# Introduction to The Department of Mathematical Sciences of KAIST

Head of Department: Professor Sijong Kwak.

The Department of Mathematical Sciences (DMS) dates back to 1982, when the Department of Applied Mathematics was established with a graduate program in mathematics. In 1985, a separate department, in charge of the undergraduate program, was founded. The two departments merged into the Department of Mathematics in 1990 and the current name, DMS, has been used since 2007.

Today the DMS has 31 full-time professors, additional 5 affiliated professors, 26 research professors, visiting professors, and post-doctoral researchers, and 8 full-time staffs who manage daily activities. There are currently 260 undergraduate and 140 graduate students in the department and these numbers are increasing regularly.

The main objectives of the DMS are research and education. The department has an outstanding faculty with expertise in both pure and applied mathematics, and it offers first-rate undergraduate, graduate, and doctoral degree programs.

## Research at the DMS

Faculty members of the DMS are expected to be leaders in their research fields. The main research areas of the DMS are:

*Algebra and Combinatorics*– 9 professors. Research fields: Number Theory, Cryptography, K-Theory, Graph Theory, Algebraic Geometry, and Combinatorial Geometry.*Analysis and Applied Mathematics*– 8 professors. Research fields: Harmonic Analysis, Sampling Theory, PDEs, Dynamical Systems, Inverse Problems, and Mathematical Physics.*Geometry and Topology*– 8 professors. Research fields: Geometric Structures of 3-manifolds, Knot Theory, Symplectic Geometry, Mirror Symmetry, Transformation Groups, Geometric Topology, and Geometric Group Theory.*Computational Mathematics and Scientific Computing*– 2 professors. Research fields: Scientific computing, Numerical Analysis, and Computational Image Processing.*Probability, Statistics and Financial Mathematics*– 4 professors. Research fields: Graphical Modeling, Queing Theory, Financial Mathematics, Statistics.

### Seminars

An essential part of the research activity at the DMS is the propagation of mathematical results and ideas. In 2010, more than 200 seminar talks were given at the DMS. Speakers consist of mathematicians from Korea and abroad, as well as faculty members. The various seminars and lecture series run by the DMS include:

- Discrete Math Seminar
- Basic Notions Seminar
- Number Theory Seminar
- Algebraic Geometry Seminar
- Face The World With a Mathematical Mind
- Applied Math Seminar
- Analysis Seminar
- Knot Theory Seminar

In addition there is a weekly Colloquium and many workshops. In 2010, the DMS hosted 8 international workshops.

## Education

The DMS is devoted to maintaining the highest level of mathematical education, both at undergraduate and graduate levels. Students are also encouraged to pursue a double major, or a minor in another field, to increase opportunities for future cooperation with experts from other scientific areas. Every student at the DMS is provided with financial support and an excellent work environment. The DMS is investing a large portion of its resources towards producing students of the highest quality who will go on to play essential roles in mathematics as well as in related areas of science and engineering.

### The Undergraduate Program

Students in our undergraduate program may choose freely from a large variety of mathematics courses according to their interests and career plan. Every student has an academic advisor among the faculty who helps plan the coursework according to his or her interests. Undergraduates also have the opportunity to embark on individual study projects where they will gain research experience under the direction of a professor specializing on the subject of their choice. In addition, the Undergraduate Research Program (URP) provides students with research experience on individual or group basis.

Other activities for the undergraduates include:

*KAIST Mathematical Problem Solving Group (M*²*)*– M² is an association which combines both academic and social activities. It publishes its own periodic journal, MATH LETTER, with articles related to various branches of mathematics as well as mathematical problems and solutions, for instance from the IMO. The association also organizes a regular seminar series, and an annual summer camp for students who want to broaden their mathematical horizons.*KAIST Math Problem of the Week*– Since 2008, the DMS has run a weekly math problem challenge for the KAIST undergraduate students. Solutions are submitted online and top problem solvers are awarded at the end of every semester.*The Undergraduate Colloquium*– A monthly lecture series organized by the undergraduate student organization, supported by the DMS. The purpose of the series is to introduce undergraduates of the DMS to the research areas and specialties of the faculty as well as other mathematicians in Korea.

### The Graduate Program

Currently about half of the students in the Master’s program will continue on to the Doctoral program, while the rest play an active role in industry or various research institutes.

