# 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:
- Mathematical Modeling MATH 635-636
- Mathematical Statistics MATH 667-668
- Probability MATH 663-664

**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 Mathematical Modeling, Mathematical Statistics and Probability. 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**

Dual degrees in Biostatistics 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 in Biostatistics.

**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 Department of Bioinformatics and Biostatistics. 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, as well as their choice of the thesis or non-thesis option for the M.S. in Biostatistics. 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, as well as the course requirements for the M.S. in Biostatistics.

**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
- Mathematical Statistics - Mathematics 667 and 668
- Probability - Mathematics 663 and 664
- Elective Courses (18 hours) * Application area courses chosen in consultation with a student’s advisory committee. These courses can be outside of the Department of Mathematics.
- Industrial Internship:Each student, with prior approval of the Graduate Studies Director and the Industrial Internship Director, has to complete an internship in an appropriate industrial or governmental setting, or have equivalent experience.
- Other Requirements:Students must pass qualifying examinations, complete an approved computing project, and pass a candidacy examination as detailed in the catalog entry for the Ph.D. in Applied and Industrial Mathematics.
- Dissertation (12-18 hours): 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.

- Two sequences, each of six (6) semester hours, chosen from:

**M.S. in Biostatistics**

**Core course requirements**(30 semester hours).- oProbability and Mathematical Statistics, PHST 661-662 or MATH 561-562 (6 hours)**
- oBiostatistical Methods I and II, PHST 680-681 (6 hours)*
- oMultivariate Statistical Methods, PHST 682 (3 hours)***
- oSurvival Analysis, PHST 683 (3 hours)
- oCategorical Data Analysis, PHST 684 (3 hours)
- oEpidemiology Elective, PHEP --- (3 hours): Fulfilled by any advisor-approved course in Epidemiology, including but not limited to PHEP 602, PHEP 618, and PHEP 650
- oClinical Trials I and Clinical Trials Stat Lab, PHCI 624 and PHST 626 (3 hours)
- oBiostatistics Seminar PHST 602 (1 hour)
- oIndependent Study PHST 675 (2 hours)****
- oPublic Health Background Courser, PH --- (0 hours):A course in public health is a requirement for any student graduating with the M.S. degree from the Department of Bioinformatics and Biostatistics. These credit hours are not applied to the M.S. degree. Course number varies from year to year.

**Additional Requirements – Optional Thesis (6 hours)**- Thesis, PHST 666 (6 hours). To be completed in accordance with the guidelines written in the catalog entry for the M.S. in Bioinformatics and Biostatistics Degree.

* Courses taken to satisfy the Biostatistics 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.

** The PHST 661-662/MATH 561-562 requirement is waived if the student takes MATH 663 and MATH 667. The PHST 681-682 requirement is waived if the student takes MATH 667-668. Both requirements (PHST 661-662/MATH 561-562 and PHST 681-682) are waived **only if** the student completes both the MATH 663-664 and MATH 667-668 sequences.

*** Can be replaced by an advisor-approved graduate-level course in Bioinformatics and Biostatistics (PHST 691, PHST 704, etc.)

**** This is a project completed under the supervision of a faculty member

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

Students will not be permitted to enroll in the Master’s Project (PHST 675) or Master’s Thesis (PHST 666) courses until at least 2 qualifying examinations toward the Ph.D. in Applied and Industrial Mathematics have been 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.

**Students Currently Enrolled in the Ph.D. in Applied and Industrial Mathematics Program**

Students currently enrolled in the Ph.D. in Applied and Industrial Mathematics program will need to submit complete application materials to the Department of Bioinformatics and Biostatistics for admission to the M.S. component of the dual degree, as well as notify his/her advisor in the Department of Mathematics of the intention to enter into the dual degree program. Letters of recommendation for admission to the M.S. program can be taken from the letters of recommendation written for admission to the Ph.D. program, provided they have been written sufficiently recently.

### Faculty

**Csaba Biro**

*Assistant Professor*

**Mary E. Bradley**

*Associate Professor*

**Udayan B. Darji**

*Professor*

**Richard M. Davitt**

*Emeritus*

**Arnab Ganguly**

*Assistant Professor*

**Roger H. Geeslin**

*Emeritus*

**Gun-Min Gie**

*Assistant Professor*

**Ryan S. Gill**

*Associate Professor*

Graduate Advisor

**Aaron Hill**

*Assistant Professor*

**Changbing Hu**

*Assistant Professor*

**Chakram S. Jayanthi**

*Adjunct Professor*

**Thomas M. Jenkins**

*Emeritus*

**Andre Kezdy**

*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*

**Jianxu Li**

*Associate Professor*

**Robert B. McFadden**

*Emeritus*

**Alicia Miller**

*Associate Professor*

**Robert Powers**

*Distinguished Teaching Professor*

Assistant Department Chair

**Thomas Riedel**

*Professor*

Department Chair

**Prasanna Sahoo**

*Professor*

**Steven Seif**

*Associate Professor*

**Daniel Smith-Tone**

*Assistant Professor*

**David Swanson**

*Associate Professor*

Undergraduate Director

**Cristina Tone**

*Assistant Professor*

**David J. Wildstrom**

*Associate Professor*

**W. Wiley Williams**

*Emeritus*

**Shi-Yu Wu**

*Emeritus Adjunct Professor*

**Yongzhi Steve Xu**

*Professor*

**Stephen Young**

*Assistant Professor*

**Wei-Bin Zeng**

*Associate Professor*