Proposed Catalog Copy
Ph.D. in Applied Mathematics
The Ph.D. degree program in Applied Mathematics is designed to enable its students to master a significant body of mathematics, including a specialty in applied mathematics; to relate this knowledge to a coherent area of science or engineering; and to carry on fundamental research in applied mathematics at a nationally competitive level. Recipients of this degree will, according to their abilities and choice of sub-specialty, be able to work effectively in a research and development environment involving mathematical or statistical analysis and modeling in business, government or industry; to teach mathematics at the college or university level; or to carry on fundamental research in their area of specialty.
Additional Admission Requirements
In addition to the requirements of the Graduate School for admission to doctoral study, applicants must have completed at least 27 credit hours of courses in the mathematical sciences at the undergraduate level, as approved by the department Graduate Committee, with grades of a C or above. Admission requires that the candidate be able to take MATH 8143 or be able to take MATH 5143 and have other factors in their record that indicate strong potential to complete the program. For prospective students who have completed work in mathematics beyond the bachelor’s degree, performance on that work will be considered in admission decisions. Candidates for admission must make satisfactory scores on the general portion of the Graduate Record Examination (GRE).
Students are admitted to the program by the Graduate School, based on the recommendation of the department Graduate Committee or its designate, the Graduate Program Director. Recommendations are based on the Committee’s judgment of the candidate’s ability to complete the program, as supported by the application materials. The department may waive certain requirements if it judges the candidate to be nonetheless capable of completing the program. If there are more candidates than can be accommodated, candidates are admitted in order of perceived mathematical ability, promise of success, and suitability to the program.
Program of Study
The student must complete an approved program of study of at least 54 credit hours, including MATH 8143, MATH 8144, at least 18 research credit hours of MATH 8994, a minor, elective hours, and MATH 8120 if the student is in statistics focus.
The minor is interdisciplinary and may be satisfied by 9 hours of graduate coursework outside the Department of Mathematics and Statistics, by 6 credit hours of MATH 8691 and MATH 8692 for a directed project in an area of application, or by a combination of external coursework and directed project in an area of application totaling 9 credit hours. It is expected that interdisciplinary minor courses shall in general be in STEM disciplines, but if there are applications in the student’s dissertation work towards the social sciences, courses in those fields are allowed too. Examples of interdisciplinary minor courses allowed for several fields include:
Physics: PHYS 5222, 5232, 5242, 5271, 6101 through 6201, 6203 through 6211, 6221 through 6271.
Optics: OPTI 8101, 8102, 8104, 8105, 8211.
Mechanical Engineering: MEGR 8102, 8113, 8116, 8125, 8141, 8142, 8143, 8164.
Computer Science: ITCS 8111, 8114, 8115, 8150, 8153, 8155, 8156, 8165, 8170, 8171, 8220, 8226.
Finance and Economics: Any of FINN or ECON courses listed under the MS in Mathematical Finance program. Examples include FINN 6203, 6210, 6211, and ECON 6206, 6112, 6113, 6218, 6219.
The elective courses shall be selected from an approved list of MATH/STAT courses: MATH 5128 through MATH 5181, MATH 6201 through MATH 6206, MATH 8028 and above, STAT 5123 through STAT 5127, STAT 6113, STAT 6115, STAT 8027, STAT 8122 and above.
The student must complete an approved program of study, including MATH 8143, MATH 8144, and a minor, typically including approximately 54 credit hours. The minor is interdisciplinary and may be satisfied by 9 hours of graduate work outside the mathematics department, by 6 credit hours for a directed project in an area of application, or by a combination of external coursework and directed project in an area of application totaling 9 credit hours.
Each student has a dissertation committee appointed by the department Graduate Committee in consultation with the student and approved by the Dean of the Graduate School. It includes the prospective dissertation advisor, as well as a department co-advisor, if the dissertation advisor is not a member of the Department of Mathematics and Statistics. The dissertation committee should be appointed as soon as is feasible, usually within a year after passing the Qualifying Examination. Once formed, it has the responsibility of constructing and approving the program of study which includes the minor. Prior to the appointment of the dissertation committee the student is advised by a graduate faculty member appointed by the department Graduate Committee.
