||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.
||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.
||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.
||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.
||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.
||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.
||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.
||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.
||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.
||Discrete Mathematics and Programming
||discrete mathematics, combinatorics, number theory & cryptography
||This course examines basic computer systems with linear algebra, linear programming, Game Theory.
||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.
||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.
||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.
||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.
||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.
||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.
||topological space, metric space, compact space
||This course includes metric spaces and topological spaces, T0 ~ T4 spaces, convergence, etc.
||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.
||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.
||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.
||complete space, homotopy, fundamental group
||The course covers compact spaces, product spaces, connected spaces, complete spaces, function spaces, uniform spaces, homotopy etc.
||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.
||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.
||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.
||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.
||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.
|| 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.
||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.
||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.
||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.
||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.
||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.
||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.
||interest, annuity, life insurance, risk distribution
||This course covers utility theory, interest, annuities, premium, risk distribution, solvency.
||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.
||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.
|| Mathematical Sciences Internship I
||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.