The advent of information society has called for the increase in high-quality professionals who are highly knowledgeable in mathematics and science. In accordance with such societal needs, the department puts its main interest on research and education of applied mathematics.
Classes offered in the program can be categorized into the three groups:
(1) courses on mathematical knowledge and principles;
(2) courses concerned with modeling on the problems caused in the fields of mathematics, engineering, social sciences, natural sciences, and medicine;
(3) such courses designed for scientific calculation as mathematics. statistics, cryptography, and insurance mathematics.

Introduction

The teaching, learning and research of mathematics have many important aspects not only for the development of mathematics itself but also as a basic science to meet demands of technical developments in modern industrial and information society. It has been emphasized that mathematical techniques are applied to theoretical statements of physical science and engineering as well as humanities and social sciences.
The department of mathematics establishes educational objectives to meet such demands as follows:

Firstly, it seeks to develop students‘ abilities to perform their job logically and efficiently by understanding basic concepts and systems of modern mathematics and by applying mathematical techniques and using computers to solve real world problems;

secondly, it aims at training students who have abilities to study mathematics including applied mathematics and other majors in graduate schools;

thirdly, it tries to bring up a capable person for the development of society.
The curriculum of the department offers basic principles which help students fulfilling their objectives. Major courses include analysis, algebra, topology, statistics, probability, applied analysis, numerical analysis, coding and cryptography and actuarial mathematics.

Educational Objectives

Department of mathematics gives a full efforts to get some aims including the following three main objects strongly demanded today;

1. development of abilities on mathematical knowledge and thoughts
2. development of abilities on solving various present problems through applied mathematics
3. development of abilities in appling the acquired knowledge to computer.

Department of mathematics opens various useful subjects including not only pure mathematics but also applied mathematics such as probabilities, differential equations, numerical analysis, cryptography and actuarial mathematics. Most of those subjects are deeply related on real life. Besides, we concentrate on the educations for the students to have essential abilities to analyze and solve overall problems by using mathematical knowledge.

Careers

graduate school, research institute, teacher at middle/high school, other education-related fields. financial computation