Grade Requirements
Students are expected to achieve As or Bs in all courses included in the program of study and must have at least a 3.0 GPA to graduate. The dissertation is graded on a pass/unsatisfactory basis and, therefore, is not be included in the cumulative average. An accumulation of more than two marginal (C) grades will result in suspension of the student’s enrollment in the program. If students make a grade of U on any course, enrollment will be suspended and students cannot take further graduate work without being readmitted to the program. Readmission to the program requires approval of the Dean of the Graduate School upon the recommendation of the department Graduate Committee.
Transfer Credit
Only courses with grades of A or B may be accepted for transfer credit. Transfer credit must be recommended by the department Graduate Committee and approved by the Dean of the Graduate School. The amount of transfer credit cannot exceed the limit set by the Graduate School.
Qualifying Examination
After being admitted to the Ph.D. program, students are expected to take the qualifying examination within three semesters. This time limit may be extended for up to two additional semesters in certain cases, depending on the background of the student and with program approval. The qualifying examination consists of two parts: (1) the first part is a written examination based on Real Analysis I and II (MATH 8143 and MATH 8144) or Probability Theory I and Real Analysis I (MATH 8120 and MATH 8143), the latter intended for a student with a statistics focus. The second part is a written examination based on two other courses chosen by the student to be specifically related to the student’s intended specialty and approved by the department Graduate Committee. Students may be allowed to retake a portion of the qualifying examination a second time if they do not pass that portion on the first attempt within the guidelines of the Graduate School regulations pertaining to the qualifying examination and as overseen by the department Graduate Committee. Students who do not complete the qualifying examination as per the regulations of the Graduate School are terminated from the Ph.D. program.
Topic Approval Defense and Admission to Candidacy
After a student completes the qualifying examination and advanced coursework deemed necessary for the student’s research as approved by the student’s doctoral dissertation committee, the student, in consultation with the student’s dissertation advisor, may propose a dissertation topic. The dissertation topic proposal must be articulated and defended at a meeting of the student’s dissertation committee. A written dissertation proposal must be submitted to the dissertation committee at least two weeks prior to the scheduled defense. The student is expected during the course of the topic defense to outline and demonstrate sufficient proficiency with the advanced knowledge and techniques to be used in the conduct of the research. The topic approval defense and the committee’s deliberations in this regard are to be conducted according to the pertinent regulations of the Graduate School. A doctoral student advances to candidacy after the student’s dissertation committee and the Dean of the Graduate School have approved the dissertation topic proposal.
Assistantships
A number of graduate assistantships are available each year (with nationally-competitive stipends) for qualified applicants. A limited number of fellowship awards can be applied to supplement these stipends or provide stand-alone stipends for up to $25,000 for especially qualified students.
Dissertation
The student must complete and defend a dissertation based on a research program approved by the student’s dissertation advisor which results in a high quality, original and substantial piece of research. The student must orally present and successfully defend the dissertation before the student’s doctoral dissertation committee in a defense that is open to the public. A copy of the dissertation must be made available to the graduate faculty of the department at least two weeks prior to the public defense. The dissertation is graded on a pass/unsatisfactory basis by the dissertation committee and must be approved by the Department Graduate Program Director and the Dean of the Graduate School.
Residency Requirement
Full-time Ph.D. students must enroll for one continuous full-time year (i.e., two consecutive semesters of at least nine graduate credit hours in each semester) following admission to the program.
Time Limit for Degree Completion
Students must achieve admission to candidacy within six years after admission to the program and complete all requirements within six years after admission to candidacy for the Ph.D. degree. All requirements for the degree must be completed within eight years after first registration as a doctoral student.
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