Korean text

Computational mathematics is the field to study how to find the effective and reliable computer solutions of mathematical problems. Such studies contain two subjects. The first subject is the classical numerical analysis, which obtains results with error bounds on the basis of relatively rigorous arguments. Another one is called the scientific computing, which studies the design of algorithms for large-scale computation and parallel computation. In addition, computational mathematics studies the computational modeling and simulation for the model problem. Such modeling and simulation have replaced the physical experiments that are too costly. The study of computational mathematics requires an in-depth knowledge of a variety of mathematical subjects which include linear algebra, analysis, ordinary and partial differential equations, asymptotic analysis, approximation theory, harmonic analysis, and nonlinear equations. Since computers are invaluable tools for computational mathematicians, students are expected to attain a highly professional level of computer literacy and gain a substantial knowledge of operating systems and hardware.

As an application of computational mathematics, we study image processing. Image is regarded as a mathematical function so that a variety of mathematical tools can be applied to image processing. There are many problems in image processing, such as denoising, segmentation, registration, optical flow, deblurring, blending etc. To solve these problems, energy functionals, partial differential equations, statistical methods are used, in addition, parallel computing is, sometimes, required to reduce the wall clock time. Recently, research using machine learning, especially deep learning techniques, have been actively conducted.