**전공 종합시험(필답시험) 교과목**

**CSE5810 Numerical Analysis 1 [수치해석1] – MAT6810**

This course is designed to acquaint students in mathematical and physical sciences and engineering with the fundamental theory of numerical analysis. This course is devoted to nonlinear equations, optimization, approximation theory, numerical quadrature and numerical linear algebra (including linear systems, least squares problems and eigenvalue problems). The course willstress both on analytic and computational aspects of numerical methods. Prerequisites: Advanced Calculus and Linear Algebra (or Engineering Math), Programming skills

**CSE5840 Numerical Partial Differential Equations [수치편미분방정식] – MAT6840**

This course focuses on the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic, and hyperbolic partial differential equations central to a wide variety of applications in science, engineering, and other fields. Topics includes : Mathematical formulations, Finite difference method, Finite element method Prerequisites: Programming skills, Advanced Calculus and Linear Algebra (or Engineering Math)

**CSE5950 Partial Differential Equation for Science and Engineering 1 [이공계 편미분방정식1] – MAT6950**

This is an introductory, graduate-level course on partial differential equations (PDE) for science and engineering. This course focuses on derivation, interpretation, and analysis for model equations including Laplace equation, heat, and wave equations. This course covers maximum principle and uniqueness results, variation principles, Lax-Milgram theorem and applications to boundary value problems. Prerequisites: Advanced Calculus, Linear Algebra (or Engineering Math), Ordinary Differential Equations.

**CSE6623 Viscous Fluid Flow [점성유체역학] - MEU6230**

Fundamental understanding of fluid phenomena and application to real flow problems. Governing equations. Flow kinematics. Vorticity dynamics, Low-Reynolds number flow, flow instability, turbulence.

**필수 이수 과목(프로그래밍 교과목) 4개 교과목 중 1개 필수 이수**

**CSE5002 Basics of Computational Fluid Dynamics [기초계산유체역학]**

The objective of this course is to offer basic knowledge of computational fluid dynamics based on fundamental understanding of fluid mechanics and numerical analysis. This course will include Navier-Stokes equation, Finite ifference method (FDM), Staggered-grid, Projection Method, Numerical simulation of unsteady viscous flows, Visualization, etc. Prerequisites: Fluid mechanics, Numerical Analysis

**CSE5851**

**DEEP LEARNING AND DATA SCIENCE**

**[딥러닝과데이터과학]**

Broad fields of machine learning, including deep learning, and data analytics have attracted a great deal of attention by virtue of not only a huge amount of available datasets but also the emergence of GPUs. This class aims at an introduction to several fundamental data mining problems based on machine learning/deep learning tools. More specifically, for the first half of the semester, this class covers data representation learning (a.k.a. feature learning) along with understanding of principles, algorithm design, and implementation, where each of three representation learning algorithms such as random-walk-based approaches and proximity-based approaches is explored on a weekly basis. For the second half of the semester, this class deals with the following two crucial problems in statistical machine learning: 1) clustering and 2) sampling. Commonly-applicable methods such as K-means, Gaussian mixture models, spectral clustering, and density-based clustering are presented in clustering. Several sampling techniques such as Gibbs sampling and Markov Chain Monte-Carlo (MCMC) as well as Bayesian modeling are also presented along with motivating examples.

**CSE5004 SCIENTIFIC COMPUTATION WITH PYTHON [파이썬을이용한과학계산]**

본 강좌는 수치 계산을 위한 NumPy 패키지, 다양한 과학 계산 작업을 위한 SciPy 도구 상자, 시각화를 위한 Matplotlib 패키지를 소개하여 과학 계산을 위한 Python 프로그래밍을 목표로 한다. 특히, 본 강좌에서는 보간, 적분, 미분, ODE 및 PDE 계산, 선형 대수와 같은 기본 수치 알고리즘의 Python 프로그래밍을 통해 과학계산을 수행한다.

**CSE5820**

**BASICS OF FINITE ELEMENT METHODS**

**[기초유한요소법]**

The finite element method is a useful tool to find an approximation of the solution to given partial differential equations in an arbitrary domain. The subject includes the introduction to the basic theories of finite element method, the implementation of finite element method and applications to partial differential equations in finite element method. This course aims to solve partial differential equations by implementing one`s own codes using finite element method and get used to using known packages.

**학부-대학원 연계 교과목**

**CSE5001 Basics of Computational Science and Engineering [기초계산과학공학]**

This course is intended for graduate students (or undergraduate) who need a rapid and uncomplicated introductions to the field of applied mathematics involving computational linear algebra and differential equations. The lecture has two themes-how to understand equations, and how to solve them . This course include numerical linear algebra(QR,SVD, singular system), Newton’s method for minimization, Equilibrium and stiffness matrix, Least squares, Nonlinear problems, Covariances and Recursive Least squares, Differential equations and finite elements, Finite Difference and Fast Poisson, Boundary value problems in Elasticity and Solid mechanics.

