Graduate Backup 20220530

Real analysis is fundamental to many of the other courses in applied mathematics. Topics include metric spaces, Banach spaces, measure theory, and the theory of integration and differentiation.

This covers certain topological-algebraic structures that can be applied analytic problems. Topics include Topological vector spaces, Completeness, Convexity, Duality in Banach spaces, Distributions, Fourier transforms, Banach algebras, Bounded and unbounded operators on a Hilbert spaces.

Basic and advanced theories in probability and stochastic processes will be covered including expectation, conditional probability, law of large numbers, central limit theorem, markov chains, martingales, and Brownian motions.

This course emphasizes the development of basic numerical algorithms for common problems formulated in science and engineering. The course covers interpolation and approximation of functions, numerical differentiation and integration, numerical solutions of ordinary differential equations and direct and iterative methods in linear algebra.

This course covers basic theory and methods for matrix computation. LU-decomposition, QR factorization, least square method. Condition numbers and accuracy. Solutions of large sparse matrix system and iterative methods.

This course covers the theory of the classical partial differential equations, the method of characteristics for first order equations, the Fourier transform, the theory of distributions in Sobolev spaces, and techniques of functional analysis.

This course covers the theory of the nonlinear partial differential equations, the method of characteristics for first order equations, Quasilinear equations, Fixed point theorems, and fully nonlinear equations.

Finite difference methods for solving ordinary and partial differential equations. Fundamental concepts of consistency, accuracy, stability and convergence of finite difference methods will be covered. Associated theory will be discussed.

Finite element methods for ordinary and partial differential equations will be covered. Algorithm development, analysis, and computer implementation issues will be addressed. Also we will discuss the generalized and discontinuous Galerkin finite element method.

This course provides tools to characterize qualitative properties of linear and nonlinear dynamical systems in both continuous and discrete time. The course covers stability analysis of differential equations, Hamiltonian systems, Pointcare mapping, and Reduction methods.

This course provides concise introductions to mathematical methods for problems formulated in science and engineering. Some selected topics are functions of a complex variable, Fourier analysis, calculus of variations, perturbation methods, special functions, dimension analysis, tensor analysis.

Brownian motion, Ito’s rule, stochastic integrals, and stochastic differential equations as well as their numerical simulations are covered. Application to chemistry, finance and partial differential equations will be also included

Mathematical backgrounds for basic statistical analyses are covered. We deal with properties of probability distributions, limit theorems including laws of larger numbers and central limit theorem, theories for hypothesis test and inference, analysis of variance, and non-parametric analysis

Linear model, multivariate analysis, survival analysis and some machine learning methods for genome and clinical data analysis using R software

This course provides fundamental techniques in scientific computation with an introduction to the theory and software of the topics: Monte Carlo simulation, numerical linear algebra, numerical methods of ordinary and partial differential equations, Fourier and wavelet transform methods. This course may involve numerical coding assignments and some use of software packages.

Topics include an overview of computer hardware, software tools and packages, commonly used numerical methods, visualization of results, high-performance computing and parallel programming. This course may involve numerical coding assignments and some use of software packages.

This course covers topics of current interest in computational mathematics for solving linear and nonlinear partial differential equations.

This course covers topics of current interest in computational mathematics for solving linear and nonlinear partial differential equations.

This course covers an introduction of L_p theory of elliptic and parabolic differential equation and theory of Navier-Stokes equations.

This course covers topics of current interest in partial differential equations.

This course covers advanced topics in mathematical biology including modeling in biochemical networks, population dynamics, and tumor cell growth.

This course covers advanced topics in mathematical biology including modeling in biochemical networks, population dynamics, and tumor cell growth.

Special topics in probability & statistics and their recent applications in science and engineering will be covered.

Special topics in probability & statistics and their recent applications in science and engineering will be covered.

This course introduces fundamental issues in image processing and provides mathematical ideas to understand and interpret images better via variational andd PDE methods. (Recommended pre-requisite courses : MTH501, MTH505)

This course covers topics of current interest in image processing for mathematical analysis and introduces efficient algorithms for mathematical solutions. (Recommended pre-requisite courses : MTH501, MTH505)

This course includes advanced topics of current interest in number theory.

This course includes advanced topics of current interest in number theory.

The purpose of this course is to extend knowledge to the state-of-the-art R & D in real scientific fields; and to get indirect experience by contacting experts in various fields. Students and professors can exchange their own ideas and information to reach creative and fine-tuned achievements through the seminars.

This course is related to the students graduate thesis. As such, students should be actively working on their research problems.

This course is related to the students graduate thesis. As such, students should be actively working on their research problems.