Graduate School
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Mathematics and Statistics (MATH)
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This program is offered in Durham.
Degrees Offered: M.S., M.S.T., Ph.D.
The Department of Mathematics and Statistics offers programs leading to a master of science for teachers in mathematics, master of science in mathematics, master of science in mathematics with an option in applied mathematics, master of science in mathematics with an option in statistics, a doctor of philosophy in mathematics, and a doctor of philosophy in mathematics education.
In general, the master’s degree programs offer the student a high level of preparation for professional employment as well as appropriate preparation for programs leading to the Ph.D. The Ph.D. programs prepare the student primarily for a career in university teaching and research.
The graduate programs have limited enrollment, allowing students to work closely with faculty members in their areas of expertise. Research within the department is currently being conducted in many areas of the mathematical sciences, including: operator theory, Hilbert spaces, geometric function theory, complex analysis, Radon transforms, integral geometry, ring theory, computational algebra, homological algebra, quantum groups, tensor categories, combinatorics, topology, algebraic topology, category theory, nonlinear dynamics and chaos, data compression, chaotic prediction and control, spectral analysis, asymptotic analysis, mathematical control theory, environmental statistics, spatial and spatio-temporal statistics, Bayesian and computational statistics, wavelets in statistics, teaching and learning of mathematics, teaching and learning of probability and statistics, mathematics curriculum and teacher education, calculus learning, K-12 mathematics education reform, and mathematics education.
Admission Requirements
Applicants for the M.S. and Ph.D. degrees must have completed significant undergraduate coursework in mathematics, preferably in algebra, analysis, and topology. Applicants for the M.S. with applied mathematics option must have completed significant coursework in analysis or applied analysis. Applicants for the M.S. with statistics option will typically have an undergraduate degree in the mathematical, physical, biological, or social sciences or in engineering; must have completed mathematical coursework at least through multivariate calculus; and must have knowledge of basic statistics and basic linear algebra at the undergraduate level. Applicants for the degree of master of science for teachers must have completed education courses sufficient for certification, or have three years teaching experience, or currently hold a full-time teaching position.
Degree Requirements
M.S. Degree Requirements
This program requires 30 credit hours, consisting of at least 10 semester courses approved by the department and chosen from courses in 801-888 and 931-998, with at least six of the courses in the 931-998 group. A comprehensive master’s examination is intended to allow the student maximum latitude in pursuing his or her mathematical interests.
Applied Mathematics Option
This program requires 30 credit hours, consisting of the courses MATH 931-932, two topics in applied mathematics courses (MATH 967/977), 6 credits of Master’s Thesis (MATH 899), and four elective courses. The elective courses need not be in mathematics, but must be at the 800 level or higher, and at least one must be a technical course in statistics or some other department. The broad elective flexibility allows the student’s application interests to have a substantial role in the content of the program. The student’s full program plan must be proposed in writing to the applied mathematics faculty and approved prior to the student’s second semester of study. The program includes a thesis, which must constitute original research in applied mathematics, conducted under the supervision of a faculty adviser. There is no comprehensive examination in this option.
Statistics Option
This program requires 30 credit hours, consisting of at least 10 semester courses approved by the department, which includes completion of a project (MATH 898) consisting of a substantial application of statistical methodology to a real problem. Most of the courses will be taken from the department’s statistics courses in the range MATH 837-979 and must include all of MATH 839, 840, 855, and 856, unless some of these or equivalent courses were taken prior to enrollment in the program. At most, three of the required 10 courses may also be taken from the department’s approved nonstatistics courses (in the range MATH 837-979) and/or approved courses offered in other departments. MATH 898, the Master’s Project, is conducted under the supervision of a faculty adviser and concluded with a written report and a public oral presentation. MATH 898 may be taken for 3 to 6 credits, depending on the level of substantial research and methodological development required for project completion; the appropriate number of credits is determined by the statistics faculty. A master’s committee of at least two statistics faculty members oversees the student’s progress and determines credit for the project. There is no comprehensive examination in this option.
M.S.T. Degree Requirements
The program requires 30 credit hours, consisting of at least 10 semester courses approved by the department. These will normally be taken from the courses numbered MATH 901-929 and will usually include the seven courses MATH 903-908 and MATH 925. A concluding experience consisting of a mathematics portfolio and a comprehensive problem set is required. The courses in this program are offered primarily during summer sessions.
Ph.D. Requirements
In each Ph.D. program, requirements 1 to 3 (below) must be completed for advancement to candidacy. Students in the Ph.D. program in mathematics who intend to write a dissertation in statistics must satisfy the alternate basic requirements 1 and 2, which replace basic requirements 1 and 2; all other Ph.D. students must satisfy requirements 1 and 2. The additional requirements 3 to 5 differ slightly for the mathematics and mathematics education Ph.D. programs; these are indicated below.
Basic degree requirements for the Ph.D. program:
1. all of the courses MATH 951, 952, 953, 954, 955;
2. Mathematics Ph.D. students passing written comprehensive examinations in algebra, analysis, topology and an elective subject. Mathematics Education Ph.D. students passing written comprehensive examinations in algebra, analysis, mathematics education and an elective subject. (Elective subjects include functional analysis, algebraic topology, applied mathematics, statistics, advanced algebra, advanced complex analysis, advanced mathematics education, et al.)
Alternate basic degree requirements for mathematics Ph.D. students:
1. all of the courses MATH 839, 840, 855, 856, 951, 953, and 954;
2. passing written comprehensive examinations in statistical theory, statistical methods, analysis, and either applied mathematics or functional analysis.
