Iksan(翼算) written by Lee Sang Hyuk(李相赫, 1810∼\ulcorner) is unique among mathematical books published in Chosun Dynasty since it is the only book which accomplishes the conceptualization of theory of equations if not that of mathematics itself. We investigate its process by his other publications and mathematical interaction with Nam Byung Gil(南秉吉, 1820∼1869).

In this article we survey the sequences and the series in Mooksajipsanbup(默思集算法) which is the seventeenth century mathematics book of Chosun dynasty. First, we classify them into three categories: arithmetics, geometric, and general sequences (series). And then we explore the old methods to find the values of terms and the sum of terms.

In this paper, we identify the essential ideas of Fundamental Theorem of Arithmetic(FTA). Then, we compare these ideas with several theorems of Euclid's Elements to investigate whether the essential ideas of FTA are contained in Elements or not. From this, we have the following conclusion: Even though Elements doesn't contain FTA explicitly, it contains all of the essential ideas of FTA. Finally, we assert two reasons why Greeks couldn't mention FTA explicitly. First, they oriented geometrically, and so they understood the concept of 'divide' as 'metric'. So they might have difficulty to find the divisor of the given number and the divisor of the divisor continuously. Second, they have limit to use notation in Mathematics. So they couldn't represent the given composite number as multiplication of all of its prime divisors.

In this paper we investigate the origin of the variational calculus with respect to the extremal principle. We also study the role the extremal principle has played in the development of the calculus of variations. We deal with Dido's isoperimetric problem, Maupertius's least action principle, brachistochrone problem, geodesics, Johann Bernoulli's principle of virtual work, Plateau's minimal surface and Dirichlet principle.

In this paper, we analyse several number theoretical proofs of the irrationality of $\sqrt{2}$ and reveal that these proofs are implied by The Completeness Axiom of the real number system.

This paper aims at investigating the algebraic solution of cubic and quartic equation and eliciting the didactical meanings of them. First, I examine the event which relates to the equation in the history of mathematics and investigate the algebraic solution of cubic and quartic equation. And then I elicit the didactical suggestions which are required of teachers and students when they investigate the algebraic solution of cubic and quartic equation. In general, the investigation of these solutions is the valuable task which requires the algebraic intuition and technique for students and certificates expert knowledge for teachers.

Discussing the history of mathematics in classrooms is often recommended as a way to help show that mathematics was not handed down unchanged from God into the students' notebooks but has been changing and growing throughout the centuries. Now that new millenium century is begun, it is appropriate for historians to look back and for teachers to show that mathematics is not only alive and well but in its most productive period ever. This paper is a brief summary that hints at the flavor of recent mathematical developments. Even if the actual content may be difficult, however, the exciting stories of the people, developments, results, and applications deserve coverage. These stories can add life to school mathematics and encourage our students to join in the fun.

This article dealt with two approaches, algebraic and geometric approaches in terms of Pythagoreans theorem. As mathematics evolves, many theorems had been developed beginning with geometric approaches. However, the algebraic techniques that survive these days are so powerful and generalized in school curriculum. So, if students have more chances to see mathematical properties in geometrical ways, they can experience how beautiful and meaningful they are through the process of the advent of them. Also, it was to try to develop an insight into their applications to other problems.

There are so many methods in population estimation such as logistic estimation and compound interest estimation. If we have some pieces of information about population of one tribe, we can estimate progenitor chronology of that tribe used by inverse estimation. In this paper, we describe several theory of population estimation, and develop mathematical method for estimation progenitor chronology from prior general data and statistical estimation theory. Several examples are illustrated.

This study estimated direct factors that have effect to completion degree of game, and we constructs structural equation model that can evaluate completion degree of game using empirical analysis. For it, we obtained weight of components of game development by eigenvector method for analytic hierarchy process. Using calculated weight, we also let that components of game development is observating variable of X, and genre of game is observating variable of Y. And we constructs structural equation model with LISREL program

Truth, goodness, and beauty are originated from the Greek philosophy and these concepts are unified by Kant. This article shows that these three concepts correspond to three conditions of axiomatics, that is, consistency, completeness, and independence, respectively.