*The Applied Mathematics graduate program is offered jointly by the University of Alabama at Birmingham, the University of Alabama (Tuscaloosa), and the University of Alabama in Huntsville.
Faculty
Alexander Blokh, Professor (Mathematics); Dynamical Systems.
Nikolai Chernov, Professor (Mathematics); Dynamical Systems, Ergodic Theory
Louis Dale, Professor (Mathematics); Ring Theory
Hassan Fathallah, Associate Professor (Mathematics); Mathematical Biology
Paul H. Jung, Assistant Professor (Mathematics); Probability Theory
Ioulia Karpechina, Professor (Mathematics); Partial Differential Equations and Mathematics Physics
Ian W. Knowles, Professor (Mathematics); Ordinary and Partial Differential Equations, Numerical Analysis
Roger T. Lewis, Professor Emeritus (Mathematics); Differential Equations, Spectral Theory
Junfang Li Assistant Professor (Mathematics); Nonlinear Partial Differential Equations.
John C. Mayer, Professor (Mathematics); Topology, Continuum Theory, Dynamical Systems
Mubenga N. Nkashama, Professor (Mathematics); Differential Equations, Dynamical Systems, Nonlinear Functional Analysis
Peter V. O'Neil, Professor Emeritus (Mathematics); Graph Theory, Combinatorics
Lex G. Oversteegen, Professor (Mathematics); Topology, Continuum Theory, Dynamical Systems
Yoshimi Saito, Professor (Mathematics); Scattering Theory, Differential Equations
Roman Shterenberg, Associate Professor (Mathematics); Mathematical Physics, Spectral Theory, Inverse Problems, Partial Differential Equations, Non-linear Partial Differential Equations
Nandor Simanyi, Professor (Mathematics); Dynamical Systems With Some Algebraic Flavour
Gunter Stolz, Professor (Mathematics); Spectral Theory, Mathematical Physics
James R. Ward, Jr., Professor Emeritus (Mathematics); Differential Equations, Nonlinear Analysis, Dynamical Systems
Rudi Weikard, Professor (Mathematics); Ordinary and Partial Differential Equations, Mathematical Physics
Gilbert Weinstein, Associate Professor (Mathematics); Partial Differential Equations, General Relativity, Differential Geometry
Yanni Zeng, Associate Professor (Mathematics); Nonlinear Partial Differential Equations, Numerical Analysis, Gas Dynamics
Henghui Zou, Associate Professor (Mathematics); Nonlinear Partial Differential Equations, Nonlinear Analysis
Program Information
Mathematics has always been divided into a pure and an applied branch. However, these have never been strictly separated. The Ph.D. program in applied mathematics stresses the interconnection between pure mathematics and its diverse applications.
Admission
Only students with a firm foundation in advanced calculus, algebra, and topology are considered for immediate admission to the Ph.D. program. A student lacking this background will be considered for admission to the M.S. program. Upon passing the qualifying examination, a student may transfer to the Ph.D. program. We expect at least a B average in a student's previous work and a score above 550 on each section of the Graduate Record Examination General Test.
Program of Study
Each student in the Ph.D. program has to take the following steps:
- Passing the Joint Program Exam (JPE), also called the Qualifying Exam. This is an exam in real analysis and applied linear algebra. It is administered by the Joint Program Committee, which includes graduate faculty from all three participating universities. A student that is admitted directly into the Ph.D. program is expected to take this exam by the end of the first year at the latest. This examination may be taken no more than twice.
- Completing 54 semester hours of graduate courses. The grade of each course has to be at least a B. The student's supervisory committee and the Joint Program Committee must approve the selection of courses. At least 18 hours must be in a major area of concentration, selected so that the student will be prepared to conduct research in an area of applied mathematics, while at least 12 hours have to be in a minor area of study, which is a subject outside mathematics.
- Passing a language or tool of research exam.
- Passing the Comprehensive Exam, which consists of a written part and an oral part.
- Preparing a dissertation, which must be a genuine contribution to mathematics.
- Passing the Final Examination (thesis defense).
Additional Information
For detailed information, contact Dr. Ioulia Karpechina, Mathematics Graduate Program Director, UAB Department of Mathematics, CH 493B, 1500 University Boulevard, Birmingham, Alabama 35294-1170.
