# Doctor of Philosophy in Applied and Industrial Mathematics

**Major:**MATH

**Degree Awarded:**Ph.D.

**Unit:**GA

**Program Webpage:**http://www.math.louisville.edu/graduate

## Program Information

**Prerequisites****:**

Undergraduate coursework equivalent to a major in mathematics from an accredited university. This should include at least a one-year course in either analysis or abstract algebra, equivalent to Mathematics 501-502 and 521-522 at the University of Louisville. Candidates who have not taken both must complete the second in their program.

## Curriculum

All students admitted to the program must complete the following or their equivalent:

**A. Core Courses - 24 semester hours**

- Two sequences, each of six (6) semester hours, chosen from:
- Algebra MATH 621-622
- Combinatorics MATH 681-682
- Real Analysis MATH 601-602

- Two sequences, each of six (6) semester hours, chosen from:
- Applied Statistics MATH 665-667
- Mathematical Modeling MATH 635-636
- Probability & Mathematical Statistics MATH 660-662

**B. Additional Topics and Area of Specialization - 18 semester hours**In addition to the core, an application area of 18 hours will be required. The courses may be in a department outside Mathematics. They will be chosen in consultation with the student's advisory committee.

**C. Qualifying Examinations**Students must pass three written examinations. Two of these will be chosen from the areas of Algebra, Combinatorics and Real Analysis. The third will be chosen from the areas of Applied Statistics, Mathematical Modeling and Probability & Mathematical Statistics. Normally, these will be taken within a year of completion of the core coursework. These examinations need not be taken together and each may be attempted at most twice.

**D. Industrial Internship**

Each student, with prior approval of the Graduate Studies Director, has to complete an internship in an appropriate industrial or governmental setting, or have equivalent experience.

**Computing Project: ** Each student must complete an approved computer project related to the student’s area of concentration.

**Candidacy Examination:** Each student must pass an oral examination in the chosen area of concentration. Usually, at most two attempts at passing this examination will be permitted. Students who wish to make a third attempt must petition the Graduate Studies Committee of the department for permissions to do so.

**Dissertation – 12 to 18 semester hours: ** A doctoral dissertation is required of each student.

**Dual Degree Program in Applied and Industrial Mathematics and Biostatistics - Decision Science**

Dual degrees in Biostatistics-Decision Science and Applied and Industrial Mathematics are offered by the College of Arts and Sciences and the School of Public Health and Information Sciences. Upon completion of the program, students will receive a Ph.D. in Applied and Industrial Mathematics and an M.S.P.H. in Biostatistics-Decision Science.

**Application Procedure**

To be admitted to the program, the student is required to apply to and be accepted by both the Department of Mathematics and the Biostatistics-Decision Science Program. A student seeking admission into this program must submit letters to both the Department of Mathematics and the Department of Bioinformatics and Biostatistics stating the intent to take advantage of the dual degree program, and stating whether the student is interested in the Biostatistics or the Decision Science concentration. Students must submit two (2) recent letters of recommendation with their letter of intent. Applicants will receive written notification stating whether their admission request has been approved or disapproved.

**Degree Requirements**

*Required Courses*

The required courses for the dual degree program consist of all non-overlapping core courses for both the Ph.D. in Applied and Industrial Mathematics and the M.S. in Biostatistics - Decision Science, as well as the requirements for either the Decision Science or Biostatistics concentration within the Biostatistics-Decision Science program.

**Core course requirements for the Ph.D. in Applied and Industrial Mathematics**(24 semester hours).- Two sequences, each of six (6) semester hours, chosen from:
- Algebra - Mathematics 621 and 622
- Combinatorics - Mathematics 681 and 682
- Real Analysis - Mathematics 601 and 602

- Two sequences, each of six (6) semester hours, chosen from:
- Mathematical Modeling - Mathematics 635 and 636
- Applied Statistics - Mathematics 665 and 667
- Probability and Mathematical Statistics - Mathematics 660 and 662

- Courses taken in requirement of the mathematics component of the dual degree program can be used to satisfy the 6 to 9 semester hours of electives required for the M.S. in Biostatistics-Decision Science.

