Curriculum

Course No. Course Title Course Title(Kor.) Prerequisite
※ For only 1st track students, up to 6 credits can be taken from outside mathematical sciences
(1트랙 학생들에 한해서 타과 선택과목 6학점까지 인정).
※ *MTH302, *MTH451 are required for the 1st track students who start from 2016 on.
(MTH302, MTH451은 2016년도에 시작하는 1트랙학생부터 전공필수 과목으로 지정됨)

Recommended Course Tracks

* : Required Course, ** : Required only for 1st track
Year/Sem. I (Spring) II (Fall)
2 *MTH251 (해석학1)
MTH203 (응용선형대수)
MTH201 (미분방정식)
MTH281 (이산수학)
MTH230 (집합론)
**MTH252 (해석학2)
**MTH202 (상미분방정식론)
MTH260 (정수론)
MTH271 (응용수학방법론)
MTH330 (기하학개론)
3 *MTH301 (현대대수학1)
*MTH311 (복소해석학1)
MTH342 (수리통계)
MTH361 (수리모형방법론)
MTH330 (기하학개론)
*MTH351 (위상수학)
**MTH302 (현대대수학2)
**MTH341 (확률론)
**MTH321 (수치해석)
MTH312 (복소해석학2)
4 **MTH411 (미분기하학1)
**MTH421 (편미분개론)
MTH420 (푸리에해석)
MTH412 (동적시스템)
MTH480 (수학특강1)
**MTH451 (고급선형대수)
MTH431 (대수위상)
MTH461 (확률과정론)
MTH412 (미분기하학2)
MTH481 (수학특강2)

Course Description

MTH230 Set theory [집합론]
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.
MTH251 Mathematical Analysis I [해석학 I]
The real number system. Set theory. Topological properties of R^n, metric spaces. Numerical sequences and series, Continuity, connectedness, compactness. Differentiation and integration.
MTH252 Mathematical Analysis II [해석학 II]
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.
MTH260 Elementary Number theory [정수론]
Divisibility, congruences, numerical functions, theory of primes. Topics selected: Diophantine analysis, continued fractions, partitions, quadratic fields, asymptotic distributions, additive problems.
MTH301 Modern Algebra I [현대대수학 I]
Groups, homomorphisms, automorphisms, permutation groups. Rings, ideals and quotient rings, Euclidean rings, polynomial rings. Extension fields, roots of polynomials.
MTH302 Modern Algebra II [현대대수학 II]
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 Methods of Applied Mathematics [응용수학방법론]
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 Discrete Mathematics [이산수학]
This course introduces discrete objects, such as permutations, combinations, networks, and graphs. Topics include enumeration, partially ordered sets, generating functions, graphs, trees, and algorithms.
MTH341 Probability [확률론]
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.
MTH311 Complex Analysis I [복소해석학 I]
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.
MTH420 Fourier Analysis [푸리에 해석학]
Introduction to harmonic analysis and Fourier analysis methods, such as Calderon-Zygmund theory, Littlewood-Paley theory, and the theory of various function spaces, in particular Sobolev spaces. Some selected applications to ergodic theory, complex analysis, and geometric measure theory will be given.
MTH321 Numerical Analysis [수치해석학]
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.
MTH330 Introduction to Geometry [기하학 개론]
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.
MTH411 Differential Geometry I [미분기하학 I]
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.
MTH412 Differential Geometry II [미분기하학 II]
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 Mathematical Statistics [수리통계학]
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.
MTH351 General Topology [위상수학]
Set-theoretic preliminaries. Metric spaces, topological spaces, compactness, connectedness. Countability and separation axioms. Covering spaces and homotopy groups.
MTH431 Algebraic Topology [대수위상]
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 Mathematical Modeling and Applications [수리모형방법론]
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.
MTH202 Ordinary Differential Equations [상미분방정식론]
Existence and uniqueness of solutions, linear systems, regular singular points. Analytic systems, autonomous systems, Sturm-Liouville Theory.
MTH412 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.
MTH421 Introduction to Partial Differential Equations [편미분방정식개론]
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.
MTH331 Scientific Computing [과학계산]
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 Financial Mathematics [금융수학]
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 Advanced Linear Algebra [고급선형대수학]
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 Stochastic Processes [확률과정론]
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 Topics in Mathematics I [수학 특강 I]
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 Topics in Mathematics II [수학 특강 II]
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.