courses all students must complete. Students may choose to write and defend a thesis or take a non-thesis option involving focus on some particular area of mathematics/statistics. The department also offers a five-year program which leads to the bachelor's and master's degrees. This program allows students to enroll in required graduate courses during their senior year.

• Base Requirement: The total base requirements is 14 credits and include:
  • MAT 523 -- Functions of a Real Variable I (3 credits)
  • MAT 527 -- Functions of a Complex Variable I (3 credits)
  • MAT 590 -- Graduate Research Seminar (1 credit - must be taken twice)
  • Two courses from the following list: MAT 531 -- Mathematical Statistics I , MAT 557 -- Mathematical Programming I , MAT 563 -- Abstract Algebra I, MAT 577 -- Topology I, MAT 587 -- Methods of Numerical Analysis
• Credit Distribution: A total of 30 credits are required for the degree, distributed according to one of the following two options:
  • Thesis Option: A minimum of 21 credits must be at the graduate level; 6 of these 21 are for the thesis. Each student's choice of credits must be approved by the advisory committee. Upon completion of the course of study and the thesis, the student must present an oral defense of the thesis.
  • Non-thesis Option: This is a broad-based extensive program designed to give the student an understanding of the basics of advanced mathematics as well as to allow focus on a particular area. A minimum of 24 credit hours must be at the graduate level, 21 of which must be from mathematics/statistics courses. Written comprehensive examinations must be taken; no oral examinations are required. The comprehensive examinations consist of three parts consisting of approximately 2/5 upper level undergraduate mathematics, 2/5 basic graduate level mathematics, and 1/5 on a specialty. Decisions for retakes are up to the student's committee.
• Seminar Requirement All graduate students must give at least two seminars with passing grades. It is suggested that one seminar be given in each of the fall and spring semesters of the second year. As this is a credit bearing requirement, it is necessary to register. The assigned course number is MAT 590. The talks should be prepared in consultation with and under the supervision of an advisor. Students should submit a short advisor-approved abstract to the graduate coordinator at least one week in advance of the seminar day, for inclusion in the announcement. The evaluation will be handled by the advisor in consultation with the members of the student advisory committee. A clear statement of the problem should be given with a brief historical sketch. All technical terms, specific to the area of expertise, should be clearly defined before they are used.

Student Avisory Committee

The student advisory committee will consist of the advisor together with at least two members of the graduate faculty. In addition, the graduate coordinator will serve as an ex officio member without the voting rights. The commitee should be formed by the end of the first year, and will meet with the student at least once each sememster of the second year to get an overview of the student's progress.

Thesis Administration

The student should have his/her program plan which would include the courses to be taken as well as the thesis topic, ready for discussion and approval by the student advisory committee by the start of the first semester of the second year of study. A copy of the thesis will be provided to the graduate coordinator at least one week in advance of the date of the defense. The coordinator will make the thesis available to any member of the faculty for perusal prior to the defense. All public announcements relating to the thesis as well as the seminars will be made by the coordinator.

Admission to the Program

Satisfactory undergraduate background as evidenced by transcripts, letters of recommendation and G.R.E. scores. Background should include one semester of advanced calculus (equivalent to MAT 425, i.e. a course from Rudin's "Principles of Mathematical Analysis") and one semester of abstract algebra (equivalent to MAT 463, i.e. an introduction to groups, rings and fields). Conditional admittance may be granted at the discretion of the graduate executive committee for students with deficient backgrounds. For example, a student with insufficient background in analysis might be admitted and required to take MAT 425. Minimum TOEFL score for non-native English speakers is 550 for admission; 580 is the minimum for an assistantship.

Teaching Assistantships

A limited number of graduate teaching assistantships are available. Teaching assistants are expected to spend approximately 17 hours per week teaching a lower level undergraduate course or assisting a faculty member and working in the Math Lab, an open tutorial center. The decision to renew an assistantship is based on performance in the first year of the student's program of study.

Courses

Graduate credit will not be given for any course below the 400 level. At most 6 credits may be taken at the undergraduate level. Normally, only a grade of A or B is acceptable for course work. A grade of C may carry graduate degree credit if a student's advisory committee so recommends and if the Graduate School approves such an exception. No student, however, will be allowed to accumulate more than six hours of C grades in a Master degree program, nor more than 12 hours of C grades in a Ph.D. or Ed.D. program.

