## Education

Undergraduate CoursesThis table demonstrates Undergraduate Courses through number, name, number, keywords, and description.
number name keywords description
20406 Calculus limits, derivatives series This course covers limits, derivatives and their applications, differentiation of transcendental functions, integrations and their applications, criteria of convergence of series, Taylor theorem, matrices and vectors, partial derivatives, multiple integrations etc.
33670 Introduction to Modern Mathematics set, function, relations This course covers elementary theory of sets, functions, product sets, relations, cardinal and ordinal numbers, transfinite induction, axiom of choice, Zorn's lemma, and Well-ordering principle.
20407 Calculus Ⅰ function, sequence, differenciation This course covers limits, derivatives and their applications, differentiation of transcendental functions, integrations and their applications, criteria of convergence of series, Taylor theorem, etc.
20408 Calculus Ⅱ vector function, partial derivative, multiple integration This course studies curves, polar coordinates, matrices and vectors, vector-valued functions, partial derivatives, multiple integrations, Green's theorem, Divergence theorem, Stokes theorem, etc.
33670 Set Theory axioms, set, cardinality This course covers the elementary theory of sets, functions, product sets, relations, cardinal and ordinal numbers, transfinite induction, axiom of choice, Zorn' lemma and "Well-ordering" principle.
35287 Mathematical Sciences and Information calculation, symbolic calculation, numeric calculation This course provides working knowledge of a UNIX-based workstation and computing in mathematical science. This includes an introduction to window environments, basic UNIX operation, Basis of the internet.
20441 Linear Algebra Ⅰ system of linear equations, vector space, matrix This is an introductory course on linear algebra. Finite dimensional vector spaces, linear transformation and matrix, determinants, system of linear equations, Eigenvectors and inner product spaces are covered.
35288 Advanced Calculus Ⅰ sequences, structure of point sets, limits and continuity This course studies the properties of real numbers, topological concepts, limits of sequences, continuous functions and uniformly continuous functions.
38188 Multivariable Calculus vector function, multivariable integration, vector analysis The further study on the differentiation and integration of multivariable function/vector function and its application to vector analysis are covered. Stokes’ theorem and its application are studied.
35289 Discrete Mathematics and Programming discrete mathematics, combinatorics, number theory & cryptography This course examines basic computer systems with linear algebra, linear programming, Game Theory.
20442 Linear Algebra Ⅱ abstract vector space, linear transformation, basis change As a sequel to Linear algebra I, we study diagonalization of matrices, Jordan canonical form, Gram Schmidt orthogonalization, normal matrices, orthogonal and unitary matrix.
35290 Advanced Calculus Ⅱ Riemann integral, series of real numbers, sequence of functions This course covers differentiations, Riemann integrals, Sequences and Series of functions, Differentiable functions of Several variables and multiple integrals.
20435 Differential Equations differential equation, linear equation, nonlinear equation The course studies solutions of ordinary differential equations of higher order, integration in series (the Legendre, Bessel and Gauss equations), Laplacian transformation, and some partial differential equations.
20454 Theory of Integers primes, congruences, primitive roots The course deals with Fermat prime number, quadratic residue Legendre symbol and properties, and Logic and Formalized Theory.
20462 Abstract Algebra Ⅰ group, group structure, ring The course covers the structure of abstract algebra through group theory and their basic properties-finitely generated abelian group and Sylow Theorem and solvable group-and basic theory of rings and ideals, morphism and the ring of polynomials.
35291 Complex AnalysisⅠ analytic function, complex integration, Cauchy's theorem This course studies geometric properties of complex numbers, elementary transformations, analytic functions, complex integration, and Cauchy's Theorems.
20449 Topology Ⅰ topological space, metric space, compact space This course includes metric spaces and topological spaces, T0 ~ T4 spaces, convergence, etc.
20445 Numerical Analysis linear equations, root finding, numerical differentiation, integral The course includes locating roots of equations, interpolation, numerical differentiation/integration, systems of linear equations, approximation by spline functions.
20463 Abstract Algebra Ⅱ field, field structure, Galois theory The course deals with polynomials over fields, irreducibility, separability, factorization of polynomials and then we study Galois theory.
