INTERDISCIPLINARY Ph.D. PROGRAM
APPLIED MATHEMATICAL SCIENCES
WITH SPECIALIZATION IN:
Applied Mathematics
Computer Science
Operations Research
Statistics
SPONSORING DEPARTMENTS:
| Computer Science and Statistics, Industrial and Manufacturing Engineering, Management Science and Information Systems, and Mathematics. | Download a PDF of this document here. |
DESCRIPTION OF PROGRAM:
A student with a B.S. degree can pursue the Ph.D. directly in the program; however, the program has been designed principally for students who have an M.S. degree. A student entering the program with an M.S. degree in a closely related area may be granted up to 30 credits toward the Ph.D. in applied mathematical sciences. Each student would be expected to satisfy all of the following requirements (no single course can be used to satisfy two course requirements):
1. The student must complete 54 credits of course work beyond the B.S. degree in addition to 18 credits for the doctoral dissertation. Courses which are normally required in the URI undergraduate program corresponding to the student's B.S. program may not be applied toward the 54 credits of course work.
2. MTH435 and MTH436, Introduction to Mathematical Analysis I and II, are required.
3. The student will be required to complete two of the following courses:
- MTH462, Functions of a Complex Variable
- MTH513, Linear Algebra MTH515, Algebra I
- MTH535, Measure Theory and Integration
- MTH545, Ordinary Differential Equations I
- MTH547, Combinatorics and Graph Theory
- MTH548, Topics in Combinatorics
- MTH561, Advanced Applied Mathematics
- MTH641, Partial Differential Equations 1
- CSC542, Mathematical Analysis of Algorithms
- CSC544, Theory of Computation
One of these courses must be either MTH513 or MTH515.
4. The student will be required to select two (2) areas of core courses and complete at least three (3) courses in each area. Students choosing core areas different from those pursued in their master's program will be required to do additional course work. Special problems and topics courses in MTH, CSC, STA, and IME can be used to satisfy this requirement if approved by the student's doctoral committee. The areas of core courses and courses included in each area are given below; asterisks (*) indicate those courses that may not be offered in every academic year.
a. Applied Mathematics
b. Basic Analysis
c. Computational Mathematics
d. Computer Science Fundamentals and Theory
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e. Applied Computer Science
f. Operations Research
g. Statistics
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5. Other courses must be selected in order to meet the 54 credit minimum. These courses should be selected in consultation with the student's Advisor or Major Professor and need not necessarily be from among those listed in Part 4.
6. All normal examination policies of the Graduate School apply to this program.
- Students admitted without an M.S. degree will be expected to take a qualifying examination, usually after 24-30 credits have been completed. Students entering the program with an M.S. degree may be required to take the qualifying examination if so notified on their letter of admission. The qualifying examination committee will consist of the student's major professor and two other faculty appointed by the Coordinating Committee. Unanimous agreement of the examining committee is required for the student to pass. The content of this examination will be discussed with the student by his major professor during his first semester of study.
- A comprehensive examination will be administered near the completion of each student's course work. On this examination, the student will be held responsible for at least ten (10) courses, including the 12 required credits in (2) and (3) above and the required 18 credits from (4) above. The oral examination committee will include at least one member from the Mathematics Department. Unanimous approval by this committee is required for passing.
- Language requirement. Reading proficiency in one foreign language will be required. The student's major professor will approve the selection of a suitable language and will arrange for the administration of an examination testing reading proficiency in the student’s area of specialization.
SAMPLE PROGRAM OF STUDY
SPECIALIZATION IN APPLIED MATHEMATICS
(This program assumes that the student has had MTH437-438 , Advanced Calculus, and MTH462 , Complex Variables, as well as MTH451 , Introductory Probability and Statistics, as an undergraduate.)
Courses |
Credit Hours |
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Total Coursework Credit Hours |
55 |
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Total Program Credit Hours |
73 |
SAMPLE PROGRAM OF STUDY
SPECIALIZATION IN COMPUTER SCIENCE
(This program assumes that the student was an undergraduate computer science major and has taken the equivalent of MTH435 , MTH436 , Introduction to Mathematical Analysis I and II.)
Courses |
Credit Hours |
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Total Coursework Credit Hours |
54 |
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Total Program Credit Hours |
72 |
SAMPLE PROGRAM OF STUDY
SPECIALIZATION IN OPERATIONS RESEARCH
(This program assumes that the student has taken the equivalent of MTH435, MTH436, Introduction to Mathematical Analysis I and II.)
Courses |
Credit Hours |
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Total Coursework Credit Hours |
54 |
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Total Program Credit Hours |
72 |
SAMPLE PROGRAM OF STUDY
SPECIALIZATION IN STATISTICS
(This program assumes that the student has taken the equivalent of MTH435 , MTH436 , Introduction to Mathematical Analysis I and II, MTH451 , Introduction to Probability and Statistics, and STA409 , Statistical Methods in Research I, as an undergraduate.)
Courses |
Credit Hours |
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Total Coursework Credit Hours |
54 |
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Total Program Credit Hours |
72 |