• Undergraduate Courses:
  • MAT 426 -- Introduction to Real Analysis II
  • MAT 434 -- Introduction to Statistics
  • MAT 435 -- Introduction to Mathematical Statistics
  • MAT 436 -- Nonparametric Statistics
  • MAT 437 -- Statistical Methods in Research
  • MAT 451 -- Differential Equations and Dynamical Systems
  • MAT 452 -- Complex Analysis
  • MAT 453 -- Partial Differential Equations I
  • MAT 454 -- Partial Differential Equations II
  • MAT 456 -- Network Optimization
  • MAT 457 -- Introduction to Mathematical Modeling
  • MAT 458 -- Seminar in Mathematical Modeling
  • MAT 459 -- Methods of Applied Mathematics I
  • MAT 464 -- Introduction to Abstract Algebra II
  • MAT 465 -- Theory of Numbers
  • MAT 471 -- Differential Geometry
  • MAT 475 -- Higher Geometry
  • MAT 481 -- Discrete Mathematics
  • MAT 487 -- Numerical Analysis
• Graduate Courses:
  • MAT 500 -- Topics in Graduate Mathematics
  • MAT 505 -- Seminar in Mathematics Education
  • MAT 523 -- Functions of a Real Variable I
  • MAT 524 -- Functions of a Real Variable II
  • MAT 527 -- Functions of a Complex Variable I
  • MAT 528 -- Functions of a Complex Variable II
  • MAT 531 -- Mathematical Statistics I
  • MAT 532 -- Mathematical Statistics II
  • MAT 533 -- Stochastic Systems
  • MAT 562 -- Advanced Linear Algebra
  • MAT 563 -- Abstract Algebra I
  • MAT 564 -- Abstract Algebra II
  • MAT 577 -- Topology I
  • MAT 578 -- Topology II
  • MAT 587 -- Methods of Numerical Analysis
  • MAT 590 -- Graduate Research Seminar
  • MAT 699 -- Graduate Thesis Grades

Graduate Faculty

Graduate Degrees Conferred Since 1994

• Doctoral:
  • Elliot Benjamin, Ph.D. 1996, "Structure and Order Properties of the Hilbert 2-Class Field of Quadratic Number Fields." Supervisor: William Snyder.
  • O. Akman, Ph.D. 1994, "On the reliability studies of weighted inverse Gaussian model." Supervisor: Ramesh Gupta.
• Master of Arts:
  • Rebecca Rozario, M.A. 2003. Supervisor: William Snyder.
  • Gabriel Perrow, M.A. 2003. Supervisor: Robert Franzosa.
  • Bing Xi Wang, M.A. 2002. Supervisor: Ramesh Gupta.
  • Jung Ah Jung, M.A. 2001. Supervisor: Ramesh Gupta.
  • Ji Hoon Ryoo, M.A. 2001. Supervisor: David Bradley.
  • Paul Corriea, M.A. 2001. Supervisor: David Bradley.
  • Nicolas Bogan, M.A. 2000. Supervisor: Henrik Bresinsky.
  • Nicole Brown, M.A. 2000. Supervisor: Ramesh Gupta.
  • Barbara Lang, M.A. 1999. "Bootstrapping a Time Series Model." Supervisor: William Halteman.
  • Han Wu, M.A. 1999. "Analyzing Survival Data by an Exponentiated Weibull Model." Supervisor: Ramesh Gupta.
  • R. Warren, M.A. 1998. "Determination of change points of non-monotonic failure rates." Supervisor: Ramesh Gupta.
  • D. Look, M.A. 1998. "Classifying Topological 2-Disk Intersections in the Plane." Supervisor: Robert Franzosa.
  • Samel Thomas Arslanian, M.A. 1998. "An Implementation of the El Gamal Elliptic Curve Cryptosystem over a Field of Characteristic p." Supervisor: Ali Özlük.
  • J. Han, M.A. 1997. "The confidence region for the common mean vector of multinormal populations with different covariance matrices." Supervisor: Ramesh Gupta.
  • R. Cyr, M.A. 1996. "The Pledge Algorithm---A Universal Maze Solver." Supervisor: Robert Franzosa.
  • T. Peterson, M.A. 1995. "A Survey of Knot Polynomials and Applications." Supervisor Robert Franzosa.
  • Stanislav B. Gyoshev, M.A. 1995. "Applications of Number Theory to Statistical and Numerical Analysis." Supervisor: Ali Özlük.
  • B. Schratzberger, M.A. 1995. "The Theory of Liapunov Exponents and a Potential Application to Data Analysis." Supervisor: Robert Franzosa.
  • R. Morse, M.A. 1994. "An Investigation into the Properties of the Planar Disk Classifying Invariant." Supervisor: Robert Franzosa.
  • D. Chan, M.A. 1994. "Chaos, Smale's Horseshoe Map, and Melnikov's Method." Supervisor: Robert Franzosa.
  • S. Ramakrishnan, M.A. 1994. "Estimation of reliability in the strength stress model." Supervisor: Ramesh Gupta.
  • S. Ma, M.A. 1994. "Testing the equality of coefficient of variation from k normal populations." Supervisor: Ramesh Gupta.