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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 A Profile of Focused Research Areas The research interests of the mathematics faculty at UCF can be classified into the following focused research areas, listed in the order of the classifications in the Mathematical Reviews. Applied mathematics and applied analysis are emphasized in several of the research areas. For the convenience of the reader we present the journals in which our faculty have published via three links: Alphabetic list of journals with a list of faculty that have published in each journal. Alphabetic list of faculty with the journals they have published in. A link to Math Sci Net for lists and reviews of individual faculty publications (can be reached by clicking on the individual faculty member's link and then publications). Algebra, Graph Theory, and Combinatorics Approximation Theory, Classical Analysis, and Computations Differential and Integral Equations Inverse and Ill-Posed Problems, Image Processing Functional Analysis, Harmonic Analysis & Applications Probability Theory and Mathematical Statistics Numerical Analysis, Scientific Computation and Simulation Nonlinear Science and Applied Mathematics in the Physical Sciences I.  Algebra, Graph Theory, and Combinatorics Commutative algebra Algebraic geometry Discrete mathematics Graph theory Combinatorics Linear algebra; computational algebra Applications to computer science Researchers: Richard Caron Peter Hilton Mourad Ismail Jeong-Hyun Kang Heath Martin Michael Reid Zixia Song Nick Zhao      Linear Algebra and Matrix Theory (Secondary Interest) Researchers: Deguanh Han Zuhair Nashed Alexander Tovbis II.  Approximation Theory, Classical Analysis, and Computations Special functions and orthogonal polynomials Approximation theory Inequalities Asymptotic expansions and perturbation methods Complex analysis; computational conformal mappings Splines and wavelets Optimization, variational methods and control theory Researchers: Joby Anthony John Cannon Roy Choudhury Mourad Ismail David Kaup Xin Li Ram Mohapatra Ziad Musslimani Zuhair Nashed Marianna Pensky Rene Rodriguez Qiyu Sun Alexander Tovbis Yanfei Wang Jiongmin Yong III.  Differential and Integral Equations Partial differential equations Integral equations Pseudodifferential operators and equations Nonlinear Schrodinger equations Free boundary problems Integral transforms Researchers: Larry Andrews John Cannon Roy Choudhury Mourad Ismail Alexander Katsevich David Kaup Ram Mohapatra Ziad Musslimani Zuhair Nashed Yuanwei Qi David Rollins Constance Schober Bhimsen Shivamoggi Alexander Tovbis Kuppalapalle Vajravelu Yanfei Wang Jiongmin Yong IV.  Inverse and Ill-Posed Problems, Image Processing Inverse problems in the applied sciences, engineering, and medicine Ill-posed problems Tomography and the Radon transform Image processing and computational methods; medical imaging Researchers: John Cannon Alexander Katsevich Mourad Ismail David Kaup Zuhair Nashed Yvonne Ou Alexander Tovbis Yanfei Wang V.  Functional Analysis, Harmonic Analysis & Applications Linear and nonlinear functional analysis Operator theory and operator algebras Linear and nonlinear operator equations Wavelets and applied harmonic analysis Signal processing and sampling expansions Measure theory and doubly stochastic measures Random operator equations Generalized functions and function spaces Set-valued analysis and variational inequalities Functional analysis methods in applied mathematics, numerical analysis and optimization Application of functional analysis and harmonic analysis in engineering Researchers: Dorin Dutkay Deguang Han Piotr Mikusinski Zuhair Nashed Marianna Pensky Gary Richardson Qiyu Sun VI.  Probability Theory and Mathematical Statistics Probability and Theoretical Statistics Convergence spaces Bayesian analysis Statistical inference Survival analysis Density estimation; parameter estimation Nonparametric models Wavelets in statistics Optimization and computations in statistics Stochastics Probabilistic metric spaces and stochastic measures Researchers: Mariana Pensky Yuanwei Qi Jian-Jian Ren Gary Richardson Jiongmin Yong VII.  Numerical Analysis, Scientific Computation and Simulation Theory of numerical analysis Numerical functional analysis and optimization Scientific computation Numerical optimization Numerical linear algebra Modeling and simulation Computational physics Researchers: John Cannon Roy Choudhury Eleftherios Gkioulekas David Kaup Ziad Musslimani Zuhair Nashed Yvonne Ou Constance Schober Qiyu Sun Alexander Tovbis Kuppalapalle Vajravelu Yanfei Wang VIII.  Nonlinear Science and Applied Mathematics in the Physical Sciences Nonlinear waves Wave propagation in random media; geophysical and optical applications Nonlinear dynamics; chaotic dynamics Integrable and near-integrable systems Fluid dynamics and turbulence theory Plasma physics and modeling Nonlinear optics; fiber optics Soliton equations Numerical fluid dynamics Laser communication Researchers: Larry Andrews John Cannon Roy Choudhury Eleftherios Gkioulekas David Kaup Ziad Musslimani Yvonne Ou Yuanwei Qi David Rollins Bhimsen Shivamoggi Constance Schober Alexander Tovbis Kuppalapalle Vajravelu Cynthia Young