In the Master’s program students receive fundamental training in mathematics, and also opportunities for specialization. Students plan their own coursework or research according to their interests. They have opportunities to experience other areas through the various extracurricular activities and double major programs with other departments at KAIST.

In 2011 the DMS established a *dual degree program* with the Department of Mathematics at the Technical University of Denmark. Through this program, graduate students have a chance to experience a semester abroad, and upon successful completion they will obtain degrees from both universities.

In the Doctoral program, students study more advanced mathematics and are expected to produce novel research results. They are given the necessary training to become competent mathematicians and independent researchers. Until now, about 45% of the PhDs produced by the DMS have become professors of mathematics, computer science, or related fields, while the rest are employed in research institutes or industry.

### Courses and Curriculum

Apart from providing the fundamental courses required to ensure a broad foundation of mathematical knowledge, the DMS also offers a wide range of special topics courses. These courses are specifically designed to connect students to the current frontiers of mathematical research. Often these courses are taught in collaboration with visiting scholars and renowned experts from around the world. In recent years these special topics courses have included:

- Topics in Hodge Theory
- Symmetric Functions
- Hyperbolic Conservation Laws in Geometry and Relativity
- Extremal Graph Theory
- Mathematical Modeling
- Frames and Riesz Bases
- Analytic Combinatorics
- Hilbert Schemes
- Arithmetic Moduli and Elliptic Curves
- Nonlinear PDEs arising in Mechanics and Geometry
- Advanced Stochastic Modeling
- Structuring and Pricing of Financial Products
- Matroid Theory
- Combinatorial Optimization
- Coxeter Groups and Reflection Symmetry
- Probabilistic Methods in Combinatorics
- Bayesian Statistical Analysis

## Research Facilities

Supplementing the facilities and resources provided by KAIST, the DMS also manages three Research Centers (BK21, ASARC, ICMS) which are funded by NRF (National Research Foundation of Korea). These centers play a vital part of the research activities of the DMS. They also provide financial support for many of the visitors to the DMS and sponsor many of the seminars.

### BK21 : Development Project of Human Resources in Mathematics

Director: Professor Sijong Kwak

The BK21 Project is intended to support the education of graduate students of the department. There are currently 24 professors, 95 students, and 11 post-doctoral researchers, 2 of which are from overseas, that participate in the BK21 Project. The project started in March 2006, and is supported by NRF. The project group concentrates its research efforts on algebra, manifold structure, arithmetic and information mathematics, analysis of applied mathematics, and the application of mathematics to other academic fields.

### ASARC (Algebraic Structures and its Applications Research Center)

Director: Professor Sunghan Bae

This SRC [Science Research Center] specializes in Algebra, Algebraic Geometry, Algebraic Combinatorics, Symplectic Structures, and applications in these areas. The goal is to lead and maintain a top-level research center and to improve the national competitiveness in Algebra and related applied fields. Currently the center consists of 16 professors, with 9 from the DMS, and 4 post-doctoral researchers. The center was established in 2007 and is supported by NRF.

### ICMS (Information Center for Mathematical Science)

Director: Professor Dong Youp Suh

The objective of the center is to provide information related to the mathematical sciences to the Korean mathematical community. The center was established in 1995 to create MathNet Korea, an electronic resource for mathematical research in Korea. The initial purpose of the center was the digitalization of academic journals, and it now maintains a huge online database of domestic and international journals.

Today the center also produces and provides a large online video archive, which documents the ongoing research activity of the DMS. In particular, all talks given at seminars, colloquia, conferences, and workshops are filmed and made available online. In addition, certain classes are filmed in order to enhance the learning experience of students at KAIST.

Some of the services of the ICMS include

- Production and Maintenance of digital database
- Information Gathering of research and academic activity
- Management of MathNet Korea internet service
- ICMS Video Archives
- MSRI Lectures Video Archive Mirror

The center is supported by NRF.

### Math Library

We have a library dedicated for mathematics, located in the first floor of E6-1 building.

## Institution Membership of IMA and MSRI

The DMS is affiliated with IMA (Institute for Mathematics and Its Applications) and MSRI (Mathematical Sciences Research Institute). Faculty and graduate students of the DMS are provided with financial support to participate in conferences and programs offered by IMA and MSRI.