This is a basic course for the first year graduate students in mathematics, which provides firm background in abstract algebra, Various topics on theories of groups, rings and modules will be covered in a more advanced level.

This basic course for the first year graduate students is a continuation of MATH611 Algebra I. Various topics in commutative algebra, field theory, Galois theory and representation theory of finite groups will be covered in-depth.

Topics of current research interest, such as advanced linear algebra, representation theory, homological algebra, category theory, algebraic combinatorics and Lie algebra will be covered.

This is a continuation of MATH711 Topics in Algebra I course.

Selected topics in current trends of the area will be treated through presentations and discussions on some selected research papers.

This is a continuation of MATH713 Seminar in Algebra I course.

This is the first semester of introductory graduate sequence in real analysis. Fundamental concepts and tools in Analysis are covered. Main topics will be measure theory, integration, signed measures, and point set topology.

This is a continuation of Analysis I. Main topics will be elementary functional analysis, spaces, elementary Fourier analysis, and elementary distribution theory.

This course covers recent progresses in analysis that are essential in related fields.

This is a continuation of Topics in Analysis I, and covers recent progresses in analysis that are essential in related fields.

This course is an introduction to real variable harmonic analysis. Main topics will be maximal functions, Fourier transform methods, singular integrals, and Littlewood-Paley theory.

This is a continuation of Harmonic Analysis I. Main topics will be Sobolev spaces, Hardy spaces, oscillatory integrals, and pseudo-differential operators.

Basic concepts and tools in functional analysis, useful in partial differential equations, scientific computation, and applied mathematics, are studied. Main topics will be topological vector spaces, properties of complete spaces and locally convex spaces, and distribution theory.

This is a continuation of Functional Analysis I. Main topics will be Banach algebras, bounded and unbounded operators in Hilbert spaces, and spectral theory.

This course is run by presentation and discussion on certain topics in analysis.

This is a continuation of Seminar in Analysis I. It is run by presentation and discussion on certain topics in analysis.

We study classification of the partial differential equations(elliptic parabolic, hyperbolic), their initial boundary value problems. Also, we study the existence, the uniqueness and the regularity of the solution of general linear partial differential equations,

We study the existence and the regularity of a solution of nonlinear partial differential equations.

Entropy, mixing properties, conjugacies, classification problems, distal systems, topological entropy, the relation between topological entropy and measure entropy, expansive systems, topological representations of ergodic systems, symbolic dynamical systems.

Expansive maps, Anosov diffeomorphism, Stable and Unstable foliation, Parry measure, Lyapunov Exponents, Oseledoc theorem.

This course treats on the properties of a manifold related to the differentiation: the definition of differentiable manifold, contact spaces, the differentiability of a function, the inverse function theorem.

This course treats on the properties of a manifold related to the integration: differential forms, tensor analysis, exterior algebra, deRham's theorem.

The aim of this course is to provide an introduction to algebraic varieties and maps between them. Topics covered will include affine varieties, projective varieties, quasi-projective varieties, rational mps, birational maps, Hilbert`s Nullstellensatz, smoothness, singularities, tangent spaces, algebraic curves.

As a sequal to “Algebraic Geometry I”, the aim of this course is to provide an introduction to the theory of complex algebraic surfaces. Topics will include sheaf cohomology, classification of complex algebraic surfaces, rational surfaces, ruled surfaces, K3 surfaces and surfaces of general type.

This course treats on the foundations of analysis on a manifold: basic properties of differentiable manifold, tangent space, vector bundle, differential form, Frobenius' Theorem, Integration etc, and does basic concepts required for the study of differential geometry.

This course is the second part of Topics in Geometry I and treats on the basic properties of Riemannian manifold and also on the concepts of Affine Connection, Riemann Connection, Geodesics, Curvature, Jacobi fields, Isometric immersion, Furthermore, this course contains a space of constant curvature, Rauch's comparison theorem, Morse index theorem, fundamental group of a manifold of negative curvature.

Seminar and discussion on papers in special subjects of geometry.

