CLASSES I teach many courses for undergraduate and graduate students. For graduate students I mainly teach Advanced Numerical Analysis courses such as Numerical Linear Algebra, Numerical Approximation, Numerical Solution of PDE's, Wavelets Analysis, and Numerical Optimization. STUDENTS Nineteen Ph.D. students have graduated under my supervision. They are in order of seniority, Dr. Wenjie He, Dr. Xiangming Xu, Dr. Gerard Awanou, Dr. V.Baramidze, Dr. K. Nam, J. Zhou, O. Cho, H. P. Liu, J. B. Wu, Bree Ettinger, Louis Y. Liu, Qianying Hong, and Leopold Matamba Messi, George Slavov, James Lanterman, Abraham Varghese, Daniel Mckenzie, Clayton Mersmann, and Yidong Xu. . Dr. Wenjie He is currently an associate professor at the University of Missouri, St. Louis. Dr. Xiangming Xu is a chief scientist in a company working on signal and image communications. The research work of Dr. Awanou's dissertation won him the best student paper award. He won a prestigeous Sloan fellowship in 2009. Dr. Awanou is a full professor at University of Illinois, Chicago now. V. Baramidze obtained the Graduate Student Excellence in Research Award from the University of Georgia. Dr. Leopold Matamba Messi is now a postdoc at Mathematical Bioscience Institute at Ohio State University. Dr. G. Slavov works for a Hedge fund company in Bogarlia. Dr. A. Varghese is an assistant professor at a region university in Viginia. Dr. J. Lanterman works for IHG. Dr. Clayton Mersmann is an instructor for University of South Florida, St. Petersburg, Florida. Dr. Daniel Mckenzie is a postdoc at UCLA. Dr. Yidong Xu returnd to his hometown, Shanghai, China to work. INTERNSHIPS I have sent one student to the Boeing company and one student to NASA Langley Reserach center for internship. POSTDOC my Ph.d. students got a postodoc training at Institute of Mathematics and Applications(IMA), University of Minnesota and Mathematical Biology Institute(MBI), Ohio State Univiersity. I have supervised 7 undergraduate students, Katie Agle, Dustin Burns, Coop Cunliffe, Grant Fiddyment, Max Mautner, and Tarik Trent for an NSF REU program during the summer of 2008. Their research work can be found here 2011-2012 FALL, 2011: MATH 2260 INTEGRAL CALCULUS The objective of this course is to learn to compute volumes of various solids by slicing and cylindrical shell, length of various arcs and solve separable differential equations. Next we will learn various techniques for integration. In addition, we will discuss infinite sequences and examine the convergence of series. Finally, we study vectors, their calculations, line and planes in the 3D space. . Course Syllabus FALL, 2011: FYOS MATHEMATICS FOR DIGITAL IMAGES I will explain the matrix theory for handling digital images. Course Syllabus FALL, 2011: MATH8550 VRG: MATHEMATICAL ANALYSIS FOR IMAGE DENOISING AND DEBLURRING I will introduce digital and analog image functions in \ell_2 and L_2 as well as BV functions. We shall discuss optimization, nonlinear PDE, wavelet/framelet and compressed sensing approaches forimage denoising, deblurring, and impainting. We shall first study the well-known Rudin-Osher-Fatemi(ROF) model and many properties of its solution and its numerical approximation by using finite difference method, finite element method, prime-and-dual algorithm, prejected gradient algorithm, and bivariate spline method. Due to the nonlinearity of the problem, iterative computation has to be used. The convergence of the iteration will be discussed. The convergence of the discrete solution to the continuum solution will be studied. The compressed sensing approach will also be studied. Removing noises from measurements over scattered locations has an extensive applications in real life. The goal of the research for this group is to extend the study to deal with problems how to remove noises from scattered data values. In particular, when data values represent a function which is a not very smooth surface, how to remove its noises and approximate the function will be investigated. Course Syllabus 2010-2011 FALL, 2010: MATH 2250 DIFFERENTIAL CALCULUS The objective of this course is to learn to take a derivative of various kinds of functions and their applications for maximal and minimal problems as well as for graphical display. Course Syllabus FALL, 2010: MATH 8500 ADVANCED NUMERICAL ANALYSIS A focus on numerical solutions to partial differential equations. Specifically using the finite difference method in addition to the finite element method. A use of multivariate splines to solve the POisson equation, biharmonic equations, heat equations over arbitrary polygonal domains, and others. Course Syllabus 2009-2010 FALL, 2009: MATH 2250 DIFFERENTIAL CALCULUS (TWO SECTIONS) The objective of this course is to learn to take a derivative of various kinds of functions and their applications for maximal and minimal problems as well as for graphical display. Course Syllabus SPRING, 2010: MATH 8550 SPECIAL TOPICS ON NUMERICAL ANALYSIS This course covers classical and modern theories on optimization. The first half of the course will focus on classical theory on constrained and unconstrained minimization. The latter half will cover advanced theories on L1 and l1 minimization as well as nonconvex minimization techniques. Course Syllabus 2008-2009 FALL, 2008: MATH 4500 NUMERICAL ANALYSIS The first of one of two courses on numerical analysis. We shall cover solving nonlinear equations, finding polynomial interpolations, numerical derivatives integrations and numerical solutions to ordinary differential equations. Course Syllabus FALL, 2008: MATH 2500 MULTIVARIATE CALCULUS Multivariate differential and integral calculus. We will cover concepts such as vectors, cross-products, partial derivatives, gradients, tangent planes, polar coordinates, parametric curves, line integrals, surface integrals, and many others. A few theorems that will be covered are the LaGrange Multiplier Theorem, Green's Theorem, Divergence Theorem, Stokes Theorem as well as integral techniques. Course Syllabus 2007-2008 FALL, 2007: MATH 8510 ADVANCED NUMERICAL ANALYSIS A focus on numerical solutions to partial differential equations. Specifically using the finite difference method in addition to the finite element method. A use of multivariate splines to solve the POisson equation, biharmonic equations, heat equations over arbitrary polygonal domains, and others. FALL, 2007: MATH 2500 MULTIVARIATE CALCULUS Multivariate differential and integral calculus. We will cover concepts such as vectors, cross-products, partial derivatives, gradients, tangent planes, polar coordinates, parametric curves, line integrals, surface integrals, and many others. A few theorems that will be covered are the LaGrange Multiplier Theorem, Green's Theorem, Divergence Theorem, Stokes Theorem as well as integral techniques. Course Syllabus SPRING, 2008: MATH 3100 SEQUENCE AND SERIES An introduction to mathematical analysis. Proof based course that will teach induction, and the analysis of the convergence of sequences, as well as the convergence of series and the various tests that aid in their analysis. We conclude with a discussion of series of functions, namely Fourier series.
