Education
Undergraduate
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 | |
|---|---|---|---|
| MTH251 | Required |
Mathematical Analysis 1
|
– |
| The real number system. Set theory. Topological properties of R^n, metric spaces. Numerical sequences and series, Continuity, connectedness, compactness. Differentiation and integration. | |||
| MTH302 | Required |
Modern Algebra 1
|
– |
| Groups, homomorphisms, automorphisms, permutation groups. Rings, ideals and quotient rings, Euclidean rings, polynomial rings. Extension fields, roots of polynomials. | |||
| MTH313 | Required |
Complex Analysis 1
|
– |
| Complex numbers and complex functions. The algebra of complex numbers, fractional powers, Logarithm, power, exponential and trigonometric functions. Differentiation and the Cauchy-Riemann equations. Cauchy’s theorem and the Cauchy integral formula. Singularities, residues, Taylor series and Laurent series. Conformal mapping: Fractional Linear transformations. Riemann Mapping Theorem. Analytic continuation. Harmonic functions. | |||
| MTH351 | Required |
General Topology
|
– |
| Set-theoretic preliminaries. Metric spaces, topological spaces, compactness, connectedness. Countability and separation axioms. Covering spaces and homotopy groups. | |||
| MTH252 | 1TR:R, 2TR:E |
Mathematical Analysis 2
|
MTH251,MTH203 |
| Sequences and series of functions: Uniform convergence and continuity, Power series, special functions. Functions of several variables: Partial derivatives, Inverse function theorem, Implicit function theorem, transformation of multiple integrals. Integration of Differential forms. | |||
| MTH342 | 1TR:R, 2TR:E |
Probability
|
– |
| Combinatorial analysis used in computing probabilities. The axioms of probability, conditional probability and independence of events. Discrete and continuous random variables. Joint, marginal, and conditional densities and expectations, moment generating function. Laws of large numbers. Binomial, Poisson, gamma, univariate, and bivariate normal distributions. Introduction to stochastic processes. | |||
| MTH321 | 1TR:R, 2TR:E |
Numerical Analysis
|
– |
| Polynomial interpolation, Polynomial approximation, Orthogonal polynomials and Chebyshev polynomials. Least-squares approximations. Numerical differentiation and integration. Numerical methods for solving initial and boundary value problems for ODEs. Direct and iterative methods for solving linear systems. Numerical solutions of Nonlinear system of equations. | |||
| MTH413 | 1TR:R, 2TR:E |
Differential Geometry 1
|
– |
| The differential properties of curves and surfaces. Introduction to differential manifolds and Riemannian geometry. Second fundamental form and the Gauss map. Vector fields. Minimal surfaces. Isometries. Gauss Theorem and equations of compatibility. Parallel transport, Geodesics and Gauss Bonet theorem. The Exponential map. | |||
| MTH315 | 1TR:R, 2TR:E |
Ordinary Differential Equations
|
MTH201, MTH203 |
| Existence and uniqueness of solutions, linear systems, regular singular points. Analytic systems, autonomous systems, Sturm-Liouville Theory. | |||
| MTH421 | 1TR:R, 2TR:E |
Introduction to Partial Differential Equations
|
MTH201,MTH203 |
| Waves and Diffusions. Reflections and Sources. Boundary value problems. Fourier series. Harmonic functions. Green’s Identities and Green’s functions. Computation of solutions. Waves in space. Boundaries in the plane and in space. General eigenvalue problems. Distributions and Transforms. Nonlinear PDEs. | |||
| MTH230 | Elective |
Set theory
|
– |
| Set-theoretical paradoxes and means of avoiding them. Sets, relations, functions, order and well-order. Proof by transfinite induction and definitions by transfinite recursion. Cardinal and ordinal numbers and their arithmetic. Construction of the real numbers. Axiom of choice and its consequences. | |||
| MTH314 | Elective |
Complex Analysis II
|
MTH313 |
| 복소해석학 II | |||
| MTH260 | Elective |
Elementary Number theory
|
– |
| Divisibility, congruences, numerical functions, theory of primes. Topics selected: Diophantine analysis, continued fractions, partitions, quadratic fields, asymptotic distributions, additive problems. | |||
| MTH303 | 1TR:R, 2TR:E |
Modern Algebra II
|
MTH302 |
| Further topics on groups, rings; the Sylow Theorems and their applications to group theory; classical groups; abelian groups and modules over a principal ideal domain. Algebraic field extensions; splitting fields and Galois theory; construction and classification of finite fields. | |||
| MTH271 | Elective |
Methods of Applied Mathematics
|
– |
| Concise introductions to mathematical methods for problems formulated in science and engineering. Functions of a complex variable, Fourier analysis, calculus of variations, perturbation methods, special functions, dimension analysis, tensor analysis. Introduction to numerical methods with emphasis on algorithms, applications and computer implementation issues. | |||
| MTH281 | Elective |
Discrete Mathematics
|
– |
