대학원 - 교육과정 소개

이수구분	과목명 (영문명)	학점
전공선택	실해석학 1,2　(RealAnalysis1,2) Lebesgue measure, Lebesgue integral, Differentiation, L^p spaces, Fourier Transform	3학점
전공선택	복소해석학　1,2 (Complex Analysis　1,2) Cauchy Integral Formula, Holomorphic and Meromorphic Functions, Infinite Series and Products, the Gamma Functions, Harmonic Functions, Conformal Mapping, Dirichlet's Problem.	3학점
전공선택	함수해석학 1,2 (Functional Analysis 1,2) Hilbert space, Banach space, Frechet space, Bounded Operators, Spectral Theory for Self adjoint Operators.	3학점
전공선택	해석학 특강 1,2 (Topics in Analysis 1,2　) Recent Topics in Analysis	3학점
전공선택	다변수복소해석학 1,2 (Several Complex Variables 1,2) Cauchy Integral Formulain Polydiscs, Domains of Holomorphy, Pseudo convexity and Plurisubharmonic Functions, Existence and Approximation Theorems for Holomorphic Functions via-operator.	3학점
전공선택	조화해석학 (Harmonic Analysis) Interpolation Theorems, Singular Integrals, Hilbert Transform, Riesz Transform, BMO, Littlewood-Payley theory	3학점
전공선택	대수학 1,2 (Algebra 1,2) Group, Ring, Module, Field, Galois Group, Group Representation	3학점
전공선택	군론 (Group Theory) Free Abelian Group, Finitely Generated Abelian Group, Sylow Theorem, Finite Group, Group Representation	3학점
전공선택	군표현론 (Group Representation Theory) Group Representation, Group Character	3학점
전공선택	대수학 특강 1,2 (Topics in Algebra 1,2) Recent Topics in Algebra	3학점
전공선택	가환대수 및 대수기하학 (Commutative Algebra and Algebraic Geometry) Properties of Communative Algebra, Affine Variety, Projective Variety, Riemann-Roch Theorem	3학점
전공선택	Homology 대수 (Homological Algebra) Tensor Product of Modules, Flatness, Chain Complex, Ext, Tor, Cohomology Group	3학점
전공선택	대수적 정수론 (Algebraic Number Theory) Principal Ideal Rings, Integers on Quadratic Fields, Norms and Traces, Noetherian Rings and Dedekind Rings, Ideal Classes and Unit Theorem 등을 다룬다.	3학점
전공선택	정수론 (Number Theory) Prime Numbers, Multiplicative Functions, Euler's Theorem, Wilson's Theorem, Primitive roots, Quadratic residues, Diophantine Equations, Continued Fractions, Quadratic Form	3학점
전공선택	일반위상수학 (General Topology) Compactification, Uniform Spaces, Completeness, Partitions of Unity	3학점
전공선택	대수적 위상수학1,2 (Algebraic Topology1,2) Simplicial Complex, Homology Group, Homotopy Theory, Fundamental Group, CW-complex, Duality	3학점
전공선택	위상수학특강 1,2 (Topics in Topology 1,2) Recent Topics in Topology	3학점
전공선택	미분기하학 1,2 (Differential Geometry 1,2) Riemannian Geometry, Connection, Covariant Derivative, Lie Group. Vector Bundles, Characteristic Classes	3학점
전공선택	미분다양체론 (Differentiable Manifolds) Concepts of Differential Manifolds, Vector Fileds, Tangent Bundle, Cotangent Bundle, Riemannian Geometry	3학점
전공선택	미분위상수학 (Differential Topology) Differentiable Mappings, Transversality, Sard's Theorem, Intersection Theory, The Euler Characteristic	3학점
전공선택	회귀 분석론 (Regression Analysis) 선형회귀 모형의 추정 및 가설검정, error term의 가정에 대한 여러 가지 문제를 고찰하고, 예측에 대한 문제들을 다룬다.	3학점
전공선택	분산분석 및 실험계획법 (Analysis of Variance and Design of Experiments) 고전적 분산 분석 모형의 자세한 소개 및 그 응용, 회귀분석, 공분산분석, 선형모형, 기하학적 해석.	3학점