Additional degree requirements for the Ph.D. in mathematics:
3. advanced coursework in a major field (that of the student’s intended dissertation work) and a minor field (usually within mathematics, but possibly in another area of the mathematical sciences) followed by qualifying examinations in each;
4. experience in teaching equivalent to at least half-time for one year;
5. a dissertation that includes original results in mathematics.
Additional degree requirements for the Ph.D. in mathematics education:
3. advanced coursework in the major field (mathematics education), including MATH 958, 968A, and 968B, and in a minor field (usually a related one, such as educational psychology or research methodology, but possibly in mathematics) followed by qualifying examinations in each;
4. experience in teaching equivalent to at least half-time for one year; and
5. a dissertation that includes original results in mathematics education.
Courses
Courses numbered MATH 903-929 may be applied to the master of science for teachers in mathematics and to no other degree in mathematics.
Courses MATH 931-958 are introductory courses for the M.S. degree in mathematics and the Ph.D. degrees in mathematics and mathematics education.
Courses numbered MATH 961-979 are more specialized topics courses offered periodically in response to faculty and student interests. Their content may vary from year to year. With the permission of the instructor, these courses may be taken more than once.
A majority of the courses required for the M.S. degree in mathematics with option in statistics are now offered in synchronous mode (live) over the Internet.
Interdisciplinary Opportunities
The College of Engineering and Physical Sciences is developing and Integrated Applied Mathematics Program (IAM). Students interested in applied and interdisciplinary work are encouraged to inquire about IAM within the college.
Courses
| Abbreviation | Course Number | Title | Credits |
|---|---|---|---|
| MATH | 835 | Statistical Methods for Research | 3 |
| MATH | 836 | Advanced Statistical Methods for Research | 3 |
| MATH | 837 | Statistical Methods For Quality Improvement | 3 |
| MATH | 839 | Applied Regression Analysis | 3 |
| MATH | 840 | Design of Experiments I | 3 |
| MATH | 841 | Survival Analysis | 3 |
| MATH | 843 | Time Series Analysis | 3 |
| MATH | 844 | Design of Experiments II | 3 |
| MATH | 845 | Foundations of Applied Mathematics | 3 |
| MATH | 846 | Foundations of Applied Mathematics | 3 |
| MATH | 847 | Introduction to Nonlinear Dynamics and Chaos | 3 |
| MATH | 853 | Introduction to Numerical Methods | 3 |
| MATH | 854 | Introduction to Scientific Computing | 3 |
| MATH | 855 | Probability and Stochastic Processes | 3 |
| MATH | 856 | Principles of Statistical Inference | 3 |
| MATH | 861 | Abstract Algebra | 3 |
| MATH | 862 | Linear Algebra | 3 |
| MATH | 864 | Advanced Algebra | 3 |
| MATH | 867 | One-Dimensional Real Analysis | 3 |
| MATH | 876 | Logic | 3 |
| MATH | 884 | Topology | 3 |
| MATH | 888 | Complex Analysis | 3 |
| MATH | 896 | Topics in Mathematics and Statistics | 1 TO 4 |
| MATH | 898 | Master's Project | 1 TO 6 |
| MATH | 899 | Master's Thesis | 1 TO 6 |
| MATH | 903 | Higher Algebra for Teachers | 3 |
| MATH | 904 | Higher Algebra for Teachers | 3 |
| MATH | 905 | Higher Geometry for Teachers | 3 |
| MATH | 906 | Higher Geometry for Teachers | 3 |
| MATH | 907 | Higher Analysis for Teachers | 3 |
| MATH | 908 | Higher Analysis for Teachers | 3 |
| MATH | 909 | Probability and Statistics for Teachers | 3 |
| MATH | 910 | Mathematics Education | 1 TO 4 |
| MATH | 914 | Topology for Teachers | 3 |
| MATH | 916 | Theory of Numbers for Teachers | 3 |
| MATH | 917 | Mathematical Proof and Problem Solving | 3 |
| MATH | 925 | Problem Solving Seminar | 3 |
| MATH | 928 | Selected Topics in Mathematics for Teachers | 1 TO 3 |
| MATH | 929 | Directed Reading | 1 TO 3 |
| MATH | 931 | Mathematical Physics | 3 |
| MATH | 932 | Mathematical Physics | 3 |
| MATH | 941 | Bayesian and Computational Statistics | 3 |
| MATH | 942 | Beyond ANOVA: Generalized Linear and Semi-parametric Smoothing Methods | 3 |
| MATH | 944 | Spatial Statistics | 3 |
| MATH | 951 | Algebra I | 3 |
| MATH | 952 | Algebra II | 3 |
| MATH | 953 | Analysis I | 3 |
| MATH | 954 | Analysis II | 3 |
| MATH | 955 | Topology I | 3 |
| MATH | 956 | Topology II | 3 |
| MATH | 958 | Foundations of Math Education | 3 |
| MATH | 961 | Topics in Algebra I | 3 |
| MATH | 963 | Functional Analysis | 3 |
| MATH | 964 | Topics in Analysis I | 3 |
| MATH | 965 | Topics in General Topology I | 3 |
| MATH | 966 | Topics in Algebraic Topology I | 3 |
| MATH | 967 | Topics in Applied Mathematics I | 3 |
| MATH | 968 | Topics in Mathematics Education I | 3 |
| MATH | 969 | Topics in Probability and Statistics I | 3 |
| MATH | 971 | Topics in Algebra II | 3 |
| MATH | 973 | Topics in Operator Theory | 3 |
| MATH | 977 | Topics in Applied Mathematics II | 3 |
| MATH | 978 | Topics in Mathematics Education II | 3 |
| MATH | 979 | Research Topics in Statistics | 3 |
| MATH | 998 | Reading Courses | 1 TO 6 |
| MATH | 999 | Doctoral Research | 0 |
