홈 Undergraduate Mathematics ( Under ) Courses & Syllabuses 
 MATH 003 TOPIC COURSE 〔 3 〕 
 The topic of this course is determined each semester . 
 MATH 201 SET THEORY 〔 3 〕 
 Axiom System , Algebraic Structure , The Foundations of Geometry , The Foundations of Continuity . 
 MATH 203 DISCRETE MATHEMATICS 〔 3 〕 
 Mathematical Induction , Basic Counting Techniques , Graphs and Trees , Algorithm , Generating Functions , Algebraic Structure . 
 MATH 211 ANALYSIS I WITH LAB 〔 3 〕 
 Basic Topology on Euclidean Space . Continuity , Convergence , Uniform Convergence , Series , Convergence Tests . Differentiation , Inverse and Implicit Function Theorems . 
 MATH 212 ANALYSIS II WITH LAB 〔 3 〕 
 Riemann - Stieltjes Integrals , Sequences and series of functions , Uniform convergence , Fourier series , Functions of Several Variables , Integration of Differential Forms , Stokes ’ Theorem . 
 MATH 221 LINEAR ALGEBRA I WITH LAB 〔 3 〕 
 Vector Spaces & Systems of Linear Equations , Linear Transformations & Matrices , Vector Spaces with an Inner Product , Determinants . 
 MATH 222 LINEAR ALGEBRA II WITH LAB 〔 3 〕 
 The Theory of Single Linear Transformation , Dual Vector Spaces & Multilinear Algebra , Orthogonal & Unitary Transformations . 
 MATH 223 NUMBER THEORY 〔 3 〕 
 Divisibility , Primes , Congruences , Quadratic Reciprocity , Farey Sequences , Euler Phi - Function , Fermat ' s Last Theorem . 
 MATH 232 INTRODUCTION TO GEOMETRY 〔 3 〕 
 We study modern methods of mathematics through the various theories of classical geometry . Non - euclidean geometry shows the concepts of duality , projectivity , hyperbolicity and also shows the role of group structures and metric structures in geometry . The study of these concepts also reveals how mathematics is applied to other sciences and solving practical problems . 
 MATH 240 DIFFERENTIAL EQUATIONS WITH LAB 〔 3 〕 
 First order differential equations , Second order linear differential equations , Series solution of second order linear Equations , Higher order linear differential equations , The Laplace transform . 
 MATH 282 ADVANCED DIFFERENTIAL EQUATIONS 〔 3 〕 
 Boundary value problem , Sturm - Liouville theory , Linear Systems theory , Oscillation theory , Stability theory . 
 MATH 315 COMPLEX ANALYSIS I 〔 3 〕 
 Complex Line Integral , Holomorphic Functions , Cauchy ' s Theorem , Power Series Representation , Zeros of Holomorphic functions , Maximum Modulus Theorem , Singularities , Residue Calculus . 
 MATH 321 ALGEBRA I 〔 3 〕 
 Groups , Subgroups , Cosets , Homomorphism Theorems , Sylow Theorems , Ring , Ideal , Field of Quotients , Ring of Polynomials , Principal Ideal Domain , Euclidean Rings . 
 MATH 331 DIFFERENTIAL GEOMETRY I 〔 3 〕 
 Tangent vectors and differential forms in euclidean spaces , Elementary vector calculus , Curves and Frenet formula , Visualization of curves , Examples of surfaces , Visualization of surfaces , Gauss curvature and mean curvature , Computation of curvatures , Geodesics . 
 MATH 333 TOPOLOGY I 〔 3 〕 
 This is an introduction to topology with an emphasis on the set - theoretical aspect of the subjects . The topics covered are topological and metric spaces , continuous functions , homeomorphisms , compactness , connectness and separation axioms . 
 MATH 342 NUMERICAL ANALYSIS AND COMPUTER EXPERIMENT 〔 3 〕 
 Root finding for nonlinear equations , interpolation theory , approximation theory , numerical integration , numerical solutions of system of linear equations . 
 MATH 343 PROBABILITY AND STATISTICS WITH LAB 〔 3 〕 
 We introduce basic concepts in probability such as random variable , distribution function , expectation , conditional expectation and limit theorems . Basic theory of mathematical statistics including estimation and testing hypotheses is developed . 
 MATH 344 STOCHASTIC PROCESSES 〔 3 〕 
 This course is intended to introduce stochastic processes by using elementary probability theory . We present basic important topics such as Poisson processes , Markov processes , and Brownian motion as well as their applications . 
