For more details on the courses, please refer to the Course Catalog
| Code | Course Title | Credit | Learning Time | Division | Degree | Grade | Note | Language | Availability |
|---|---|---|---|---|---|---|---|---|---|
| MTH5117 | Functional Analysis | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| Basic concepts, principles and methods of Functional Analysis and its Applications: Hahn-Banach theorem, Riesz Representation Theorem for Hilbert Spaces, Compact Self-Adjoint Operators, Locally Convex Spaces and Weak Topologies. Spectral Theory for various Operators; Banach Algebras, C* -Algebras, Spectral Theory of a Compact Operator, Normal Operators on Hilbert space, Unbounded Operators and Fredholm Operators. | |||||||||
| MTH5119 | Stchastic Processes | 3 | 6 | Major | Master/Doctor | 1-4 | Korean | Yes | |
| Empirical process theory and convergence are dealt with. Convergence in distribution in a Eucleadean space, Convergence in distribution in a metric space, Skorohod space, Central limit Problems. | |||||||||
| MTH5123 | Advanced Applied Numerical Analysis | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| Mathematical aspects of numerical methods including Monte Carlo method for Stochastic Differential Equations and finite difference method, finite element method, and boundary element method for integral and partial differential equations. Many applications to important problems in physics, engineering, and bio-medicine are also given. | |||||||||
| MTH5124 | Advanced Cryptography | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| Communication and information security are increasingly important due to the recent development of internet and computer based society. Cryptography gives a way of realizing secure communication of various information. In this course, we cover the basic secret and public key algorithms such as AES and RSA. We also study more advance topics such as Elliptic Curve Cryptography, Torus Based Cryptography, and Pairing Based Cryptography. | |||||||||
| MTH5125 | Algebraic Geometry | 3 | 6 | Major | Master/Doctor | 1-8 | - | No | |
| This course is the introduction to algebraic geometry for the students who studied abstract algebra in undergraduate course. We study the following subjects : projective space, affine space projective geometry on the plane, projective Nullstellensatz and dimension theorem, extension property of projective manifold, Riemann-Roch theorem of algebraic curve, and removal of singularity of algebraic curve. | |||||||||
| MTH5127 | Topics in Financial Mathematics | 3 | 6 | Major | Master/Doctor | - | No | ||
| The aim of this course is to introduce Levy processes or Malliavin Calculus, which are recently investigated and studied, and provide a comprehensive understanding of their structure and properties. | |||||||||
| MTH5128 | Dynamical System | 3 | 6 | Major | Master/Doctor | - | No | ||
| In most of the cases, it is impossible to derive explicit solution formula for a system of differential equations. Therefore, we should study them either theoretically or numerically. This course is on the theoretical investigation of the behavior of solutions for systems of ordinary differential equations. More precisely, we cover topics such as the stability/instability issues and asymptotic behaviors of solutions, qualitative properties of orbits, Poincare Bendixon theorem, Invariant manifold, bifurcation theory and chaos theory. | |||||||||
| MTH5129 | Representation Theory of Groups | 3 | 6 | Major | Master/Doctor | - | No | ||
| Representation theory is a branch of modern mathematics, which studies an algebraic structure by representing it in terms of linear transformations or matrices. It provides a powerful method in various areas in mathematics or mathematical physics. In this course, we introduce classical results on representations of a finite group over the complex numbers. The main goal is to prove the classification of complex irreducible modules over a finite group and orthonormality of irreducible characters. Furthermore, we introduce a general theory on representations of a finite dimensional algebra. | |||||||||
| MTH5130 | Machine Learning for Big Data | 3 | 6 | Major | Master/Doctor | - | No | ||
| In this course, we will cover the basic theory, algorithms, and applications in the mathematical as well as the heuristic view. In particular, we will study the challenges related to data sets with massive size and dimension by canonical examples of big data applications in science and industry. We will also study the computational aspects of these challenges in the context of parallel architectures. | |||||||||
| MTH5133 | Matrix Analysis | 3 | 6 | Major | Master/Doctor | - | No | ||
| Matrix theory has long been fundamental tools in mathematical disciplines as well as fertile fields for research. A good part of matrix analysis theory is functional analytic, operator theory, and geometry. The course handles classical and recent results of matrix analysis that have proved to be important to applied mathematics, and geometric analysis problems. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand and follow the course. Theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. This course also treats the convex cone of positive definite matrices equipped with Riemannian trace metric and recent topics of matrix geometries. | |||||||||
| MTH5134 | Algebraic Number Theory | 3 | 6 | Major | Master/Doctor | 1-8 | - | No | |
| In this course we study arithmetic properties of number fields, which are defined as finite extension fields of the rational number field. We investigate the structure of ring of algebraic integers in a given number field, and define class numbers, which measure how far the ring is f away from the unique factorization domain. We also study basic theorems in algebraic number theory, such as finiteness of class numbers, Dirichlet’s unit theorem, decomposition of primes in number fields, decomposition of primes in Galois extensions and analytic class number formula, ect. Two important examples of number fields are quadratic fields and cyclotomic fields. We introduce their Dedekind zeta functions and develop their analytic properties to derive explicit class number formulas of such fields. We also provide a lot of theorems and conjectures in relation to their class numbers. | |||||||||
| MTH5135 | Computational Complexity | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| Theory of computational complexity includes all problems related with computings and their related algorithms. For example, it is discussed whether a specific problem can be solved at all on a computer, but also how efficiently the problem can be solved. Two major aspects are considered: time complexity and space complexity, which are respectively how many steps does it take to perform a computation, and how much memory is required to perform that computation. Some standard notations such as Big O, Small O, Big Omega, Small Omega will be introduced to allow functions to be compared and analyzed in an abstract way such that only the asymptotic behavior as the inputs become large is emphasized. | |||||||||
| MTH5138 | Capstone Design | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| This course is for students who are interested in industrial mathematics and in working with real problems arising in industries. The capstone course gives students deep exposure to realistic challenges in the dynamic and stimulating and commercial technology environment. Learning to embed in, interface with, and understand diverse technical environments is a key aspect of the experience, as is acquiring the ability to grasp and address an ambiguous problem in a variety of industries. | |||||||||
| MTH5139 | Combinatorics | 3 | 6 | Major | Master/Doctor | - | No | ||
| This course is an advanced level course after "Introduction to Combinatorics and Graph Theory. We study in more details on combinatorics but not on graph theory. We study several methods to count combinatorial objects including bijections, generating functions. Topics cover permutations, lattice paths, integer partitions, trees, and symmetric functions. | |||||||||
| MTH5141 | Mathematical Understanding of Neural Network Learning and Application | 3 | 6 | Major | Master/Doctor | 1-4 | - | No | |
| Mathematical understanding of basic neural network architectures and learning rules. Subjects covered include the perceptron learning rule, linear transformations for neural networks, optimization, backpropagation, associative learning, competitive learning and their applications. measurement | |||||||||