•       Analysis I and Practice Topics for algebraic and topological properties of the real line and complex plane, Limits, continuity, differentiation, integration which are necessary for the study of advanced analysis and measure theory. Applied Linear Algebra I Study matrices, linear systems, determinant, vector spaces, linear transformations, permutations, and eigenvalues. Set Theory Topics includes the following as the basic of modern mathematics: statements, elementary logic, axiomatic system, sets, relations and functions, cardinal numbers, order structure, etc. Differential Equation Topics includes solution of ordinary differential equations and integral transforms with applications to mathematical models arising in sciences and engineering. Vector Analysis Study limit, continuity, directional derivative, and multiple integration of multi-variable functions. Moreover, Green’s theorem, Stokes’ theorem, and divergence theorem are included. Mathematical Statistics I As fundamental concepts of probability theory and statistics to analyze random phenomena, topics covers probability spaces, random variables, distributions, limit theorems, etc. Itroduction to Modern Mathematics Topics to be fundamental in modern mathematics are introduced and practice them in this course. Main goals of this course are to understand and practice the concepts in geometry, algebra, topology, and analysis. Differential Geometry I and Practice Based under vector analysis and analytic geometry, this course examines the theory of curves in 3-dimensional space. Topics includes representations and classifications of curves, length of arc, curvature, torsion, etc. Complex Variables I and Practice Topics includes algebraic and geometric preliminaries, topological and analytic preliminaries, bilinear transformations and maps, complex elementary functions, analytic functions, power series, complex integration and Cauchy's theorem. Number Theory Basic concepts of classical number theory and elementary computing algorithm. Analysis II Continues Analysis I. Topics includes sequences, limits, continuity, differentiation, Riemann and Riemann-Stieltjes integrations, sequence of functions, series which are necessary for the study of advanced analysis and measure theory. Appliea Linear Algebra II Study advanced concepts in linear algebra such as invariant subspaces, direct sums, Jordan canonical factorization, inner product, quadratic form. Mathematical Statistics II Continues Mathematical Statistics I. Topics includes fundamental theory of statistical inferences and tests of hypothesis. Modern Algebra I and Practice Topics provides basic introduction to groups, classes and properties of groups with applications. Emphasizes axiomatic development. Real Analysis I and Practice Topics includes Lebesgue measure, measurable sets, Lebesgue integral, differentiation, etc. Differential Geometry II Continues Differential Geometry I. Based under vector analysis and analytic geometry, this course examines the theory of surface in 3-dimensional space. Topics includes representations of surfaces, curvature, simple surfaces, fundamental theorems for surfaces, etc. Complex Variables II Continues Complex Variables I. Topics includes Cauchy theorem, Laurent series, residue theorem, etc. Introduction to Topology As an extension of usual topology, general topological space is introduced. Topics includes limits, convergences, continuity, metric space, normed space, etc, in general topology. Numerical Analysis This course provides methods to find numerical solutions for problems modeled in science and engineering. Topics includes convergences and stability of numerical solution. Topology Ⅰand Practice Topics provides characteristic properties and structures of the first and second countable topological space, Lindelof space, separable space, T1-space, Hausdorff space, regular space, normal space, compact space, compactification, connected space, product space. Modern Algebra II Continues Modern Algebra I. Topics provides basic introduction to rings, structures and properties of rings with applications. Emphasizes axiomatic development. Indutrial Mathematics and Practice Study numerical analysis to solve a variety of mathematical problems appearing in applied area and study how to develop and apply numerical method using computer program. Real Analysis II Continues Real Analysis I. Topics includes absolutely continuity, Holder and Minkowski inequalities, Banach space, Signed measure, properties of integration, etc. Modern Geometry This course provides properties of figures in 3-dimensional Euclidean space. Topics includes directional derivative, differential forms, covariant derivative, frame fields, connection forms, isometric transformations, orientation of curve, coordinate patches, etc. Discrete Mathematics Enhance the mathematical ability to find discrete problems in real life, to make a logical decision, and to solve them with creative idea. Study fundamental theories in the following subjects; logic and deduction, set theory, order set, relation and function, probability, combinatorics, Bool algebra, graph theory, algorithm, and optimization, etc. Topology II Continues Topology I. This course introduces product space, complete metric space, function space and provides several structures of the topological spaces. Topics includes uniform convergence, compact-open topology, homotopy, fundamental group, etc. Topics in Algebra Study one or two topics of advanced number theory (algebraic, analytic number theory, and p-adic analysis), advanced ring theory, module theory, basic algebraic geometry, and group representation. Mathematical Biology This is the subject to study many problems in biology, ecology, and medical science using mathematical tools. Main goals are to construct models for difference equations and differential equations of biological systems, to investigate their qualitative-quantitative solutions, and to simulate them using mathematical software. Theory of Mathematics Education Based on connection between theory and realization, study topics related to psychological and philosophical idea, resolution, and educational evaluation for studying mathematics. Mathematical Finance Study mathematical methods to understand fundamental knowledge of finance. such as derivatives, discrete stochastic processes, binomial models, price decision of underlying assets, interest rates, and option price, etc. Information Theory/Combinatorics/Introduction to cryptograpy Study mathematical theories in information science such as basic probability theory, concepts and applications of entropy, and coding theory. Study a variety of discrete structures such as pigeonhole principle, graph theory, recursive sequence, and generating function. Study the fundamental subjects in cryptography such as congruence, Fermat’s little theorem, finite fields, elliptic curves, and public key cryptosystem. Topics in Geometry Study how to apply fundamental theories of geometry to physics, engineering, and medical science. Moreover, study their applications in real life. (Inrtoduction to Partial Differential Equations Study the existence of solutions for partial differential equations (elliptic, parabolic, and hyperbolic), separation of variables, Fourier transform, Sturm-Liouville theory, and Bessel functions. In particular, study mainly heal equations, wave equations, and Laplace equations appearing in sciences and engineering. For prerequisite courses, Analysis and Differential Equations are recommended. Study on Teaching Materials and Teaching Methods in Mathematical Education Study curriculum, material analysis, syllabus, and teaching method of mathematical education in middle and high schools. Logic and Essay Writing in Mathematics Education Main goal of this course is to enhance the ability to write essay logically in mathematical education.

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