대수학Ⅱ(Algebra II)

This course deals with the topic of algebra based on the theory of algebra. The main purpose of this course is to develop not only the ability to read and write thesis as a graduate student majoring in algebra, but also the ability to present. This course is centered on seminars, and discussions and research problems are presented during the seminars to seek solutions.

선형프로그래밍(Linear Programming)

This course covers the theory and technique for solving linear programming problems. Linear programming is a special case of mathematical optimization and is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. The aim of this course is to study the basic methods of solving linear programming problems ？ the simplex and geometric methods, and to consider the applications in different areas of human activity. Upon completion of the course, students must be able to classify the types of linear prigramming problems and to use appropriate methods for their solution.

위상수학Ⅰ(Topology I)

위상수학이란 개괄적으로 말하면, 연속성, 근접성과 같은 기하학적인 생각을 추상화하여 연속적인 변형에도 변하지 않는 성질을 연구하는 학문이다. 점-집합론적 위상수학(point-set topology) [일반위상수학(general topology)]의 기초 개념인 위상, 근방, 기저와 부분기저,닫힌 집합과 닫힘, 집적점, 내부, 외부, 경계, 연속성과 위상적 불변성, 부분공간, 곱공간, 몫공간, T0, T1, T3-공간 등을 학습한다.

응용대수학Ⅰ(Applied Algebra I)

The purpose of this course is to cultivate the ability to write a dissertation after taking this class by dealing with areas related to algebra related areas such as number theory and combinatorial mathematics and other applications of algebra. In particular, when writing a paper and submitting it, reviewers always ask about the application of the results. So I want to cultivate these abilities.

최적제어이론(Optimal Control Theory)

Some basic problems such as controllability, observability, identification, necessary and sufficient conditions of optimality for linear models will be considered in this corse. We will formulate maximum principle and learn how to use it for determining optimal processes in minimum time problem. The methods of determining of feedback control will be discussed.

최적제어이론Ⅱ(Optimal Control Theory II)

The course Optimal Control II is devoted to the theory of nonlinear dynamical systems. The material is presented following a rise in complexity - from the simplest optimal control problem to the general nonlinear control problem. Here we will discuss only one problem - necessary and sufficient conditions of optimality of the processes and the methods of their determining. The focus of corresponding theory is Pontryagin’s maximum principle, and its justification, analysis, application, and modification depend on the type of problem of general nonlinear systems. We will consider one of the many known proofs of the maximum principle based on the formula of the small increments of the trajectory.

확률론(Probability Theory)

Based on basic knowledge related to number theory, it deals with many application parts which are related to random variables, stochastic process etc.

현대대수학2(Abstract Algebra II)

Recently, many researchers have focused on the study of connecting p-ary calculus with umbral algebras and have published many results. Umbral algebras date back to the 19th century, but they were first established by Gian-Carlo Rota and his disciple Steven Roman in the 1970s and early 1980s. However, they have been almost forgotten among mathematicians since then. However, recently, active research has been conducted as it has been discovered that many parts of p-ary calculus, special functions, and combinatorics can be explained by umbral algebras. In line with this period, the purpose of this course is to present Roman's Umbral Calculus, which is widely used in this field, in a seminar format and to foster the ability to further expand the area in which umbral algebras can be applied by exchanging opinions. This course is conducted in a seminar format.

현대대수학1(Abstract Algebra I)

Seminars and classes are held in parallel, focusing on the contents of algebra that are essential for graduate school. However, the class will be centered on seminars, and the reason is to improve the presentation skills of graduate students and cultivate them as excellent researchers.

해석학I(Introduction to Analysis I)

기본적인 측도론과 르베크 적분, L^p,공간 및 l^p 공간등을 공부한다.

현대대수학I(Abstract Algebra I)

Seminars and classes are held in parallel, focusing on the contents of algebra that are essential for graduate school. However, the class will be centered on seminars, and the reason is to improve the presentation skills of graduate students and cultivate them as excellent researchers.

응용대수학특론I(Topics in Applied Algebra I)

Recently, many results have been published by many researchers with an emphasis on research linking p-adic analysis to Umbral algebra. Umbral algebra dates back to the 19th century, but it was only established by Gian-Carlo Rota and his student Steven Roman throughout the 70s and early 80s. However, it almost became a forgotten field among mathematicians after that. However, in recent years, active research has been conducted as it has been revealed that much of p-adic analysis, special functions, and combination theory can be explained by Umbral algebra. In line with this time, Roman's Umbral Calculus book, which is widely used in the field, is presented in the form of a seminar, and the purpose of this course is to cultivate the ability to further expand the area where Umbral algebra can be applied while exchanging opinions. This class is conducted in the form of a seminar.

응용대수학특론2(Topics in Applied Algebra 2)

This course provides an overview of significant analytical achievements in number theory. It spans classical topics such as prime number theory, continued fractions, the transcendence of $e$ and $\pi$, and the resolution of Hilbert’s seventh problem―to recent advances in the irrationality of values of the Riemann zeta function, the study of sizes of non-cyclotomic algebraic integers, and applications of hypergeometric functions to integer congruences. The primary objective is to introduce a variety of analytic techniques employed in number theory in a clear and accessible manner, making the material suitable both for graduate-level instruction and for self-study.

정수론(Number Theory)

The purpose of this course is to cultivate the ability to write a dissertation after taking this class by dealing with areas related to algebra related areas such as number theory and combinatorial mathematics and other applications of algebra. In particular, when writing a paper and submitting it, reviewers always ask about the application of the results. So I want to cultivate these abilities.

확률론과그응용Ⅰ(Probability theory with its applications Ⅰ)

Based on basic knowledge related to number theory, it deals with many application parts which are related to random variables, stochastic process etc.

수론특강(Topics in number theory)

As a problem of finding solutions related to polynomials with integer coefficients, we observe the structure of algebraic numbers, transcendental numbers, and special functions or special polynomial parent functions, and from these structures cultivate application capabilities in various fields of mathematics and intuition to solve certain problems.

비아르키메디언적분과그응용(Non-archimedean integrals and their application)

Focusing on the topic of p-adic analysis, which has become a hot topic in recent years, this class is aimed at cultivating research capabilities as a researcher through seminars and discussions.

신경망과심층학습(Neural Networks and Deep Learning)

- 심층 신경망 이해하기
- 심층 신경망 구현하기
- 심층 신경망을 사용해 문제 해결하기

p-진함수해석학Ⅱ(p-Adic Functional Analasis Ⅱ)

Focusing on the topic of p-adic analysis, which has become a hot topic in recent years, this class is aimed at cultivating research capabilities as a researcher through seminars and discussions. This is an in-depth seminar and lecture on the contents taught in p-adic functional analysis 1.

위상수학Ⅱ(Topology Ⅱ)

위상수학II 과목은 주당 3시간, 3학점 과목으로 개설되며, 위상수학I에서 다룬 내용들을 바탕으로 좀 더 심도있는 분야를 공부하게 된다. 위상수학II를 효율적으로 공부하기 위해서는 위상수학I의 내용들 외에 기본적인 해석학적 개념, 논리학적 개념 등이 필요하며 특히 집합론의 이해가 필수적이다.

최적화이론특강(Topics of Optimal Control)

Linear and general models of the optimal control systems are considered. Methods of the solution of the different problems of dynamical optimization are discussed.