전공선택	다변량 분석 (Multivariate Analysis) 다변량자료분석론 및 그 응용, 다변량회귀분석, 판별분석, Pattern분류, 집락분석, 인자분석, 주성분분석.	3학점
전공선택	확률 과정론 (Stochastic Processes) 확률 과정론의 이론 및 그 응용, Random walk, Gambler's ruin, Recurrent events, Discrete-time Markov chains, Branching processes, Poisson processes, Renewal theory, Continuous-time Markov chains, Birth and Death processes, Queueing theory, Brownian motion.	3학점
전공선택	비모수 통계학 (Nonparametric Statistics) Distribution-free Tests, U Statistics, Asymptotic Efficiency, Hodges-Lehman Estimator, M-estimator 등의 문제를 다룬다.	3학점
전공선택	통계적 의사 결정론 (Statistical Decision Theory) 결정이론적 관점에서 본 통계적 추측이론과 Bayesian 분석을 이용한 통계분석으로서 결정이론을 중심으로 여러 문제를 다룬다.	3학점
전공선택	시계열 분석 (Time Series Analysis) 시계열 자료분석에 쓰이는 통계적 기법, Estimation of Trends and Seasonal Adjustment, Stationary Series-Autocorrelation and Spectrum, Estimation and Interpretation of Spectra, ARIMA Models and Fitting Theorem to Data.	3학점
전공선택	범주형 자료분석 (The Analysis of Categorical Data) log-linear 모형의 이론 및 그의 multi-way contingency table 과 종속변수가 범주형인 자료들에의 응용, Poisson distribution, one-way, two-way, and multi-way frequency tables, logistic regression, MLE.	3학점
전공선택	축차적 통계분석 (Sequential Analysis) SPRT 및 Sequential 추정이론, 정규분포 및 이산형분포에서의 응용 및 축차적 의사결정론에 관한 응용.	3학점
전공선택	표준추출법, 모의실험 및 몬테칼로 방법 (Sampling, Simulation, and Monte Carlo Method) Survey를 목적으로 한 표본추출법의 기본원리와 기법, simple random sampling, stratified sampling, systematic sampling, cluster sampling, Monte Carlo 방법과 모의실험의 통계적 배경, variance reduction, conditional Monte Carlo, control variates, antithetic variates, regression methods, 통계적 추정문제의 응용.	3학점
전공선택	통계상담 및 실습 1,2 (Statistical Consulting and Practices1,2 ) 통계자문 및 실무를 위한 다양한 연습을 목표로 실질적인 project에 참여하여 통계자료분석 및 보고서 작성법을 배운다.	3학점
전공선택	확률론 특강 1,2 (Topics in Probability 1,2) Recent Topics in Probability	3학점
전공선택	통계학 특강 1,2 (Topics in Statistics 1,2) Recent Topics in Statistics	3학점
전공선택	다변량분석 특강 1,2 (Topics in Multivariate Analysis 1,2) Recent Topics in Multivariate Analysis	3학점
전공선택	확률과정론 특강 1,2 (Topics in Stochastic Processes 1,2) Recent Topics in Stochastic Processes	3학점
전공선택	수치 해석학 1,2 (Numerical Analysis 1,2) 방정식의 수치해법 및 오차분석, 근사값, Interpolation, 수치미분과 적분, 상미분 방정식의 수치해법과 이론, 초기치 문제의 수치해법 및 안정도 분석, 경계치 문제의 수치해법 및 안정도분석, 유한차분법, 편미분방정식의 수치해법 및 오차분석, Navier-Stokes Equation의 수치해법.	3학점
전공선택	수치 선형대수학 (Numerical Linear Algebra) 형대수와 관련된 문제의 수치해법 및 이론, 유한요소법, Eigenvalue 문제, 특수행렬의 수치해법, 수렴비율, 오차분석 등을 다룬다.	3학점
전공선택	응용수학 1,2 (Applied Mathematics 1,2) Analysis for applied mathematics, Numerical Analysis, Cryptography, Mathematical	3학점
전공선택	응용수학특강 1,2 (Topics in Applied Mathematics 1,2) 수치해석 및 암호학을 비롯한 다양한 응용수학의 이론과 방법론 등을 다룬다.	3학점
전공선택	수리통계학 1,2 (Mathematical Statistics 1,2) Sufficient Statistics, UMVU Estimators, Performance of the Estimators, The Information Inequality, Linear Models, Large Sample Theory, Asymptoic Optimality, Randomization, Bayesian Statistics, Uniformly Most Powerful Tests, Linear Hypotheses, Nonparametric Statistics, Robust Statistics.	3학점