 MATH 358 COMPLEX ANALYSIS Ⅱ 〔 3 〕 
 Mapping properties of holomorphic functions , Riemann mapping theorem , Harmonic functions , Maximum principle , Mean value property , Poisson integral formula , Analytic continuation , Infinite products , Special functions . 
 MATH 362 ALGEBRA II 〔 3 〕 
 We study the topics of fields , extension fields , algebraic elements , transcendental elements , finite fields , function fields , Galois theory and algebraic solutions of polynomial equations . 
 MATH 372 DIFFERENTIAL GEOMETRY II 〔 3 〕 
 Calculus of variations and geodesics , Completeness , Isometries , Parallel translation and geodesic curvatures , Riemann curvature tensor , Gauss - Bonnet theorem , Geodesic coordinates . Also some topics chosen from the followings : Minimal surfaces and surfaces of constant mean curvature ( CMC ) , Visualization of minimal and CMC surfaces , Calculus of variations and applications to physics , Geometry of manifolds , Geometry of metric spaces . 
 MATH 374 TOPOLOGY II 〔 3 〕 
 Beginning with the classification of surfaces , this course introduces Euler characteristic , fundamental groups and its applications to 2 and 3 manifolds . 
 MATH 453 REAL ANALYSIS 〔 3 〕 
 Lebesgue measure , Lebesgue integrals , Lpspaces , Hilbertspaces , Duality . 
 MATH 458 TOPICS IN ANALYSIS 〔 3 〕 
 Topics will be selected from various advanced subjects of functions of complex or real variables . For functions of complex variables , topics include conformal mappings , analytic continuation , properties of analytic functions , harmonic functions , infinite products . For functions of real variables , Topics include complex measures , Hilbert spaces , Dual spaces and normed linear spaces . 
 MATH 462 APPLIED NUMBER THEORY 〔 3 〕 
 The theory of finite fields , the theory of polynomial rings , the theory of elliptic curves , RSA system , ECC system , XTR system , NTRU system , coding theory . 
 MATH 464 COMBINATORICS 〔 3 〕 
 Permutations and combinations , generating functions , recurrence relations , inclusion and exclusion , Polya ' s enumerations . 
 MATH 469 TOPICS IN ALGEBRA 〔 3 〕 
 We study the topics of representations of groups , mathematical cryptology , computational algebra , algebraic geometry . 
 MATH 476 TOPICS IN GEOMETRY 〔 3 〕 
 Topics will be chosen from the subjects of recent interests related to geometry . Topics vary accordingly and may include one of may the followings : Metric geometry , Minimal surfaces , Combinational geometry , Geometric analysis , Complex geometry , CAGD ( Computer Aided Geometric Design ) , Mathematical mechanics , etc . 
 MATH 477 TOPICS IN TOPOLOGY 〔 3 〕 
 In this course , we are going to discuss the Knot theory which is applied to physics and biology . Moreover we will explore other related areas of mathematics such as group theory , differential geometry and algebraic topology . 
 MATH 481 PARTIAL DIFFERENTIAL EQUATIONS AND COMPUTER EXPERIMENT 〔 3 〕 
 Fourier series , Wave equations , Heat equations , Laplace equations , Special functions , Existence and Uniqueness theorem . 
 MATH 483 MATHEMATICAL FINANCE 〔 3 〕 
 We study the important problems in finance such as derivatives , interest rate models , and risk managements based on probability theory , PDE , and numerical computations . 
 MATH 484 ACTUARIAL MATHEMATICS 〔 3 〕 
 Probability theory , Statistical Inference , Risk model , Loss distribution , Risk premium , Experience rating , Life insurance , Annuities , Population theory . 
 MATH 485 TELECOMMUNICATION MATHEMATICS 〔 3 〕 
 Basic queueing theory and its applications to telecommunication systems are covered : Introduction to queueing theory and telecommunication systems , M / M / C queue , M / G / 1 queue , modeling of various traffics such as voice and video , delay and loss probability of networks , performance analysis of various transmission schemes . 
 MATH 487 TOPICS IN APPLIED MATHEMATICS 〔 3 〕 
 We study mathematical theories and methods which are used to analyze the physical and industrial problems . 
 MATH 488 TOPICS IN PROBABILITY THEORY 〔 3 〕 
 Special topics are chosen from recent developments of research in probability theory . Topics covered vary from year to year .