College of Science, Department of Mathematics

The undergraduate and graduate programs of the Department of Mathematics aim to foster the talent that our future society will need, namely those who are able to actively work in all areas related to mathematics, whether in academia or professionally. To this end, the Department offers not only education in the fundamental principles of mathematics but also world-class research experience and extensive education applicable to diverse areas. The Department also provides facilities, including its own dedicated library, seminar room, lecture rooms, Workstation room equipped with cutting-edge tools and materials, and computer lab. Moreover, some 50 broadband-linked LAN computers in the facilities allow students to search for the latest articles and information on the Internet.

After graduating from the Department, many alumni work for leading Korean businesses in areas ranging from insurance and security to finance and digitization, thereby demonstrating their world-class skills. In addition, a number of Master degree-level graduates serve as professors or researchers. The Department has fifteen full-time professors who collectively represent each field of mathematics. Graduate students, excluding those related to the Graduate School of Information Security, are also eligible to study under the supervision of professors from both the Department of Mathematics Education (College of Education) and the Department of Information Mathematics (College of Natural Science). The major research fields of the faculty members of the Department are as follows.

Major Research Fields

**Algebra and Number Theory** studies primarily aim to understand and develop representation, ring and number theories. In terms of number and representation theories, studies on automorphic form and Langlands program relate to representation theory of symmetric spaces. For analytic number theory, matters related to Q-sequence and special functions, which play an important role in the field of quantum mechanics and various applied mathematics, are the main subject of research. Ring theory is also included.

**Analysis** is mainly focused on the theory of single variable or multivariable functions, operator theory in function spaces, theory of harmonic functions, non-regular optimization theory, and game theory. The primary areas of function theory include Hardy, Bergman, Bloch, and BMOA, although Toeplitz, Projection and Composition operators are studied as well.

**Geometry** studies cover differential geometry, distance geometry, complex geometry, and minimal surface as well as various applied geometries for other fields. One field of research focuses on developing a generic methodology to create various and physically interesting manifolds by adopting partial differential equation theory.

**Knot and Topology :** Knot theory in three-dimensional space not only presents a method to solve mathematical problems inherent in categorizing three-dimensional manifolds but also applies to research of super-string theory (physics) and DNA structures. Imposing hyperbolic mensuration on a majority of knot complements enables calculation of hyperbolic volume, which explains correlative relations between the topology of three-dimensional manifolds and hyperbolic structures.

**Probability** as a discipline aims to demonstrate mathematically random phenomena in natural environments. A major research field in finance and telecommunication mathematics, probability focuses on limit theorem, stochastic process theories, Markov process, Queuing theory and relevant applications in IT and finance. The latter aims to optimize telecommunication systems through mathematical modeling of random phenomena in the systems based on queueing theory, one area of probability studies. The former analyzes and studies probable fluctuations of financial products through modeling of probable processes.

**Applied Mathematics** reminds us of the role and significance of mathematics as a foundation of all disciplines in an ever increasingly modernized and specialized society. Through education, Applied Mathematics also promotes overall applications of mathematics and statistics and connection of numeric interpretation and differential equation to engineering. For this research goal, the Department is mainly focused on mathematical interpretation and modeling of the flow of moving objects. Based on such studies, we offer a mathematical foundation and quantitative output that can be utilized directly or indirectly in civil engineering, shipbuilding and machinery engineering as well as aeronautical engineering and telecommunications.

In November 2001, the research team led by Professor Choe Bong-dae attracted the attention of the Telecommunication Mathematics Research Center (http://elie.korea.ac.kr/~tmrc), supported by the Ministry of Information and Communication of Korea. The Center’s primary mission is analysis of the performance of telecommunication systems by establishing and studying mathematical models of random phenomena, based on probability and queueing theory in particular. To contribute to the industrial development of Korea and the world, the Center strives to design and implement algorithms and software to optimize telecommunications systems, develop original core technologies in the IT sector, strengthen the joint academic-industrial partnership system and its research capabilities, and promote new technologies in relevant fields. The Telecommunication Mathematics Research Center is funded by grants from Korea University and the Korean government totaling KRW 400 million annually.

**Website : **http://math.korea.ac.kr

**Department Office**

- Tel. 02-3290-3070

- Fax. 02-929-8562

- Location : Room 514, College of Science Asan Hall.