Department of Mathematical Sciences
URL : http://mathsci.kaist.ac.kr
Dept. Phone : +82-42-350-2702~3, 350-5702~3
Introduction
Mathematics is the study on numbers, space, sets and functions with the basic human mental abilities such as classification, calculation, estimation and proof. It is used to abstract and quantify the natural phenomena, and serves as the language of science, essential to understand the law of nature.
As human civilization develops and matures, the role of mathematics continues to increase in its use and importance, not only in the development of the natural sciences and engineering but also in the study of humanities, social studies, economics and related disciplines. In our information society advanced mathematics is essential in many areas such as communication, computer science, information security and finance.
The Department of Mathematical Sciencess has two objectives, research and education. It does research on algebra, analysis, geometry, probability, statistics, topology, bio-mathematics, computational mathematics, financial mathematics, etc. It also emphasizes contribution to the society by producing leading experts in Mathematical Sciencess. To achieve the goal, The Department maintains the highest level of education and research, expands interdisciplinary studies with science, engineering and business administration, stimulates interaction with other universities, research institutes and industry, to induce synergy effects. To contribute to the development of new technology, the Department encourages students to pursue a minor or dual major so that they can be ready for future cooperation with experts from other fields. The Department wishes, by establishing close ties between energetic faculty and creative students, to lead 21st century mathematics of Korea with an effective transfer of mathematical knowledge from faculty to students.
Recently the demand for KAIST graduates majoring Mathematical Sciencess is increasing. Graduates with bachelor's degree find various career paths, those with master's degree go mostly into research institutes or areas related to finance, computer science and information, those with Ph. D. take positions in universities, research institutes and industry.
Undergraduate Program
In the undergraduate program, students take various courses chosen from a variety of courses offered by the Department, according to their interests and career plan, to learn a broad foundation of mathematical knowledge. Every student has an academic advisor who helps in planning coursework, and one can do independent study to build research experience under the direction of a professor specializing on the subject of one's choice.
The graduates of the Department of Mathematical Sciencess find diverse career paths. Some go on to graduate schools to study and research more mathematics, some take the advantage of applicability of mathematics and enter graduate schools in other fields such as physics, biology, engineering, computer science, finance, business administration and economics, others begin a career in industry related to communication, information security, computers, securities, insurance, finance and banking.
Graduate Program
In the master's program, students go through advanced level mathematical training in preparation to use mathematics after graduation, or they concentrate on the fundamental mathematics required for more advanced study in the doctoral program. Currently about half of the students in the master's program continue to study mathematics in the doctoral program, while the rest play an active role in industry or government research institutes.
Students learn basics to be experts in Mathematical Sciencess and make plan for their coursework or research according to their own interests. They have opportunities to experience other areas through the various extracurricular activities such as colloquia and exchange programs with foreign universities.
The Department encourages interdisciplinary research with other academic fields. In the master's program there are many students who have not majored in Mathematical Sciencess for bachelor's degree. In fact, students with various backgrounds make valuable and creative research environments.
In the doctoral program, students study more advanced mathematics and produce their own new research results. They are well-trained to be competent mathematicians or researchers in industry and government research institutes. Until now, about 70% of Ph.D. produced in the Department have become professors of mathematics, computer science, or related fields, while the rest have been employed in government research institutes or industry.
Research Areas
Analysis and Applied Mathematics
In this area, real analysis, harmonic analysis, complex variables, ordinary differential equations, partial differential equations, integral equations, operator theory and all analytical problems originating from applied science are studied. Applications of the research results are employed to solve concrete problems that arise in natural science, engineering, and financial mathematics. Computerized tomography(CT) using the Radon transform and image processing using the wavelets are conspicuous applications of analysis.
Topology
Here, the structures and the properties of manifolds are studied using algebraic, geometric, and combinatorial methods. Active research areas include (i) knots, links, braids, and 3-manifolds (ii) the geometric structures on low-dimensional manifolds including hyperbolic and discrete group theory (iii) 4-manifolds through Seiberg-Witten theory, symplectic and contact structures, and (iv) symmetries of manifolds in terms of group actions on differential manifolds, algebraic varieties, and semi-algebraic sets. In addition applications are effectively being made to computer graphics and non-commutative cryptography, in which braid groups are used.
Geometry
Using differential manifold theory and Riemannian manifolds, those working in geometry study such topics as curvature pinching problems, curvature and group actions, closed geodesics, finiteness theorems, comparison theorems, geometric structure and isometric immersions, harmonic maps and non-linear problems.
Scientific Computational Mathematics
Computational mathematics involves the study of methods of representing complex phenomena as mathematical models and discovering techniques of numerically solving the models. Research is also directed towards theoretical studies based on the analysis and developments of new techniques applicable to science and engineering.
Combinatorics
Combinatorics is an area of mathematics that studies mathematical objects having discrete or combinatorial structures. It involves combinatorial problems from various fields of mathematics and allows for the development of theories about diverse combinatorial objects. Emphasis is put on enumerative combinatorics, graph theory and algebraic combinatorics.
Information Mathematics
Topics studied in this field include Shannon's information theory, computation theory, complexity theory, Hoffman code, entropy, data compression, error correcting codes, cryptography, and information security.
Financial Mathematics
The area of financial mathematics involves the study and design of mathematical models of financial derivatives and markets using stochastic integral equations or stochastic differential equations. Real data from the markets are used to test mathematical models and the techniques to predict the market movements are studied.
Probability and Statistics
In probability, random phenomena in nature and society are studied rigorously in terms of measure theory. Research emphasis is on stochastic process, martingale, Markov chain, stochastic differential equations, queueing theory for the analysis of telecommunication systems, stochastic control theory and optimization.
In statistics, emphasis is on multivariate statistical analysis, data analysis, learning theory, neural network models, graphic models, time series analysis, Bayesian analysis, parameter estimation, hypothesis verification, regression analysis, etc.