**학과 전공 교과목**

**CSE5970 Medical Imaging System: Physical Principles and Applications [의료영상시스템의 원리와 응용]**

This lecture presents a comprehensive introduction and overview of electromagnetic tissue property imaging techniques using MRI focusing on Magnetic Resonance Electrical Impedance Tomography(MREIT), Electrical Properties Tomography(EPT) and Quantitative Susceptibility Mapping (QSM). The contrast information from these novel imaging modalities is unique since there is currently no other method to reconstruct high-resolution images of the electromagnetic tissue properties including electrical conductivity, permittivity, and magnetic susceptibility. These three imaging modalities are based on Maxwell`s equations and MRI data acquisition techniques. They are expanding MRI`s ability to provide new contrast information on tissue structures and functions. Prerequisites: Vector calculus, Linear algebra, Differential equation, Numerical analysis

**CSE6126 PARALLEL SCIENTIFIC COMPUTING [병렬과학계산]**

The major goal of this course is to develop parallel solvers for typical Partial Differential Equations (PDE) in science and engineering. We review numerical methods for the PDE including DDM and develop serial programs based on iterative methods for solving the PDEs. Next, we develop parallel algorithms based on OpenMP and MPI programming.

**CSE6642 Special Topics in Turbulence Simulations [전산난류특론] - MEU6420**

Fundamentals for advanced computation technology of turbulence will be treated including spectral method, Simple algorithm, immersed boundary method. Prerequisites: Turbulence theory

**CSE6820 Finite Element Methods [유한요소법] – MAT6820**

This course focuses on the fundamentals of finite element methods for a wide range of linear and nonlinear elliptic, parabolic, and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Finite element method is a numerical technique for finding approximate solutions to partial differential equations. It uses variational methods to minimize an error function and produce a stable solution. The theory of finite elements and their applications is such a lively area in science and engineering. This course introduces the finite element methods which features important material for both research and application. Prerequisites: Numerical analysis

**CSE6990 Scientific writing and Presentation skills 1, 2 [논문작성법 및 발표1, 2]**

The objective of this course is to offer strategies and tools to plan, develop, and deliver scientific presentations. Also students will be naturally exposed to cutting-edge technologies from invited seminars. Through questions and answers (Q & A) sessions, this course encourages the students to have a critical thinking and to enhance their communication skills.

**CSE7726 Theory of Hydrodynamic Stability [유동안정성이론] - MEU7260**

The flow of particles and droplets in fluids has a wide application in thermo-fluid systems: pollution dispersions in the atmosphere, fluidization in combustion process, aerosol deposition, etc. This course introduces graduate students to knowledge of particle-laden flows with an emphasis on the effect of disperse phase particles on flows. This course will include properties of dispersed phase flows, particle-fluid interaction, particle-particle interaction, continuous phase equations, etc. Prerequisites: Fluid mechanics, Viscous fluid Flows

**CSE7730 Theory of Turbulent Flow [난류이론] - MEU7300**

Fundamentals and application of turbulent flows are considered through investigation of theories and analysis on turbulence. Governing equations and various definitions and statistical tools to describe turbulence are introduced. Particularly scales of turbulence are considered for the better understanding of turbulence. Various models for engineering applcations are considered. Prerequisites: Viscous fluid flow

**CSE7777 Advanced Computational Fluid Dynamics [고급전산유체역학]**

The objective of this course is to study on numerical analysis for fluid mechanics and thermal/mass transports. To this end, the course will include projection methods on staggered grid for solving Navier-Stokes equation, immersed boundary methods for complex geometry, level-set methods for tracking phase interface, etc. Prerequisites: CSE5002 Basic of Computational Fluid Dynamics

**CSE7820 Programming for Image Processing/Analysis and Visualization [영상처리 프로그래밍]**

Image processing has become one of the most important components in medical imaging modalities such as MRI, CT, ultrasound and other functional imaging modalities. Image processing techniques such as image restoration and sparse sensing are being used to deal with various imperfections in data acquisition processes of the imaging modalities. Image segmentation, referred to the process of partitioning an image into multiple segments, has numerous applications including tumor detection, quantification of tissue volume, computerguided surgery, study of anatomical structure and so on. In this lecture, we begin with mathematical theories on PDE-based image restoration, sparse sensing, level set methods. We apply their theories to MRI, CT, QSM, and other medical imaging area. Prerequisites: Basic numerical analysis, Partial differential equations

**CSE7850 Stochastic Methods [스토케스틱 수치해법]**

This course is to focus on fundamental aspects of numerical methods for stochastic computations. We consider a class of numerical methods including generalized polynomial chaos (gPC). Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. In this course we introduce polynomial approximation theory and probability theory; describes the basic theory of gPC methods through numerical examples and rigorous development; details the procedure for converting stochastic equations into deterministic ones; using both the Galerkin and collocation approaches; and discusses the distinct differences and challenges arising from high-dimensional problems. The last section is devoted to the application of gPC methods to critical areas such as inverse problems and data assimilation. Prerequisites: Numerical Analysis, PDE for Science and Engineering

**CSE7880 Particle-Laden Flows [입자와 유동]**

This course is to study various numerical methods for convection dominated diffusion equations. Mathematical models that involve a combination of convective and diffusive processes are among the most widespread in all of science and engineering. Following topics will be discussed: finite difference method, finite element method, finite volume method, stability, streamline diffusion methods, discontinuous Galerkin methods, variational multiscale method.

