Objectives
This program is designed for students interested in research careers in mathematics in the military, industry or government. It also prepares individuals to teaching and/or do research at college.
Admission Requirement
All applicants must submit to the Director of Graduate Programs, Department of Mathematical Sciences, their Graduate Record Examination scores, three letters of references from professionals in the area of interest of the applicant, and transcripts from all colleges attended. A minimum of 3.0 on a scale of 4.0 overall and in the courses related to the field of the Ph.D. is required.
APPLIED MATHEMATICS CONCENTRATION
Students who desire to enter the Applied Mathematics concentration with Master’s degree must have successfully completed the following courses, by examination or by successfully completing the graduate courses with a grade of B or above: Abstract Algebra, Real Analysis, and Complex Analysis. Depending upon the student’s educational background, some students may also be required to take some master level graduate mathematics courses.
Students who desire to enter the Imaging Applied Mathematics concentration from baccalaureate degree must have successfully completed the following courses, by examination or by successfully completing the undergraduate courses: Advanced Calculus I, Linear Algebra, Statistics, Probability, and Algebraic Structures I. The plan of study for this scenario will be agreed upon by the student, his/her advisor, and the Graduate Committee, Department of Mathematical Sciences. Depending upon the student’s educational background, some students may also be required to take some undergraduate mathematics courses.
MATHEMATICAL PHYSICS CONCENTRATION
Students who desire to enter the Mathematical Physics concentration with Master’s degree in physics or a related area must have successfully completed the following courses, by examination or by successfully completing the graduate courses with a grade of B or above: Thermodynamics and Kinetic Theory, Classical Mechanics, Advanced Electromagnetic Theory, and Quantum Mechanics. Depending upon the student’s educational background, some students may also be required to take some masters level graduate mathematics and physics courses.
Students with baccalaureate degrees may enter the mathematical physics concentration with the approval of the Graduate Committee. Depending upon the student’s educational background, some students may also be required to take some undergraduate mathematics and physics courses.
Graduate Assistantship and Fellowship
Graduate research or teaching assistantships and fellowships are available. Detailed information and application forms may be obtained from the Applied Mathematics Research Center, or the Department of Mathematical Sciences.
Curriculum
The Ph.D. program in interdisciplinary applied mathematics and mathematical physics is flexible enough to accommodate students with diversified backgrounds. In consultation with the Director of Graduate Programs, each student develops a course of study in applied mathematics (Applied Mathematics concentration) or physics (Mathematical Physics concentration) whichever is most relevant to his/her professional and career objectives.
Ph.D. Requirements
Courses and Qualifying Examinations
I. CONCENTRATION A: APPLIED MATHEMATICS
A student who enters the program with a baccalaureate degree must complete his/her Master’s degree in the related area. Students who have Master’s degrees with no prior Ph.D. graduate course work must complete 30 credit hours of graduate level courses listed below. In addition at least 9 credit hours of research on dissertation are required. A G.P.A. of 3.0 on a 4.0 scale or above must be maintained.
The program requires the Ph.D. candidate to have reading knowledge of at least one foreign language approved by the Director of Graduate Programs.
Required Courses (12 Credit Hours)
MTSC863 Functional Analysis

3 Hours

MTSC861 Real Analysis

3 Hours

MTSC871 Complex Analysis

3 Hours

One of the following two courses:
MTSC887 Image Processing

3 Hours

MTSC821 Scientific Computation I

3 Hours

Electives (18 credit hours)
Students may take an additional 18 credit hours from the list of elective courses to satisfy the credit hours requirement with the approval of the student's advisor. Students must take any two of the following courses:
Students may take an additional 18 credit hours from the list of elective courses to satisfy the credit hours requirement with the approval of the student's advisor. Students must take any two of the following courses:
PHYS657 Mathematical Methods

