Education
Graduate
합리적이고 창의적인 수학 교육
수리과학과는 전통적인 분야인 대수학, 해석학, 위상수학, 기하학에서부터 확률, 통계, 계산수학, 금융수학, 생물수학에 이르기까지 순수수학과 응용수학을 아우르는 교육을 통하여, 합리적이고 창의적인 사고 능력을 갖춘 인재와 수학의 기본이론과 응용이론에 정통한 전문인력 양성을 추구합니다.
오늘날 서로 다른 분야를 종합하는 통합의 학문으로 재조명 받고 있는 수리과학의 위상에 발맞추어, 자연과학, 공학, 경영학 등과의 학제간 연구를 이끌고 연구소 및 산업체들과의 적극적 교류를 통하여 한국 수리과학 연구의 산실이 되고자 합니다.
Reasonable and creative math education
Department of Mathematical Science explores the connections between mathematics and its applications at both the research and educational levels. In addition to focusing on traditional study in pure mathematics, our research at UNIST is devoted to encompass some of the most diverse and interdisciplinary research in the physical, business, economics, engineering, and biological sciences. The department provides a dynamic and engaging research environment in scientific computing, mathematical biology, finance, dynamical systems, image processing, number theory and analysis in PDEs.
The undergraduate and graduate curriculum is planned with the following varied objectives: (1) to offer students an introduction to the fundamental study of quantity, structure, space, and change; (2) to prepare students for graduate study in pure or applied mathematics; (3) to serve the needs of students in fields that rely substantially on mathematics, such as the physics, biology, engineering, business and economics.
| Course No. | Course Title | Prerequisite |
|---|---|---|
| MTH501 |
Real Analysis
|
3-3-0 |
| 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
|
3-3-0 |
| 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 process
|
3-3-0 |
| 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
|
3-3-0 |
| 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
|
3-3-0 |
| 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
|
3-3-0 |
| 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
|
3-3-0 |
| 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 PDEs I
|
3-3-0 |
| 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 PDEs II
|
3-3-0 |
| 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
|
3-3-0 |
| 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
|
3-3-0 |
| 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
|
3-3-0 |
| 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
|
3-3-0 |
| 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 Biological Sciences
|
3-3-0 |
| Linear model, multivariate analysis, survival analysis and some machine learning methods for genome and clinical data analysis using R software | ||
| MTH531 |
Scientific Computing
|
3-3-0 |
| 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
|
3-3-0 |
| 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
|
3-3-0 |
| This course covers topics of current interest in computational mathematics for solving linear and nonlinear partial differential equations. | ||
| MTH712 |
Selected Topics in Computational Mathematics II
|
3-3-0 |
| This course covers topics of current interest in computational mathematics for solving linear and nonlinear partial differential equations. | ||
| MTH590 |
Seminar
|
1-1-0 |
| 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
|
Value of credit |
| This course is related to the students graduate thesis. As such, students should be actively working on their research problems. | ||
| MTH890 |
Doctoral Research
|
Value of credit |
| This course is related to the students graduate thesis. As such, students should be actively working on their research problems. | ||
| MTH551 |
Algebra
|
3-3-0 |
| 대수학 | ||
| MTH555 |
Number theory
|
3-3-0 |
| 정수론 | ||
| MTH561 |
Differentiable manifolds
|
3-3-0 |
| 미분다양체 | ||
| MTH563 |
Differential geometry
|
3-3-0 |
| 미분기하학 | ||
| MTH571 |
Algebraic geometry
|
3-3-0 |
| 대수적 위상수학 | ||
| MTH721 |
Selected topics in partial differential equations I
|
3-3-0 |
| 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
|
3-3-0 |
| This course covers topics of current interest in partial differential equations. | ||
| MTH731 |
Selected topics in mathematical biology I
|
3-3-0 |
| 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
|
3-3-0 |
| 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
|
3-3-0 |
| Special topics in probability & statistics and their recent applications in science and engineering will be covered. | ||
| MTH742 |
Selected topics in probability and statistics II
|
3-3-0 |
| Special topics in probability & statistics and their recent applications in science and engineering will be covered. | ||
| MTH751 |
Selected topics in image processing I
|
3-3-0 |
| 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
|
3-3-0 |
| 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
|
3-3-0 |
| This course includes advanced topics of current interest in number theory. | ||
| MTH762 |
Selected topics in number theory II
|
3-3-0 |
| This course includes advanced topics of current interest in number theory. |