**CSE7890 Numerical Optimization [수치최적화]**

This course covers numerical optimization. We will concentrate on convex optimization. For such purpose we will briefly cover the convex theory including convex set, convex function, sublevel set, epigraph, separating hyper-plane theorem, conjugate function, etc. Concerning duality, we will study Lagrange dual function, weak and strong duality, Karush-Khun-Tucker (KKT) conditions. For unconstrained optimization, we study algorithm including descent method, line search method, Newton’s method, for constrained optimization, Newton method will be covered for equality constraint problems and interior point methods including barrier method and primal dual method for inequality constraint problems. After that we will consider applications, approximation and fitting, l1 minimization, for examples. If time permits, other methods may be introduced: penalty methods, augmented Lagrangian methods, etc. Prerequisites: CSE5810 Numerical Analysis, MATLAB Coding skill

**CSE8820 Advanced Finite Element Method [고급유한요소법]**

This course is to study advanced topics in finite element methods. The methods under consideration include standard Galerkin methods, Adaptive FEMs, Nonstandard finite element methods, Mixed FEMs, and discontinuous Galerkin (DG) methods. Applications will include Darcy equations, Stokes equations, and linearized Navier-Stokes known as Oseen equations.

**특강 교과목**

CSE7830 Physics based modeling and simulation for visualization 1 [물리기반모델링과 시뮬레이션1]

CSE7840 Physics based modeling and simulation for visualization 2 [물리기반모델링과 시뮬레이션2]

CSE7860 Mathematical modeling and Numerical analysis 1 [수학적모델링 및 수치해석1]

CSE7870 Mathematical modeling and Numerical analysis 2 [수학적모델링 및 수치해석2]

CSE8810 Topics in mathematical modeling and analysis 1 [수학적모델링 및 해석특강1]

CSE8830 Topics in numerical simulation based science 1 [수치시뮬레이션기반 과학특강1]

CSE8850 Topics in numerical simulation based engineering 1 [수치시뮬레이션기반 공학특강1]

CSE8860 Mathematical Modeling and Simulation and Visualization for Science 1 [수리모델링 및 수치모사와 시각화1]

CSE8861 Mathematical Modeling and Simulation and Visualization for Science 2 [수리모델링 및 수치모사와 시각화2]

CSE9810 Topics in mathematical modeling and analysis 2 [수학적모델링 및 해석특강2]

CSE9830 Topics in numerical simulation based science 2 [수치시뮬레이션기반 과학특강2]

CSE9850 Topics in numerical simulation based engineering 2 [수치시뮬레이션기반 공학특강2]

**비교과과목**

CSE7999 Directed Research 1 [연구지도1]

CSE9999 Directed Research 2 [연구지도2]

YSG6003 Research Ethics [연구윤리]

**타학과 인정 교과목**

**수학계산학부(수학)**

MAT6400 Real Analysis 1 [실해석학1]

MAT6450 Real Analysis 2 [실해석학2]

MAT6460 Theory of Partial Differential Equations 2 [편미분방정식2]

MAT6710 [확률론1]

MAT6760 [확률론2]

MAT6800 Applied Partial Differential Equations [응용편미분방정식]

MAT6970 Analysis for Science and Engineering 1 [이공계 해석학1]

MAT7400 Functional Analysis 1 [함수해석학I]

MAT7450 Functional Analysis 2 [함수해석학2]

MAT7810 Introduction to Continuum Mechanics [연속체 역학개론]

**기계과**

MEU5040 INVISCID FLOW THEORY [비점성유체역학]

MEU6210 Conduction Heat Transfer [전도열전달]

MEU6240 Combustion Engineering (연소공학)

MEU6260 Computational Fluid Dynamics [전산유체역학]

MEU6290 Particle Engineering (입자공학)

MEU6520 Convective Heat Transfer [대류열전달]

MEU7030 Theory of Elasticity [탄성이론]

MEU7930 Compressible Fluid Dynamics [압축성유체역학]

**대기과학과**

ATM6102 Cloud and Precipitation Process (구름 및 강수과정)

ATM6103 Atmospheric Dynamics I (대기역학1)

ATM6104 Atmospheric Dynamics II (대기역학2)