전공선택	확률론 1,2 (Probability Theory 1,2) Probability Measures, Existence and Extension, Denumerable Probabilities, Random Variables, Expected value, The Law of Large numbers, Weak Convergence, Characteristic Functions, The Central Limit Theorem, The Radon-Nikodym Theorem, Conditional Probability, Conditional Expectation, Martingales.	3학점
전공선택	편미분방정식론 1,2 (Partial Differential Equations 1,2) Harmonic Functions, Heat Equations, Wave Equations, Sobolev Spaces, Elliptics Equations, Parabloic Equations, Hyperbolic Equations, Variational Methods	3학점
전공선택	편미분방정식론 특강 1,2 (Topics in Partial Differential Equations 1,2) RecentTopicsin Partial Differential Equations	3학점
전공선택	환과 Module론 1,2 (Rings and Modules 1,2) Noether Rings, Artin Rings, Jacobson Radical, Semisimple Rings, Free Module, Projective Module, Injective Module	3학점
전공선택	가환대수 1,2 (Commutative Algebra 1,2) Primary Decomposition, Integral Dependence, Discrete Valuation Rings, Dedekind Domain, Completion, Graded Rings, Dimension Theory, Local Rings	3학점
전공선택	비가환대수 1,2 (Non-commutative Algebra 1,2) Local Rings, Semilocal Rings, Perfect Rings, Semiperfect Rings, von Neumann regular Rings, PI-algebra, Group ring, Division algebra	3학점
전공선택	수치 미분 방정식 (Numerical Solutions of Ordinary Differential Equations) Numerical solution of initial-value problems by Runge-Kutta methods, general one-step methods, and multistep methods; analysis of truncation error, discretization error, and rounding error; stability of multi-step methods; numerical solution of boundary value and eigen-value problem by initial-value techniques and finite difference methods; topics of current interest.	3학점
전공선택	수치 편미분 방정식 (Numerical Solution of Part Differential Equations) The numerical solution of hyperbolic, and elliptic equations by finite difference methods. finite element methods, and collocation methods; iterative methods(Gauss-Seidel, over relation, alternating direction) for solving elliptic equations, discretization and round-off errors; explicit and implicit methods for parabolic and hyperbolic systems; the methods of characteristic; the concept of stability initial value problems ; topics of current interest.	3학점
전공선택	Fourier 해석학 (Fourier Analysis) Fourier Seires, Fouries Transform, Application	3학점
전공선택	암호론 1,2 (Cryptography 1,2) This course provides an introduction to cryptography. The material covered includes various models of encryption - symmetric and asymmetric, pseudorandomness, digital signatures, and network applications to cryptography.	3학점
전공선택	양자정보론 1,2 (Quantum Information Theory 1, 2) This provides an introduction to quantum information theory. Topics covered; quantum algorithms including Shor's factoring algorithm and Grover's search algorithm; quantum error correction; quantum communication and cryptography.	3학점
전공선택	논문지도 I (Thesis Research I) 학위청구논문을 체계적이고 논리적으로 쓸 수 있도록 지도한다.	0학점
전공선택	논문지도 II (Thesis Research II) 학위청구논문을 체계적이고 논리적으로 쓸 수 있도록 지도한다.	0학점
전공선택	논문지도 III (Thesis Research III) 학위청구논문을 체계적이고 논리적으로 쓸 수 있도록 지도한다.	0학점