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

Course #          DescriptionCredit 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 Hours24

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

Course #          DescriptionCredit 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 Hours24

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.)

Course #          DescriptionCredit Hours
Core Course Requirements
Select one of the following sequences:16
PHST 661
& PHST 662
Probability
& Mathematical Statistics
MATH 561
& MATH 562
Probability
& Mathematical Statistics
PHST 680
& PHST 681
Biostatistical Methods I
& Biostatistical Methods II2
6
PHST 682Multivariate Statistical Analysis 33
PHST 683Survival Analysis3
PHST 684Categorical Data Analysis3
Select an Epidemiology Elective43
PHST 620Introduction to Statistical Computing3
PHST 624
& PHST 626
Clinical Trials I: Planning and Design
& Clinical Trials Statistics Laboratory
3
PHST 626Clinical Trials Statistics Laboratory1
PHST 602Biostatistics Seminar1
PHST 675Independent Study in Biostatistics 52
Public Health Background Courser, PH6
Additional Requirements - Option Thesis
PHST 666Master's Thesis Research 76
Minimum Total Hours40
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 only if the student completes both the MATH 663-MATH 664 and MATH 667-MATH 668 sequences.

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)

The Industrial Internship required by the Department of Mathematics and the Master's Project or 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 biostatistics so that it satisfies the Project or Thesis, and contain advanced mathematical content so that it satisfies the Industrial Internship. Likewise, the technical report must meet two requirements: it must satisfy the requirements for a Master's Project report or Master's Thesis for the M.S. degree and it must be written at an advanced mathematical level expected Industrial Internship. Students should enroll in the Master's Project (PHST 675) or Master's Thesis (PHST 666) courses during or shortly after completion of the Industrial Internship to take advantage of the combined Industrial Internship and Master's Project/Thesis.

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