# Department of Mathematics

*Harvey Wolff, Chairperson Janice L. Roe, Associate Chairperson Donald B. White, Graduate Adviser in Statistics Geoffrey Martin,
Graduate Adviser in Pure Math H. Westcott Vayo, Graduate Adviser in Applied Math *

A full description of programs and requirements, with syllabi for exams, is available from the department office. The paragraphs below represent a synopsis of the essentials.

**Requirements for the Master's Programs **

**Master of Arts **

Toobtain the Master of Arts degree in mathematics, students must complete a minimum of 30 semester hours of graduate credit (note: Colloquium and Proseminar do not count toward the 30 hours) and meet the following requirements:

1.Complete two semester sequences in Abstract Algebra, Real Analysis, Topology and a course in Complex Analysis.

2.Complete one two-semester sequence at the 6000-level in Algebra, Topology, Differential Geometry, Differential Equations, or Analysis.

3.Complete one of the following courses: Classical Differential Geometry, Ordinary Differential Equations, Partial Differential Equations, Calculus of Variation and Optimal Control, or any course at the 6000 level.

4.The student must either pass comprehensive examinations or write a Master's thesis. If a thesis is elected, the student must take an oral examination on the general area of the thesis.

**Master of Science **

The degree of Master of Science can be obtained in either of two options.

Option A: Applied Mathematics

Toobtain the degree of Master of Science in the Applied Mathematics Option, the student must complete a minimum of 30 semester hours of graduate credit (note: Colloquium and Proseminar do not count toward the 30 hours) and meet the following requirements:

1.Complete two semester sequences in Numerical Analysis, Real Analysis, Differential Equations, and a course in Complex Analysis.

2.Remaining courses may be chosen from: Applied Functional Analysis, Linear and Nonlinear Programming, Infinite Dimensional Optimization, Differential Geometry, Differential Equations, Methods of Mathematical Physics, Functional Analysis, Complex Analysis, Discrete Structures, Probability and Statistics, Operational Mathematics, or Calculus of Variations.

3.The student must pass comprehensive examinations or submit and defend a Master's thesis.

Option B: Statistics

Toobtain the degree of Master of Science in the Statistics option, the student must complete a minimum of 35 semester hours of graduate credit (note: Colloquium and Proseminar do not count toward the 35 hours) and meet the following requirements:

1.Complete: Applications of Statistics I, Applications of Statistics II, Linear Statistical Methods, Theory and Methods of Sample Surveys, Statistical Computing, Statistical Consulting I, Statistical Consulting II, Categorical Data Analysis, Distribution Free and Robust Statistical Methods, Statistical Inference, and Multivariate Statistics.

2.Complete one of the following: Applied Probability, Measure Theoretic Probability, Theory of Statistics, Topics in Statistics.

3.Complete one of the following: Linear Algebra I, Applied Linear Algebra, Introduction to the Theory of Probability, Advanced Calculus.

4.Pass a comprehensive examination.

**Master of Science and Education **

For the degree of Master of Science and Education the following requirements must be met:

1.a minimum of 32 hours of graduate credit must be completed. Colloquium and Proseminar do not count toward the 32 hours. At least 18 hours must be in Mathematics and 9 hours in Education, with an additional 6 hours to be assigned in conference with the adviser. As part of the additional 6 hours the student may elect to write a paper in Mathematics Education or one of expository character in Mathematics.

2.The total graduate and undergraduate program must include the following: at least 6 hours of Abstract Algebra and/or Linear Algebra, 6 hours in Geometry, Statistics, Probability and/or Computer Programming, 3-6 hours of Analysis (beyond Calculus), 3 hours of Complex Analysis, and one course in Logic and Foundations.

3.The student must pass comprehensive examinations in three of the areas of study of mathematics. The exact areas are to be arranged with the adviser.

4.For information on the Education course requirements see the program description provided by the College of Education and Allied Professions.

**Requirements for the Doctoral Program**

The doctorate in Mathematics is offered with concentrations in either Mathematics or Statistics. The broad requirements for these programs are as follows.

1.Each student must pass a qualifying examination within two years of entering the program. In Mathematics students must pass two examinations chosen from Algebra, Topology, and Analysis. In Statistics students must pass qualifying examinations in Analysis and Probability and Statistics.

2.A minimum of 90 hours of graduate credit must be completed. Colloquium and Proseminar do not count in the 90 hours. Of the 90 hours, at least 18 but no more than 36 shall be allotted for the dissertation. In Mathematics students must complete year-long sequences in Algebra, Topology, Real Analysis, and Complex Analysis. In Statistics students must complete Probability and Statistics, Real Analysis, Statistical Methods, Data Analysis, and Multivariate Statistics.

3.The student must pass an oral examination in the general area of the intended thesis research.

4.The student must demonstrate the ability to read mathematical literature in one foreign language, ordinarily chosen from among French, German, or Russian. Another language may be substituted if it is necessary for the student's specific program. The language requirement must be met before dissertation research is begun.

5.All doctoral students are expected to participate in a seminar on undergraduate teaching methods and to spend two consecutive semesters in supervised teaching. This requirement should be met before dissertation research is begun.

6.The student must write a Ph.D. dissertation under the direction of a faculty member. Before completing the dissertation, the student must report on it in an open seminar. A completed dissertation must be approved by an outside examiner and the student must defend it before a faculty committee appointed for that purpose.