For more details on the courses, please refer to the Course Catalog
| Code | Course Title | Credit | Learning Time | Division | Degree | Grade | Note | Language | Availability |
|---|---|---|---|---|---|---|---|---|---|
| MTH2020 | Matrix Methods in Data Analysis and Machine Learning | 3 | 6 | Major | Bachelor | 2-3 | - | No | |
| It is an introductory course to applied linear algebra with emphasis on applications. Linear algebra concepts are key for understanding and applying data analysis tools and machine learning algorithms. Actually, applications are not limited to the above; they include time-series prediction, tomography, optimal control, and portfolio optimization. This course reviews linear algebra with applications to probability, statistics and optimization such as singular value decomposition, matrix factorizations, least-squares and model fitting, regularization and cross-validation, principal component analysis, covariance and correlation matrices. | |||||||||
| MTH3002 | Numerical Analysis | 3 | 6 | Major | Bachelor | 3-4 | Korean | Yes | |
| Numerical methods for solving Nonlinear equations, Systems of Simultaneous equations, Eigen value problems, Interpolating polynomials, Differentiations and Integrations,Ordinary Differential Equations, Partial Differential Equations will be treated. | |||||||||
| MTH3007 | Cryptology | 3 | 6 | Major | Bachelor | 3-4 | Korean | Yes | |
| Secrete key cryptosystem and its application,basic notation of public key crytosystem,RSA,EIGamal cryptosystem,discret logarithm,knapsack problem,digital signature are studied | |||||||||
| MTH3008 | Topics in Algebra | 3 | 6 | Major | Bachelor | 3-4 | - | No | |
| This course will be a continuation of Algebra Ⅱ. Topics include : algebraic extensions ; finite fields ; splitting fields ; separable extensions fields ; Galois thory and its applications ; cyclotomic extensions ; solvable poly- nomial by radicals. | |||||||||
| MTH3011 | Partial Differential Equations | 3 | 6 | Major | Bachelor | 3-4 | Korean | Yes | |
| fundamental theories of partial differential equations: first order equations, the Cauchy problem of the quasi-linear equations, second order equations, propagation of singularities, one dimensional wave equations, the Cauchy-Kowlevsky theorem Holmgren's theorem of uniqueness, Laplace equation, Green's function, maximum principle, Perron's method, Hilbert space method, higher order hyperbolic equation, symmetric hyperbolic system, heat equation, maximum principle for heat equation. | |||||||||
| MTH3012 | Applications of Partial Differential Equations | 3 | 6 | Major | Bachelor | 3-4 | - | No | |
| applications of the partial differential equations to the physics and mechanics problems: mathematical approaches to the classical field theories, Lagrangian field theories, basics of the tensor calculus, gaugetheories, self-dual gauge theories, general relativity and Einstein's field equations, formulations of the Cauchy problems, Schwartzschild solution, partial differential equations arising from fluid mechanics and the gas dynamics, basic properties of the Euler and the Navier-Stokes equations. | |||||||||
| MTH3013 | Topics in Analysis | 3 | 6 | Major | Bachelor | 3-4 | - | No | |
| General Measure and Lebesgue Measure, Banach Spaces, Hilbert spaces, Metric spaces, Compact spaces. General Measure and Lebesgue Measure, Banach Spaces, Hilbert spaces, Metric spaces, Compact spaces. | |||||||||
| MTH3015 | Applied Numerical Analysis | 3 | 6 | Major | Bachelor | 3-4 | Korean | Yes | |
| The theory and methodology of the numerical solution of partial differential equations and integral equations are presented. After constructing and exploring realistic mathematical models of problems arising in the natural sciences and engineering, we apply the theory and methods to obtain their solutions. | |||||||||
| MTH3016 | Real Variables | 3 | 6 | Major | Bachelor | 3-4 | Korean | Yes | |
| Lebesgue Measure, The Lebesgue Integral, Differentiation and Integration, Measure and Integration, Measure and outer Measure. | |||||||||
| MTH3017 | Surface Topology | 3 | 6 | Major | Bachelor | 3-4 | - | No | |
| As an introduction to algebraic topology, we study methods of calculation of fundamental group, Van-Campan Theorem, covering spaces, vetor fields and fixed point thoerem etc.. | |||||||||
| MTH3019 | Differential Geometry Ⅱ | 3 | 6 | Major | Bachelor | 3-4 | Korean | Yes | |
| This course is a continuation of Differential Geometry Ⅰ and necessary for students willing to study Differential Topology, Global Analysis and TheoreticalPhysics for future study. In this course, Gaussian curvature, properties of geodesic on a surface are treated. Also we study Gauss-Bonnet Theorem which explains how the Gaussian curvature influences to the topology of a surface. | |||||||||
| MTH3020 | Mathematical Statistics Ⅰ | 3 | 6 | Major | Bachelor | 3-4 | - | No | |
| Mathematical probability as a basis for the theory of statistics. Discrete and continuous probability models. Conditional probability and independence. Random variables. Central limit theorem. Sampling distribution. | |||||||||
| MTH3021 | Mathematical Statistics Ⅱ | 3 | 6 | Major | Bachelor | 3-4 | - | No | |
| Point estimation. Confidence interval. Neyman-Pearson theory of testing of hypotheses. Sufficiency. Completeness Rao-Blackwellization. Some nonparame-tric methods. Linear models (Continuation of Mathematical Statistics I) | |||||||||
| MTH3022 | Probability Theory | 3 | 6 | Major | Bachelor | 3-4 | English | Yes | |
| Introduction to probability using techniques of measure and integration theory. Probability space. Densities. Fubini theorem. Convergence of random variables, Laws of large number for iid random variables. Central limit theorem for independent random variables. | |||||||||
| MTH3023 | Applied Mathematics | 3 | 6 | Major | Bachelor | 3-4 | - | No | |
| Introduction to mathematical solutions of problems arising from natural sciences, biomedicine, engineering, and mathematical finance after studying basic parabolic PDE, integral transforms, and stochastic differential equations. | |||||||||