- Two sequences, each of six (6) semester hours, chosen from:
**Core course requirements derived from the M.S. in Biostatistics-Decision Science**(12 to 18 semester hours).- The following courses are required for both tracks:

- Introduction to Public Health and Epidemiology - PHEP 511 (3 semester hours)
- Social and Behavioral Sciences in Health Care - PHCI 631 (2 semester hours)
- Introduction to Environmental Health
- Health Economics
- Biostatistics-Decision Science Seminar - PHDA 602 (4 semester hours)
- Probability and Mathematical Statistics - PHST 661 and 662 (6 semester hours
*)**

* * This requirement is waived if the student takes the Mathematics 660, 662 sequence listed above.*

- Requirements from one of the two possible concentrations for the M.S. in Biostatistics - Decision Science. (5 to 6 semester hours)
- Biostatistics Concentration Requirements:
- Biostatistical Methods I and II - PHDA 680 and 681 (6 semester hours)

- Decision Science Concentration Requirements:
- Ethical Issues in Decision Making - PHDA 605 (2 semester hours)
- Decision Analysis - PHDA 663 (3 semester hours)

- Biostatistics Concentration Requirements:

Courses taken to satisfy the Biostatistics-Decision Science component of the dual degree program can be applied to the 18 semester hours of electives which are required for the Ph.D. in Applied and Industrial Mathematics.

**Combined Industrial Internship, Practicum and Masters Thesis. (6-8 semester hours)**

The Industrial Internship required by the Department of Mathematics and the Public Health Practicum and Masters thesis required for the M.S. can be satisfied by a single internship and technical report which simultaneously satisfies the requirements for both degrees. Specifically, the internship must both focus on public health so that it satisfies the Public Health Practicum (PHDA 603 and PHDA 604), and contain advanced mathematical content, so that it satisfies the Ph.D.-level Industrial Internship (Math 694). Likewise, the technical report must meet two requirements: it must satisfy the requirements for a Master’s thesis for the M.S. degree (PHDA 666) and it must be written at an advanced mathematical level expected for the Ph.D.-level Industrial Internship. The six (6) to eight (8) semester hours of the internship will be divided evenly between the Department of Mathematics and the Biostatistics-Decision Science Program.

**Dissertation and Qualifying Examinations**

In order for the student to fulfill the Ph.D. requirements, the student must satisfy both the qualifying examination and dissertation requirements for the Ph.D. in Applied and Industrial Mathematics. Failure to complete these requirements will not jeopardize the M.S. degree, if all its requirements have been satisfactorily completed.

**Special Considerations: Students who have already completed a Master’s degree in the Department of Mathematics**

To preserve the spirit of a dual degree, such students need to complete 36 semester hours of courses as required for the M.S. in Biostatistics-Decision Science. Six (6) semester hours from the previous Master’s degree coursework can be applied to this requirement. The remaining semester hours must be chosen from the list of not covered by core courses approved electives for the Department of Bioinformatics and Biostatistics, with preference given to courses in the Departments of Mathematics and Bioinformatics and Biostatistics. Combined Industrial Internship, Practicum and Masters Thesis cannot be replaced by a previous Master’s thesis. This requirement must be satisfied as previously described, meeting the specifications of both departments.

## Departmental Faculty

**Thomas Riedel***Professor*

Department Chair

**Csaba Bíro***Assistant Professor*

**Mary E. Bradley**

*Associate Professor*

**Udayan B. Darji***Professor*

**Richard M. Davitt***Emeritus*

**Arnab Ganguly***Assistant Professor*

**Roger H. Geeslin***Emeritus*

**Ryan S. Gill***Associate Professor Graduate Advisor*

**Changbing Hu***Associate Professor*

**Chakram S. Jayanthi***Adjunct Professor*

**Thomas M. Jenkins***Emeritus*

**André Kézdy***Professor Director*

*of Graduate Studies*

**Lael F. Kinch***Emeritus*

**Ewa Kubicka***Professor*

**Grzegorz Kubicki***Professor*

**Hamid Kulosman***Associate **Professor*

**Lee Larson**

*Professor*

**Kiseop Lee**

Associate Professor

**Bingtuan Li***Professor*

**Jiaxu Li***Associate Professor*

**Jinjia Li***Assistant Professor*

**Robert B. McFadden***Emeritus*

**Alica Miller***Associate **Professor*

**Robert Powers***Distinguished Teaching Professor **Assistant Chair*

**Prasanna Sahoo***Professor*

**Steven Seif***Associate Professor*

**David Swanson***Associate Professor Undergraduate Director*

**Cristina Tone***Assistant Professor*

**David J. Wildstrom***Associate Professor*

**W. Wiley Williams***Emeritus*

**Shi-Yu Wu***Adjunct Professor*

**Yongzhi Steve Xu***Professor*

**Stephen Young***Assistant Professor*

**Wei-Bin Zeng***Associate Professor*