Academics
Subjects
MATH611 Algebra I
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.
MATH612 Algebra II
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.
MATH711 Topics in Algebra I
Topics of current research interest, such as advanced linear algebra, representation theory, homological algebra, category theory, algebraic combinatorics and Lie algebra will be covered.
MATH712 Topics in Algebra II
This is a continuation of MATH711 Topics in Algebra I course.
MATH713 Seminar in Algebra I
Selected topics in current trends of the area will be treated through presentations and discussions on some selected research papers.
MATH714 Seminar in Algebra II
This is a continuation of MATH713 Seminar in Algebra I course.
MATH621 Analysis I
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.
MATH622 Analysis II
This is a continuation of Analysis I. Main topics will be elementary functional analysis, spaces, elementary Fourier analysis, and elementary distribution theory.
MATH721 Topics in Analysis I
This course covers recent progresses in analysis that are essential in related fields.
MATH722 Topics in Analysis II
This is a continuation of Topics in Analysis I, and covers recent progresses in analysis that are essential in related fields.
MATH627 Harmonic Analysis I
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.
MATH628 Harmonic Analysis II
This is a continuation of Harmonic Analysis I. Main topics will be Sobolev spaces, Hardy spaces, oscillatory integrals, and pseudo-differential operators.
MATH623 Functional Analysis I
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.
MATH624 Functional Analysis II
This is a continuation of Functional Analysis I. Main topics will be Banach algebras, bounded and unbounded operators in Hilbert spaces, and spectral theory.
MATH723 Seminar in Analysis I
This course is run by presentation and discussion on certain topics in analysis.
MATH724 Seminar in Analysis II
This is a continuation of Seminar in Analysis I. It is run by presentation and discussion on certain topics in analysis.
MATH625 Partial Differential Equations I
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,
MATH626 Partial Differential Equations II
We study the existence and the regularity of a solution of nonlinear partial differential equations.
MATH665 Dynamical System I
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.
MATH666 Dynamical System II
Expansive maps, Anosov diffeomorphism, Stable and Unstable foliation, Parry measure, Lyapunov Exponents, Oseledoc theorem.
MATH638 Differential Geometry I
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.
MATH639 Differential Geometry II
This course treats on the properties of a manifold related to the integration: differential forms, tensor analysis, exterior algebra, deRham's theorem.
MATH636 Algebraic Geometry I
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.
MATH637 Algebraic Geometry II
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.
MATH731 Topics in Geometry I
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.
MATH732 Topics in Geometry II
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.
MATH733 Seminar in Geometry I
Seminar and discussion on papers in special subjects of geometry.
MATH734 Seminar in Geometry II
This course is the second part of Seminar in Geometry I
MATH645 Algebraic Topology 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.
MATH646 Algebraic Topology II
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.
MATH741 Topics in Topology I
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
MATH742 Topics in Topology II
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.
MATH747 Seminar 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.
MATH748 Seminar in Topology II
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.
MATH651 Probability Theory I
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.
MATH652 Probability Theory II
Continuation of Probability I, Martingales and Markov processes, convergence of limits, branching process, random walk, Brownian motion and its applications.
MATH751 Probability Theory Seminar I
Topics in probability leading to up to date research.
MATH752 Probability Theory Seminar II
Topics in probability leading to up to date research.
MATH753 Statistics Seminar I
Selected topics in current trends of Statistics will be treated through presentations and discussions on research papers.
MATH754 Statistics Seminar II
This is a continuation of MATH753 Statistics Seminar I course.
MATH683 Scientific Computation I
This course provides an introduction to the fundamental issues and techniques of numerical computation for the mathematical, computational, and physical sciences.
MATH663 Numerical Analysis I
The main topics in this class are Interpolation, Quadrature, Numerical Linear Algebra and Numerical Differential Equations.
MATH664 Numerical Analysis II
The main topics in this class are basic theories in numerical methods of integral equations and partial differential equations.
MATH661 Applied Mathematics I
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.
MATH662 Applied Mathematics II
This course is the second part of Applied Mathematics I.
MATH763 Topics in Numerical Analysis
Topics on the latest development in theory of numerical differential equations or integral equations are studied relying on articles or books.
MATH761 Topics in Applied Mathematics I
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.
MATH762 Topics in Applied Mathematics II
This course is the second part of Topics of Applied Mathematics I.
MATH767 Seminar in Numerical Analysis I
Topics on the latest development in theory of applied mathematics, numerical analysis and computational mathematics are studied relying on articles or books.
MATH768 Seminar in Numerical Analysis II
This course is the second part of Seminar of Numerical Analysis I.
MATH765 Seminar in Applied Mathematics 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.
MATH766 Seminar in Applied Mathematics II
This course is the second part of Seminar of Applied Mathematics I.
MATH681 Mathematical Modeling 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.
MATH685 Mathematical Bioinformatics
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.
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