For more details on the courses, please refer to the Course Catalog
| Code | Course Title | Credit | Learning Time | Division | Degree | Grade | Note | Language | Availability |
|---|---|---|---|---|---|---|---|---|---|
| MTH5002 | Research Course II | 3 | 0 | Major | Master/Doctor | 1-4 | Korean | Yes | |
| Independent study for the advanced research. | |||||||||
| MTH5003 | Research Course III | 3 | 0 | Major | Master/Doctor | 1-4 | Korean | Yes | |
| Independent study for the advanced research. | |||||||||
| MTH5004 | Research Course IV | 3 | 0 | Major | Master/Doctor | 1-4 | Korean | Yes | |
| Independent study for the advanced research. | |||||||||
| MTH5018 | Differentiable Manifolds | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| We study differentiable structures of a given topological manifold. We mention Milnors results and exotic structures. | |||||||||
| MTH5024 | Finite Element Methods | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| Mathematical aspects of the finite element method applied to elliptic, parabolic, and hyperbolic partial differential equations. Finite element spaces, Galerkin method, local error estimates. | |||||||||
| MTH5026 | Operator Theory | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| Recent main topics of the Operator Theory; Spectral Theory for Compact Operators on a Banach Space, Normal Operators on a Hilbert Space, Unbounded Operators and the spectral Theorem, Freholm and Toeplitz Operators. | |||||||||
| MTH5028 | Combinatorial Matrix Theory | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| This course devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa). We deal with the many connections between matrices, graphs, digraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix, and Latin squares. The final chapter deals with algebraic characterizations of combinatorial properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jordan Canonical Form. It will be an essential purchase for combinatorialists, matrix theorists, and those numerical analysts working in numerical linear algebra. | |||||||||
| MTH5045 | Algebraic Topology | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| We study CW-complexes, relative homeomorphism theorem, cellular homology and basic cohomology. | |||||||||
| MTH5053 | Lie Groups and Lie Algebra | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| We study groups which are also differentiable manifolds and algebraic structures of its tangent space and integrability. | |||||||||
| MTH5056 | Harmonic Analysis | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| In close connection with Fourier Analysis, main subjects are Topological Groups, Integration on Locally Compact Spaces, Invariant Functionals, Convolutions and Group Representations. | |||||||||
| MTH5057 | Several Complex Variables | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| In a viewpoint of applications to Partial Differential Equations, Fourier Analysis and Integration Operators, main subjects are Intergral Formulas for Solutions, Convexity, Solution of the Levi problem, Zero Set of a Holomorphic Function and some Harmonic Analysis. | |||||||||
| MTH5060 | Nonlinear Functional Analysis | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| In Nonlinear Functional Analysis, main subjects are Monotone Operators, Implicit Functions and Problems at Resonance, Solutions in Cones, Approximate Solutions, Extremal Problems and Bifurcation Theory. | |||||||||
| MTH5073 | Analysis Seminar | 3 | 6 | Major | Master/Doctor | 1-4 | Korean | Yes | |
| Recent articles and selected topics in Analysis, Nonlinear Analysis and Numerical Analysis are presented for graduate students and post doctoral researchers. | |||||||||
| MTH5082 | Metric Geometry | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| In metric geometry, spaces which are determined by distance and angle are studied. Relations between curvatures, area, vilumes and other geometric properties are studied. | |||||||||
| MTH5092 | Commutative Algebra | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| Commutative rings and modules, Primary Decomposition, Noetherian rings and modules, Artin-Rees Lemma, Artinian rings and modules, Hilbert Nullstellensatz. Dimension and Multiplicity, Regular Local Rings, Regular Sequences and the Depth of a module, Cohen-macaulay Rings, Gorenstein Rings. | |||||||||