Telephone 205-934-2154
E-mail karpeshi@uab.edu
Web www.math.uab.edu
Course Descriptions
For courses at cooperating universities, see the graduate catalogs of the University of Alabama (Tuscaloosa) and the University of Alabama in Huntsville. Unless otherwise noted, all courses are for 3 semester hours of credit. Course numbers preceded with an asterisk indicate courses that can be repeated for credit, with stated stipulations.
In addition to courses offered in the M.S. program, the following courses are offered in the Ph.D. program. All courses carry 3 hours of credit unless otherwise noted.
740. Advanced Complex Analysis. Varying topics. May be repeated for credit. Prerequisites: Having passed the Qualifying Exam or permission of instructor.
745. Functional Analysis I. Normed and Banach spaces, inner product and Hibert spaces, linear functionals and dual spaces, operators in Hilbert spaces, theory of unbounded sesquilinear forms, Hahn-Banach, open mapping, and closed graph theorems, spectral theory. Prerequisites: Having passed the Qualifying Exam or permission of instructor.
746. Functional Analysis II. Varying topics. May be repeated for credit. Prerequisites: Having passed the Qualifying Exam or permission of instructor.
747. Linear Operators in Hilbert Space. Hilbert space, Bessel's inequality, Parseval's formula, bounded and unbounded linear operators, representation theorems, the Friedrichs extension, the spectral theorem for self-adjoint operators, spectral theory for Schrödinger operators. Prerequisites: Having passed the Qualifying Exam or permission of instructor.
748. Fourier Transforms. Fourier transform and inverse transform of tempered distributions; applications to partial differential equations. Prerequisites: Having passed the Qualifying Exam or permission of instructor.
750. Advanced Ordinary Differential Equations. Varying topics. May be repeated for credit. Prerequisites: Having passed the Qualifying Exam or permission of instructor.
753. Nonlinear Analysis. Selected topics including degree theory, bifurcation theory, and topological methods. Prerequisite: Having passed the Qualifying Exam or permission of instructor.
755. Advanced Partial Differential Equations. Selected topics varying with instructor. : Having passed the Qualifying Exam or permission of instructor.
760. Dynamical Systems I. Continuous dynamical systems. Limit sets, local sections, minimal sets, centers of attraction, recurrence, stable and wandering points, flow boxes, and monotone sequences in planar dynamical systems, Poincare-Bendixson theorem. Prerequisites: Having passed the Qualifying Exam or permission of instructor.
761. Dynamical Systems II. Discrete dynamical systems. Hyperbolicity, symbolic dynamics, chaos, homoclinic orbits, bifurcations, and attractors (theory and examples). Prerequisite: Having passed the Qualifying Exam or permission of instructor.
770. Continuum Theory. Pathology of compact connected metric spaces. Inverse limits, boundary bumping theorem, Hahn-Muzukiewicz theorem, composants, chainable and circle-like continua, irreducibility, separation, unicoherence, indecomposability. Prerequisite: Having passed the Qualifying Exam or permission of instructor.
772. Complex Analytic Dynamics. Riemann surfaces, iteration theory of polynomials, rational functions and entire functions, fixed point theory, Mandelbrot set, Julia sets, prime ends, conformal mappings. Prerequisite: Having passed the Qualifying Exam or permission of instructor.
774. Algebraic Topology. Covering spaces; introduction to homotopy theory, singular homology, cohomology. Prerequisites: Having passed the Qualifying Exam or permission of instructor.
776. Advanced Differential Geometry. Varying topics. May be repeated for credit. Prerequisite: Having passed the Qualifying Exam or permission of instructor.
781. Differential Topology I. A study of differentiable structures on manifolds, primarily from a
global viewport: smooth mappings including diffeomorphisms, immersions and submersions; submanifolds and transversality.
782. Differential Topology II. A continuation of MA 781, with further applications such as Morse Theory.
790,791. Mathematics Seminar. This course covers special topics in mathematics and the applications of mathematics. May be repeated for credit when topics vary. Prerequisites vary with topics.
792-797. Special Topics in Mathematics. These courses cover special topics in mathematics and the applications of mathematics. May be repeated for credit when topics vary. Prerequisites Permission of instructor. 1, 2, or 3 hours.
798. Nondissertation Research. Prerequisite: Permission of instructor. 1-6 hours.
799. Dissertation Research. Prerequisite: Admission to candidacy and permission of instructor. 1-6 hours.
Biomathematics (BST)
Please see Biostatistics (BST) course descriptions for additional graduate courses in applied mathematics
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