3 Hours

MTSC885 Computational Geometry

3 Hours

PHYS671 Advanced Electromagnetic Theory

3 Hours

MTSC883 Wavelet Analysis

3 Hours

Qualifying Examinations
Upon completing the course requirement, each student must successfully pass two written examinations. One examination is based on two courses selected by the student from Functional Analysis, Real Analysis and Complex Analysis. The other examination is based on two courses selected by the student from Image Processing, Mathematical Methods, Advanced Electromagnetic Theory, Computational Geometry, Wavelet Analysis, Numerical Analysis and Scientific Computation I and courses approved by the Graduate Committee. A student must pass an oral examination on a subject area directly related to his/her dissertation.
Upon completing the course requirement, each student must successfully pass two written examinations. One examination is based on two courses selected by the student from Functional Analysis, Real Analysis and Complex Analysis. The other examination is based on two courses selected by the student from Image Processing, Mathematical Methods, Advanced Electromagnetic Theory, Computational Geometry, Wavelet Analysis, Numerical Analysis and Scientific Computation I and courses approved by the Graduate Committee. A student must pass an oral examination on a subject area directly related to his/her dissertation.
II. CONCENTRATION B: MATHEMATICAL PHYSICS
A student who enters the program with a baccalaureate degree must complete his or her Master’s degree in the related area. Students who have Master degrees with no prior Ph.D. graduate course work must complete 39 credit hours of graduate level courses listed below. In addition at least 9 credit hours of research on dissertation are required. A G.P.A. of 3.0 or above on a 4.0 scale must be maintained.
The program requires the Ph.D. candidate to have reading knowledge of at least one foreign language approved by the Graduate Committee. Each candidate is required to take a foreign language reading in mathematics or physics approved by Department of Mathematical Sciences.
A sequence of core courses required by all Ph.D. candidates includes the following: PHYS665 Statistical Mechanics, PHYS672 Advanced Electromagnetic Theory, PHYS676 Quantum Mechanics, PHYS655 Computational Methods, MTSC863 Functional Analysis or MTSC857 Integral Equations, and MTSC871 Complex Analysis. Any student found deficient in any of these areas may be required to take appropriate courses to remove that deficiency.
Required Courses (18 credit hours)
PHYS655 Computational Methods

3 Hours

PHYS665 Statistical Mechanics

3 Hours

PHYS672 Advanced Electromagnetic Theory

3 Hours

PHYS676 Quantum Mechanics

3 Hours

MTSC863 Functional Analysis

3 Hours

MTSC871 Complex Analysis

3 Hours

Electives (12 credit hours)
Students may take an additional 12 credit hours from the list of elective courses to satisfy the credit hours requirement with the approval of the student's advisor.
Qualifying Examinations
Each student must successfully pass the written general examination in physics which encompasses the area of Thermodynamics and Kinetic Theory, Classical Mechanics, Advanced Electromagnetic Theory, and Quantum Mechanics. In addition, a student must pass an oral examination on a subject area chosen by his/her advisor.
Elective Courses:
MTSC821 Scientific Computation I

3 Hours

MTSC822 Scientific Computation II

3 Hours

MTSC833 Stochastic Processes

3 Hours

MTSC853 Partial Differential Equations

3 Hours

MTSC867 Numerical Analysis

3 Hours

MTSC851 Ordinary Differential Equations

3 Hours

MTSC885 Computational Geometry

3 Hours

MTSC857 Integral Equations

3 Hours

MTSC875 Inverse Problems

3 Hours

MTSC887 Image Processing

3 Hours

MTSC811 Abstract Algebra

3 Hours

PHYS655 Computational Methods

3 Hours

PHYS665 Statistical Mechanics

3 Hours

PHYS671 Advanced Electromagnetic Theory I

3 Hours

PHYS672 Advanced Electromagnetic Theory II

3 Hours

PHYS652 Classical Mechanics

3 Hours

PHYS657 Mathematical Methods

3 Hours

PHYS661 Solid State Physics

3 Hours

PHYS675 Quantum Mechanics

3 Hours

MTSC883 Wavelet Analysis

3 Hours

MTSC889 Topics in Applied Mathematics

3 Hours

Dissertation
Each student must select or have assigned by the Ph.D. Program Committee, two dissertation advisors, one in mathematics and one in physics or a related applied area. The most important requirement for the Ph.D. degree is the satisfactory completion of a scientific investigation, and the writing of a dissertation on that investigation represents a significant contribution to the research literature. Each student must complete a dissertation with his/her dissertation advisors and successfully defend the dissertation before his/her Ph.D. Program Committee of five members including one external examiner.
MTSC890 Dissertation

39 Hours

Sustaining Status
Once a student has completed all the course requirements, passed the Qualifying Examinations, met the language requirements, and registered for 9 credits of dissertation (MTSC890), but has not completed his/her dissertation, then the student is required to maintain his/her matriculation in the degree program by registering for Doctoral Sustaining (MTSC899). A student must be registered in the semester in which the degree is awarded.
MTSC899 Doctoral Sustaining

0 Hours