Course Descriptions

• Computational Mathematics
  This course gives students experiences in using mathematical softwares such as Matlab, Mathematica and Maple to solve problems from various areas of mathematics. It also provides students with tools for the further study of numerical methods or numerical analysis.
• Topics in Algebra
  This course covers several concepts not in the course of Modern Algebra 1,2 such as the extension fields, algebraic extensions, Galois theorem, modules. Besides, this course provides various concepts needed in algebra course.
• Differential Geometry
  Vectors, vector functions of a real variable, concept of a curve, curvature and torsion, frame fields, Euclidean geometry. Vector functions of a vector variable, concept of a surface, fundamental forms, tensor analysis, Riemannian geometry.
• College mathematics 1
  The derivative of a function (geometric interpretation and analytic definition) and its applications; linear approximation; limits and continuity; critical points and max/min problems; mean value theorem; second derivative; definite integral and its applications; the fundamental theorem of integral calculus; Series; Power Series, Ratio Test; Taylor's Theorem
• Vector Calculus
  This course introduces students to the fundamental concepts and basic elementary theorems from vector calculus with emphasis on functions of several variables. TOPICS : vector spaces, linear independence, linear transformation, inner product, orthogonality; partial derivatives, differentiablity, Taylor's Theorem, multiple integrals, surface area, surface integrals, curves, arclength, curvature, line integrals, vector fields, Green's Theorem, Divergence Theorem, Stokes Theorem.
• Actuarial Mathematics
  Interest, mortality table, life insurance, life annuity, net premium, liability reserve, office's premium.
• Complex Analysis 1
  The geometry of complex numbers, Cauchy-Riemann equations, harmonic functions, mapping properties of logarithm, exponential, and other functions, contour integrals, the Cauchy-Goursat Theorem, Cauchy integral formulas,
• Complex Analysis 2
  Morera's Theorem, maximum modulus principle, Liouville's theorem, linear fractional transformations as mappings, preservation of angles, harmonic conjugates, applications of conformal mapping to physical problems.
• Introduction to Ordinary Differential Equations
  The objective of this course is primarily to introduce the students in disciplines which emphasize methods of explicit solutions and the theory of ordinary differential equations. Topics: Linear differential equations, series solutions of linear differential equations, higher order equations; Laplace transform, systems of differential equations, linear systems, stability of solutions, qualitative behavior of non-linear systems, Lyapunov's second method; boundary value problems and Sturm-Liouville theory.
• Linear Algebra 1
  This course is an introduction to linear algebra providing the basic concepts such as properties of matrices, determinants, methods to solve systems of linear equations by using matrices, vector spaces, linearly independent vectors, linearly dependent vectors, bases and dimensions, linear maps, relations between matrices and linear maps.
• Linear Algebra 2
  This course provides more concepts about linear algebra such as eigenvalues, eigenvectors, characteristic polynomials, minimal polynomials of matrices and linear transformations, diagonalization of matrices, inner product spaces, Gram-Schmidt orthogonalization process, Jordan canonical form.
• Mathematical Statistics 1
  This course will offer essentially all the distribution theory, estimation and tests of statistical hypotheses, expectation, random variables, multiple random variables.
• Mathematical Statistics 2
  Many of the topics of this course are estimation and tests of statistical hypotheses including nonparametric methods, sufficient statistics, Rao-Cramer inequality, and robust estimation after measures of the quality of estimators. Multiple comparisons and the analysis of variance, multi-variable normal distributions will be provides.
• Numerical Analysis 1
  Taylor polynomial, the error in the Taylor's polynomial, binary number system errors: definitions, sources, and examples, bisection method, Newtons's method, secant method, fixed point iteration, polynomial interpolation, divided differences, error in polynomial interpolation, spline functions, best approximation problem Chebyshev polynomials, trapezoidal and Simpson rules, Gaussian numerical integration
• Numerical Analysis 2
  System of linear equations, Gaussian elimination, LU factorization, error in solving linear systems, least squares data fitting, eigenvalue problem iteration methods, Euler method, convergence of Euler's method, Taylor and Runge-Kutta methods, multistep methods, stability of numerical methods systems of differential equations, introduction to finite element method
• History of Mathematics
  The historical developments of the various fields of mathematics, such as numerical systems, Euclidean and non-Euclidean geometry, analytic geometry, calculus and analysis, algebra, probability, set theory, topology, mathematical logic and philosophy.
• Real Analysis
  Caratheodory extension theorem, Lebesgue measure on the real line, general measure theory, convergence theorems, Lusin's theorem, Egorov's theorem, Lp-spaces, Fubini's theorem, functions of bounded variation, absolutely continuous functions, Lebesgue differentiation theorem.
• Topology 1
  The fundamental concepts of point-set or general topology - topological spaces, basic open sets, subspaces and continuity, homeomorphisms, product spaces, connected spaces, and so on - are covered rigorously but at an elementary level. The student is required to explain each problem logically.
• Topology 2
  We study the basic topics - connectedness, compactness, separation properties, metric spaces, and so on. In particular Topology 1 is a prerequisite.
• Topics in Topology
  We study the application of general topology and introduce some special topics. Topology 1 and Topology 2 are prerequisites.
• Topics in Applied Mathematics
  This course deals with mathematical methodology and many kinds of subjects in applied mathematics
• Cryptography and Its Applications
  Using the number theory and abstract algebra, cryptography provide the security in information and communication era. In this course, we deal with the various cryptographic algorithm, like symmetric key, public key cryptosystem and digital signature and authentication. Also, we study the cryptographic protocol, like zero knowledge interactive proof, public key infrastructure. Most of the classes would have the chance to use the advanced computer language and library.
• Number Theory
  Arithmetic properties of integers. Congruences, arithmetic functions, diophantine equations. Other topics chosen from quadratic residues, the quadratic reciprocity Law of Gauss, primitive roots, and algebraic number
• Set Theory
  Elementary logic, set operations, relations and functions, denumerable and nondenumerable sets, cardinal numbers and cardinal arithmetic, the axiom of choice, ordinal numbers and ordinal arithmetic.
• Introduction to Partial Differential Equations
  The objective of this course is to provide students with the techniques necessary for the formulation and solutions of partial differential equations and prepare students for further study in partial differential equations. Topics: Derivations of partial differential equations; classification of linear partial differential equations; separation of variables applied to the heat equation, the wave equation and Laplace's equations in various geometries; Sturm-Liouville theory for second order ordinary differential equations; Bessel functions; Fourier series; Existence and uniqueness; Fourier transforms.
• Analysis 1
  Supremum and infimum, completeness properties of the real numbers, limits of numerical sequences and series; limits and continuity, properties of continuous functions on closed bounded intervals; the intermediate value theorem; derivatives in one variable;
• Analysis 2
  sequences and series of functions, power series, uniform convergence, term by term differentiation and integration Riemann integration in one variable; open and closed sets and convergence of sequences in R^n; limits and continuity in several variables, properties of continuous functions on compact sets
• Modern Algebra 1
  This course provides the important concepts of group theory such as the definition of groups, subgroups, cyclic groups, Lagrange theorem, normal subgroups, factor groups, isomorphism theorems, direct sums of groups, orbits, Sylow theorem.
• Modern Algebra 2
  This course provides the basic concepts of ring theory such as the definition of rings, subrings, ideals, integral domains, the relations between maximal ideals and prime ideals, factor rings, polynomial rings, Euclidean domain, principal ideal domain, unique factorization domain.
• College Mathematics 2
  This course introduces students to the fundamental concepts and basic elementary theorems of matrix and linear algebra and vector calculus with emphasis on functions of several variables. Topics: Matrix algebra, Determinants, Vector spaces, Linear independence, bases, dimension, linear transformations, inner product, orthogonality; partial derivatives, multiple integrals, iterated integrals, Curves, vector fields, line integrals, surface integrals, Green's Theorem, divergence theorem, Stokes Theorem.
• Probability Theory
  This course is intended for introduction of on probability theory and random processes. Markov chains, queueing theory and sequences of independent identically distributed random variables will be provided. Random processed, analysis and processing of random signals will be also provided.
• Selected topics in Mathematics
  This course deals with mathematical subjects selected from the contemporary mathematical interests.