### Curriculum

Course No. Course Title Course Title(Kor.) Prerequisite

### Credit Description

##### MTH501 Real analysis [실해석학]
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.
##### MTH502 Functional analysis [함수해석학]
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.
##### MTH503 Probability and stochastic processes [확률 및 확률과정론]
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.
##### MTH505 Numerical Analysis and applications [수치해석 및 응용]
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.
##### MTH507 Numerical linear algebra [수치 선형대수]
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.
##### MTH509 Partial Differential Equations [편미분방정식]
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.
##### MTH510 Nonlinear Partial Differential Equations [비선형 편미분방정식]
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.
##### MTH511 Numerical Methods for partial differential equations I [편미분방정식의 수치방법 I]
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.
##### MTH512 Numerical Methods for partial differential equations II [편미분방정식의 수치방법 II]
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.
##### MTH513 Dynamical systems [동적 시스템]
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.
##### MTH515 Mathematical Methods for Engineers [공학자를 위한 수학방법]
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.
##### MTH517 Stochastic Calculus and applications [확률 미적분과 응용]
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
##### MTH519 Advanced statistics [고급 통계]
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
##### MTH521 Computational Statistics for Bioscience [생명과학을 위한 계산 통계]
Linear model, multivariate analysis, survival analysis and some machine learning methods for genome and clinical data analysis using R software
##### MTH531 Scientific Computing [과학계산]
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.
##### MTH532 Advanced Scientific Computing [고급과학계산]
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.
##### MTH711 Selected topics in computational mathematics I [계산수학 특론 I]
This course covers topics of current interest in computational mathematics for solving linear and nonlinear partial differential equations.
##### MTH712m Selected topics in computational mathematics II [계산수학 특론 II]
This course covers topics of current interest in computational mathematics for solving linear and nonlinear partial differential equations.
##### MTH721 Selected topics in partial differential equations I [편미분방정식 특론 I]
This course covers an introduction of L_p theory of elliptic and parabolic differential equation and theory of Navier-Stokes equations.
##### MTH722 Selected topics in partial differential equations II [편미분방정식 특론 II]
This course covers topics of current interest in partial differential equations.
##### MTH731 Selected topics in mathematical biology I [생물수학 특론 I]
This course covers advanced topics in mathematical biology including modeling in biochemical networks, population dynamics, and tumor cell growth.
##### MTH732 Selected topics in mathematical biology II [생물수학 특론 II]
This course covers advanced topics in mathematical biology including modeling in biochemical networks, population dynamics, and tumor cell growth.
##### MTH741 Selected topics in probability and statistics I [확률과 통계 특론 I]
Special topics in probability & statistics and their recent applications in science and engineering will be covered.
##### MTH742 Selected topics in probability and statistics II [확률과 통계 특론 II]
Special topics in probability & statistics and their recent applications in science and engineering will be covered.
##### MTH751 Selected topics in image processing I [이미지 프로세싱 특론 I]
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)
##### MTH752 Selected topics in image processing II [이미지 프로세싱 특론 II]
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)
##### MTH761 Selected topics in number theory I [정수론 특론 I]
This course includes advanced topics of current interest in number theory.
##### MTH762 Selected topics in number theory II [정수론 특론 II]
This course includes advanced topics of current interest in number theory.
##### MTH590 Seminar [세미나]
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.
##### MTH690 Master's Research (1-3 credits) [석사 연구]
This course is related to the students graduate thesis. As such, students should be actively working on their research problems.
##### MTH890 Doctoral Research (3-9 credits) [박사 연구]
This course is related to the students graduate thesis. As such, students should be actively working on their research problems.