# 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

#### Doctor of Philosophy in Applied and Industrial Mathematics

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

**Core Courses**

Code | Title | Hours |
---|---|---|

Course # Description | Credit Hours | |

Select two sequences from the following: | 12 | |

MATH 621 & MATH 622 | Algebra I & Algebra II | |

MATH 681 & MATH 682 | Combinatorics and Graph Theory I & Combinatorics and Graph Theory II | |

MATH 601 & MATH 602 | Real Analysis I & Real Analysis II | |

Select two sequences from the following: | 12 | |

MATH 635 & MATH 636 | Mathematical Modeling I & Mathematical Modeling II | |

MATH 667 & MATH 668 | Statistical Inference & Linear Statistical Modeling | |

MATH 663 & MATH 664 | Theory of Probability I & Therory of Probability II | |

Minimum Total Hours | 24 |

**Additional Topics and Area of Specialization**

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.

**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.

**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

**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**

Code | Title | Hours |
---|---|---|

Course # Description | Credit Hours | |

Select two sequences from the following: | 12 | |

MATH 621 & MATH 622 | Algebra I & Algebra II | |

MATH 681 & MATH 682 | Combinatorics and Graph Theory I & Combinatorics and Graph Theory II | |

MATH 601 & MATH 602 | Real Analysis I & Real Analysis II | |

Select two sequences from the following: | 12 | |

MATH 635 & MATH 636 | Mathematical Modeling I & Mathematical Modeling II | |

MATH 667 & MATH 668 | Statistical Inference & Linear Statistical Modeling | |

MATH 663 & MATH 664 | Theory of Probability I & Therory of Probability II | |

Minimum Total Hours | 24 |

**Elective Courses**

(18 hours) * Application area courses are 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.

#### Biostatistics (M.S.)

Code | Title | Hours |
---|---|---|

Course # Description | Credit Hours | |

Core Course Requirements | ||

Select one of the following sequences:^{1} | 6 | |

PHST 661 & PHST 662 | Probability & Mathematical Statistics | |

MATH 561 & MATH 562 | Probability & Mathematical Statistics | |

PHST 680 & PHST 681 | Biostatistical Methods I & Biostatistical Methods II ^{2} | 6 |

PHST 682 | Multivariate Statistical Analysis ^{3} | 3 |

PHST 683 | Survival Analysis | 3 |

PHST 684 | Categorical Data Analysis | 3 |

Select an Epidemiology Elective^{4} | 3 | |

PHST 620 | Introduction to Statistical Computing | 3 |

PHST 624 & PHST 626 | Clinical Trials I: Planning and Design & Clinical Trials Statistics Laboratory | 3 |

PHST 626 | Clinical Trials Statistics Laboratory | 1 |

PHST 602 | Biostatistics Seminar | 1 |

PHST 675 | Independent Study in Biostatistics ^{5} | 2 |

Public Health Background Courser, PH^{6} | ||

Additional Requirements - Option Thesis | ||

PHST 666 | Master's Thesis Research ^{7} | 6 |

Minimum Total Hours | 40 |

**Footnotes**

^{1} | The PHST 661-PHST 662/MATH 561-MATH 562 requirement is waived if the student takes MATH 663 and MATH 667. The PHST 681-PHST 682 requirement is waived if the student takes MATH 667-MATH 668. Both requirements (PHST 661-PHST 662/MATH 561-MATH 562 and PHST 681-PHST 682) are waived |

^{2} | 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. |

^{3} | Can be replaced by an advisor-approved graduate-level course in Bioinformatics and Biostatistics (PHST 691, PHST 704, etc.) |

^{4} | Fulfilled by any advisor-approved course in Epidemiology, including but not limited to PHEP 602, PHEP 618, and PHEP 650 |

^{5} | This is a project completed under the supervision of a faculty member |

^{6} | 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. |

^{7} | To be completed in accordance with the guidelines written in the catalog entry for the M.S. in Bioinformatics and Biostatistics Degree. |

**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 of 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

**Thomas Riedel**

*Professor*

Department Chair

**Csaba Biro**

*Associate *Professor

**Mary E. Bradley**

*Associate Professor*

**Udayan B. Darji**

*Professor*

**Richard M. Davitt**

*Emeritus*

**Roger H. Geeslin**

*Emeritus*

**Gun-Min Gie**

*Assistant Professor*

**Ryan S. Gill**

*Associate Professor*

Graduate Advisor

**Aaron Hill**

*Assistant Professor*

**Changbing Hu**

*Associate 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*

**Bingtuan Li**

*Professor*

**Jiaxu Li**

*Associate Professor*

**Jinjia Li**

*Assistant Professor*

**Robert B. McFadden**

*Emeritus*

**Alicia Miller**

*Associate Professor*

**Robert Powers**

*Distinguished Teaching Professor*

Assistant Department Chair

**Prasanna Sahoo**

*Professor*

**Steven Seif**

*Associate Professor*

**Daniel Smith-Tone**

*Assistant Professor*

**David Swanson**

*Associate Professor*

Undergraduate Director

**Cristina Tone***Associate Professor*

**David J. Wildstrom**

*Associate Professor*

**W. Wiley Williams**

*Emeritus*

**Shi-Yu Wu**

*Emeritus Adjunct Professor*

**Yongzhi Steve Xu**

*Professor*

**Wei-Bin Zeng**

*Associate Professor*

**Xuwen Zhu***Assistant Professor*