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PH.D. PROGRAM IN INTERDISCIPLINARY APPLIED MATHEMATICS AND MATHEMATICAL PHYSICS
1. 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.
2. ADMISSION REQUIREMENT
All applicants must submit to the Department of Applied Mathematics and Theoretical Physics 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.
2.1 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 Department of Applied Mathematics and Theoretical Physics. Depending upon the student’s educational background, some students may also be required to take some undergraduate mathematics courses.
2.2 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 Department of Applied Mathematics and Theoretical Physics. Depending upon the student’s educational background, some students may also be required to take some undergraduate mathematics and physics courses.
3. 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 Applied Mathematics and Theoretical Physics.
4. 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 Department of Applied Mathematics and Theoretical Physics, 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. 5. Ph.D. REQUIREMENTS
5.1 Courses Qualifying Examinations
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 in a foreign language approved by the Department of Applied Mathematics and Theoretical Physics. Required Courses (12 Credit Hours)
25-863 Functional Analysis 3 Hours 25-861 Real Analysis 3 Hours 25-871 Complex Analysis 3 Hours
One of the following two courses: 25-887 Image Processing 3 Hours 25-821 Scientific Computation I 3 Hours
Electives (18 credit hours)
Students may take an additional 18 credit hours from the list of elective courses on page 4 and 5 to satisfy the credit hours requirement with the approval of the student's advisor. Students must take any two of the following courses:
26-857 Mathematical Methods 3 Hours 25-885 Computational Geometry 3 Hours 26-871 Advanced Electromagnetic Theory 3 Hours 25-883 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 Department of Applied Mathematics and Theoretical Physics. A student must pass an oral examination on a subject area directly related to his/her dissertation.
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 in a foreign language approved by the Department of Applied Mathematics and Theoretical Physics. Each candidate is required to take a foreign language reading in mathematics or physics approved by Department of Applied Mathematics and Theoretical Physics. A sequence of core courses required by all Ph.D. candidates includes the following: 26-865 Statistical Mechanics, 26-872 Advanced Electromagnetic Theory, 26-876 Quantum Mechanics, 26-855 Computational Methods, 25-863 Functional Analysis, and 25-871 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)
26-855 Computational Methods 3 Hours 26-865 Statistical Mechanics 3 Hours 26-872 Advanced Electromagnetic Theory 3 Hours 26-876 Quantum Mechanics 3 Hours 25-863 Functional Analysis 3 Hours 25-871 Complex Analysis 3 Hours
Electives (12 credit hours)
Students may take an additional 12 credit hours from the list of elective courses on page 4 and 5 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:
25-821 Scientific Computation I 3 Hours 25-822 Scientific Computation II 3 Hours 25-833 Stochastic Processes 3 Hours 25-853 Partial Differential Equations 3 Hours 25-861 Numerical Analysis 3 Hours 25-851 Ordinary Differential Equations 3 Hours 25-885 Computational Geometry 3 Hours 25-857 Integral Equations 3 Hours 25-875 Inverse Problems 3 Hours 25-887 Image Processing 3 Hours 25-811 Abstract Algebra 3 Hours 26-855 Computational Methods 3 Hours 26-865 Statistical Mechanics 3 Hours 26-871 Advanced Electromagnetic Theory I 3 Hours 26-872 Advanced Electromagnetic Theory II 3 Hours 26-852 Classical Mechanics 3 Hours 26-857 Mathematical Methods 3 Hours 26-861 Solid State Physics 3 Hours 26-875 Quantum Mechanics 3 Hours 25-883 Wavelet Analysis 3 Hours 25-889 Topics in Applied Mathematics 3 Hours
5.2 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.
25-890 Dissertation 3-9 Hours 26-890 Dissertation 3-9 Hours
Once a student has completed all the course requirements, passed the Qualifying Examinations, met the language requirements, and registered for 9 credits of dissertation (25-890 or 26-890), 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 (25-999 or 26-999). A student must be registered in the semester in which the degree is awarded.
25-999 Doctoral Sustaining 3-9 Hours 26-999 Doctoral Sustaining 3-9 Hours
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