35292 Complex Analysis Ⅱ Cauchy's integral formula, singularity, harmonic function This course covers Cauchy　 inequality, maximum modulus theorem, singularities, Laurent series, Residue Theorem, harmonic functions and Poisson integral formula.
20450 Topology Ⅱ complete space, homotopy, fundamental group The course covers compact spaces, product spaces, connected spaces, complete spaces, function spaces, uniform spaces, homotopy etc.
34223 Numerical Differential Equations ordinary differential equation, partial differential equation, least squares & optimization The course includes ordinary differential equations(Taylor Series Method, Runge-Kutta Method, stability, and adaptive Runge-Kutta Method), systems of ordinary differential equations, boundary value problems for ODE, smoothing data and the method of least squares, partial differential equations, minimization of multivariate functions.
35294 Cryptography public key cryptography, discrete log problem, factoring problem The purpose of this course is to acquaint the student with classical and modern methods of cryptography. We also learn he applications of mathematical theory in cryptography. We learn complexities, private key system, public-key system, especially, RSA and Elliptic Curve Cryptosystem etc.
35296 Real Analysis Lebesgue measure, measurable functions, Lebesgue integral This course covers the real number systems, continuous functions, sequences, Lebesgue measure and Lebesgue integral, differentiation and integration Lp-space.
20433 Differential Geometry I curve, surface, curvature This course covers tangent vectors, directional functions, differential forms, frame fields, structural equations, Euclidean geometry, analysis of surfaces and theory of manifolds.
38190 Mathematical modeling mathematical model, numerical method, visualization In this course, we develop mathematical models for real-world phenomena in physical sciences, engineering, and social sciences. Mathematical models in the forms of dynamical systems, statistical models, differential equations, or game theoretic models will be solved by analytic and numerical methods. And we try to visualize the solution for better understanding of the situation.
37429 Topics in Mathematics I specialization, exploration, convergent thinking The goal of this course is to introduce the very recent development of mathematics and the interesting current trend of research activities in mathematics. The main topics covered for this course are various from pure math to applied math.
37430 Topics course in Mathematics II specialization, exploration, convergent thinking The goal of this course is to introduce the very recent development of mathematics and the interesting current trend of research activities in mathematics. The main topics covered for this course are various from pure math to applied math.
32856 Combinatorial Theory counting, graph, order This course introduces the basic combinatorial theory including permutation, combination, countability, inclusion-exclusion principle, graph, order-set, generating function, Burnside Lemma, Polya enumeration, extremal problem and design theory.
35980 Introduction to Modern Cryptography private key cryptosystem, lattice, pairing This subject covers the secret key system, public-key system, key management, authentications, signatures etc. We also cover the mathematical backgrounds for the crypto schemes and learn the current public-key schemes.
32854 Functions of Several Variables multivariable differentiation, multivariable integration, manifold This course covers n-dimensional Euclidean space, differentiation of real-valued functions and vector-valued functions, line integrals, and integrations of severable variables.
20434 Differential Geometry II isometry, Gauss theorem, Gauss-Bonnet theorem This course deals with the topological properties of surfaces, normal curvature, Gaussian curvature, surface geometry, Riemannian geometry and Gauss-Bonnet Theorem.
35979 Digital Image Processing image processing, Fourier Series, multi-resolution Mathematical theories for image processing will be studied. Fourier series, Fourier transform, spline, wavelets, scaling function and Multiresolution analysis will be discussed. Some Basic theories of approximation will be studied also.
35298 Actuarial Mathematics interest, annuity, life insurance, risk distribution This course covers utility theory, interest, annuities, premium, risk distribution, solvency.
35297 Mathematics of Finance pricing model, stochastic calculus, Black-Scholes equation This course provides students with an introduction to some baic models of finance and the associated mathematical machinery. This course covers the development of the basic ideas of hedging and pricing by arbitrage in the continuous model setting. Brownian motion, stochastic calculus, change of measure, Black-Scholes option pricing formula, and models of the interest rate market.
35293 Partial Differential Equations integral curves, surfaces of vector fields, first order partial differential equations, linear partial differential equations This course studies integral curves, surfaces of vector fields, first order partial differential equations, and linear partial differential equations.
37742 Mathematical Sciences Internship I internship This course is designed for math major students to enhance the empolyability and build better links between cirricula of Mathematical Sciences and skills in companies in need of mathematical sciences by working in the companies.