| This course introduces discrete objects, such as permutations, combinations, networks, and graphs. Topics include enumeration, partially ordered sets, generating functions, graphs, trees, and algorithms. | |||
| MTH422 | Elective |
Particial Differential Equations
|
– |
| 편미분방정식 | |||
| MTH330 | Elective |
Introduction to Geometry
|
– |
| A critical examination of Euclid’s Elements; ruler and compass constructions; connections with Galois theory; Hilbert’s axioms for geometry, theory of areas, introduction of coordinates, non-Euclidean geometry, regular solids, projective geometry. | |||
| MTH414 | Elective |
Differential Geometry II
|
MTH331 |
| Plane curves: rotation index, isoperimetric inequality, Fenchel’s theorem. Space curves: congruence, total curvature of a knot. Submanifolds of Euclidean spaces as level sets, Gauss map. Curves on a surface, geodesics. Gauss Lemma and a proof that geodesics minimise distance locally. Isometries and conformal maps. | |||
| MTH342 | Elective |
Mathematical Statistics
|
– |
| Probability and combinatorial methods. Discrete and continuos univariate and multivariate distributions. Expected values, moments. Estimation. Unbiased estimation. Maximum likelihood estimation. Confidence intervals. Tests of hypotheses. Likelihood ratio test. Nonparametric methods. | |||
| MTH431 | Elective |
Algebraic Topology
|
– |
| Fundamental group and covering spaces, simplicial and singular homology theory with applications, cohomology theory, duality theorem. Homotopy theory, fibrations, relations between homotopy and homology, obstruction theory, and topics from spectral sequences, cohomology operations, and characteristic classes. | |||
| MTH361 | Elective |
Mathematical Modeling and Applications
|
– |
| Formulation and analysis of mathematical models. Applications to physics, biology, economics, social sciences and other areas of science. Use of Mathematical and scientific software packages: Mathematica, Matlab, Maple, e.t.c. | |||
| MTH412 | Elective |
Dynamical Systems
|
– |
| 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. | |||
| MTH331 | Elective |
Scientific Computing
|
– |
| 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. Nonlinear equations. Numerical continuation methods. Optimization. Gas and Fluid dynamics. | |||
| MTH341 | Elective |
Financial Mathematics
|
– |
| Review of random variables, expectation, variance, covariance and correlation. Binomial distribution. Properties of Normal random variables and the central limit theorem. Time value of money, compound interest rates and present value of future payments. Interest income. The equation of value. Annuities. The general loan schedule. Net present values. Comparison of investment projects Option pricing techniques in discrete and continuous time. Black-Scholes option pricing formula. | |||
| *MTH451 | 1TR:R, 2TR:E |
Advanced Linear Algebra
|
MTH203 |
| More abstract treatment of linear algebra than Linear Algebra (MTH103). Tools such as matrices, vector spaces and linear transformations, bases and coordinates, eigenvalues and eigenvectors and their applications. Characteristic and minimal polynomial. Similarity transformations: Diagonalization and Jordan forms over arbitrary fields. Schur form and spectral theorem for normal matrices. Quadratic forms and Hermitian matrices: variational characterization of the eigenvalues, inertia theorems. Singular value decomposition, generalized inverse, projections, and applications. Positive matrices, Perron-Frobenius theorem. Markov chains and stochastic matrices. M-matrices. Structured matrices (Toeplitz, Hankel, Hessenberg). Matrices and optimization. | |||
| MTH461 | Elective |
Stochastic Processes
|
– |
| Exponential Distribution and Poisson Process. Markov Chains. Limiting Behavior of Markov Chains. The main limit theorem and stationary distributions, absorption probabilities. Renewal theory and its applications. Queueing theory. Reliability theory. Brownian Motion and Stationary Processes. Martingales. Structure of a Markov process: waiting times and jumps. Kolmogorov differential equations. | |||
| MTH480 | Elective |
Topics in Mathematics 1
|
– |
| This course is designed to discuss contemporary topics in Mathematics. Actual topics and cases will be selected by the instructor and may vary from term to term. | |||
| MTH481 | Elective |
Topics in Mathematics 2
|
– |
| This course is designed to discuss contemporary topics in Mathematics. Actual topics and cases will be selected by the instructor and may vary from term to term. | |||
| PHY201 | Elective | – | – |
| 고전역학 | |||
| PHY311 | Elective | – | – |
| 수리물리 1 | |||
| PHY312 | Elective | – | – |
| 수리물리 2 | |||
| PHY437 | Elective | – | – |
| 비선형동력학 | |||
| MEN220 | Elective | – | – |
| 유체역학 | |||
| MEN301 | Elective | – | – |
| 수치해석학 | |||
| MEN302 | Elective | – | – |
| 유한요소법 | |||
| EE211 | Elective | – | – |
| 확률과 랜덤프로세서 | |||
| EE311 | Elective | – | – |
| 신호 및 시스템 | |||
| CSE232 | Elective | – | – |
| 이산수학 | |||
| CSE331 | Elective | – | – |
| 알고리즘개론 | |||
| CSE463 | Elective | – | – |
| 기계학습 | |||
| DME321 | Elective | – | – |
| 수치모델링 및 분석 | |||
| FIA401 | Elective | – | – |
| 금융공학 | |||