This course is the second part of Seminar in Geometry I

This is designed as a first-year graduate course, and it usually covers the fundamental group of topological space as a topological and homotopical invariant. In order to compute it, we study the covering space, the Seifert-van Kampen theorem, and we apply them to prove the Brouwer fixed-point theorem, Borsuk-Ulam theorem. In addition, we study several important topological spaces, and, especially, we classify two-dimensional closed surfaces topologically.

This course is a continuation of Algebraic Topology 1 and deals with more advanced topics, such as homology theory, exact sequence, application of homology, universal coefficient theorem, Kunneth formula, cohomology, cup product and cap product, orientation of manifolds, Poincare`s duality theorem, and signature of manifolds.

This course treats Fundamental Group, Deformation Retracts, Homotopy Equivalence, Covering Space, Circle and Sphere, Some Group Theory, Free Products, Free Group, Free Abelian Group, Seifert-Van Kampen Theorem, Classification of Covering Space, Higher Homotopy Group, etc.

Prerequisite: Topology Ⅰ

This is a continuation of Topics in Topology Ⅰ and this course consists of Curves and Surfaces, Classification of Surface, Space Filling Curves, the Jordan-Brower Separation Theorem, the Jordan Curve Theorem, Fixed Point Theory, Pancake Problem, Category and Functor, etc.

Prerequisite: Topology Ⅰ, Topics in Topology Ⅰ.

Recent research papers are studied under the guidance of a thesis supervisor. By giving a talk about them, each student improves his/her own research ability.

Recent research papers are studied under the guidance of a thesis supervisor. By giving a talk about them, each student improves his/her own research ability.

Foundations of probability, probability space and random variable, independence, conditional probability, generating functions, Martingales, stopping time, law of large numbers, central limit theorem, characteristic functions.

Continuation of Probability I, Martingales and Markov processes, convergence of limits, branching process, random walk, Brownian motion and its applications.

Topics in probability leading to up to date research.

Topics in probability leading to up to date research.

Selected topics in current trends of Statistics will be treated through presentations and discussions on research papers.

This is a continuation of MATH753 Statistics Seminar I course.

This course provides an introduction to the fundamental issues and techniques of numerical computation for the mathematical, computational, and physical sciences.

The main topics in this class are Interpolation, Quadrature, Numerical Linear Algebra and Numerical Differential Equations.

The main topics in this class are basic theories in numerical methods of integral equations and partial differential equations.

This course ties together many of the themes from courses on linear algebra, calculus and differential equations and applies them to problems, derived from engineering, physics, biology, chemistry and economics. The emphasis is on the underlying unity of the different mathematical subjects and the problems in the different sciences. The central topics are differential equations and matrix equations - the continuous and discrete. They reinforce each other because they go in parallel. Topics covered are minimum principles, eigenvalues and dynamical systems, constraints and Lagrange multipliers, differential equations of equilibrium, calculus of variations, stability and chaos, nonlinear conservation laws.

This course is the second part of Applied Mathematics I.

Topics on the latest development in theory of numerical differential equations or integral equations are studied relying on articles or books.

This course offers advanced topics in various areas of applied mathematics. Possible topics include computational fliud dynamics, nano fluid flows, molecular dynamics, bio infomatics, stochastic processes, optimization, actuarial mathematics, calculus of variations, and multiscale computations.

This course is the second part of Topics of Applied Mathematics I.

Topics on the latest development in theory of applied mathematics, numerical analysis and computational mathematics are studied relying on articles or books.

This course is the second part of Seminar of Numerical Analysis I.

Seminar in applied mathematics about topics including computational fliud dynamics, nano fluid flows, molecular dynamics, bio infomatics, stochastic processes, optimization, actuarial mathematics, calculus of variations, and multiscale computation. In this course, students will learn how to read and write paper.

This course is the second part of Seminar of Applied Mathematics I.

This course offers a powerful, indispensable tool for studying a variety of problems in scientific research, product and process development, and manufacturing. The main tool will be computational science which seeks to gain an understanding of science through the use of mathematical models on computers. The topics are differential equations discretiztion methods, linear system, nonlinear system, algorithms which are arising from real world problem.

An introduction to the theory and practice of bioinformatics and computational biology. Topics include: Sequence comparison, sequence assembly, gene finding, phylogeny construction, DNA microarrays, association between polymorphims and disease.