• 한국수학교육학회지시리즈A:수학교육
• /
• 제40권2호
• /
• pp.335-343
• /
• 2001

Algebra is important part of mathematics education. Recent days, many mathematics educators emphasize on real world situation. Form real situation, pupils make sense of concepts, and mathematize it by reflective thinking. After that they formalize the concepts in abstract. For example, operation in numbers develops these course. Operation in natural number is an arithmetic, but operation on real number is algebra. Transition from arithmetic to algebra has the cutting point in representing the concepts to mathematics sign system. In this note, we see the cognitive tendency of 10th grade about operation of real number, their cutting point of transition from arithmetic to algebra, and show some methods of helping pupils.

• 대한수학회지
• /
• 제31권4호
• /
• pp.659-667
• /
• 1994

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operators on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the ultraweak operator topology on $L(H)$. Note that the ultraweak operator topology coincides with the weak topology on $L(H) (cf. [6]). Several functional analysists have studied the problem of solving systems of simultaneous equations in the predual of a dual algebra (cf. [3]). This theory is applied to the study of invariant subspaces and dilation theory, which are deeply related to the classes $A_{m,n}$ (that will be defined below) (cf. [3]). An abstract geometric criterion for dual algebras with property $(A_{\aleph_0}, {\aleph_0})$ was first given in [1].

• 한국정보과학회논문지:소프트웨어및응용
• /
• 제30권3_4호
• /
• pp.202-211
• /
• 2003

객체지향 방법론에서 정적 및 동적 모델에 관한 구문(Syntax)과 의미론(Semantics)의 형식적 정의는 잘 이루어 졌으나 객체 상호작용의 행위에 대한 형식론은 아직까지 제시되지 않았다. 본 논문에서는 객체 상호작용을 묘사하는 UML의 순서(Sequence) 다이어그램을 토대로 프로세스 대수를 사용하여 객체 상호작용을 정의하고 객체 상호작용의 특성을 정규화 시킨다. 이러한 결과는 M. Snoeck과 G. Dedene[9]가 제시한 종속존재 관계의 개념을 상호작용 관계의 개념으로 대체하여 형식론을 전개할 수 있음을 보여준다.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제52권1호
• /
• pp.97-109
• /
• 2013

Research in undergraduate mathematics education has been active very recently. The purpose of the paper is to investigate how college students make ion from some known informations about integer and rational numbers in algebra. Three college students were involved in the study. We analyze student's personal answers in order to find where their misunderstandings and difficulties come from based on the theoretical frameworks on mathematical understanding such as APOS-model and P-K-model. Finally we discuss about constructivist teaching ways for algebra and propose new paradigm for teaching undergraduate mathematics.

• 한국수학교육학회지시리즈E:수학교육논문집
• /
• 제26권4호
• /
• pp.351-362
• /
• 2012

행렬 및 벡터공간을 다루는 선형대수학은 사회의 복잡한 현상을 선형화 과정을 거쳐 선형연립방정식이라는 단순한 형태의 수학 문제로 바꾼 후 실제로 해결하는 데 결정적으로 기여한다. 이와 같은 이유로 20세기 중반까지 추상적인 고등수학 과목으로만 여겨지던 선형대수학이 현재는 자연-공학-사회계열 분야 학생의 대부분이 배우는 기본 교과목이 되었다. 본 연구에서는 초기 선형대수학의 발전에 기여한 중국, 일본, 그리고 서양의 수학자들에 대하여 다룬다. 선형대수학은 <산수서>, <구장산술>, 세키 고와, 뫼비우스, 그라스만 실베스터, 케일리 등을 거치면서 비선형적으로 발전해왔다. 우리는 새로 발굴한 내용을 중심으로 초기 선형대수학의 발전과정을 소개한다.

• 한국수학사학회지
• /
• 제14권2호
• /
• pp.29-44
• /
• 2001

The concept of ideals has played an important role as an inception of the structural approach to algebra. As a sequel to [51], we first deal with the gradual emergence of tile abstract concepts of fields and rings, and study the history of ideals initiated fly Dedekind and then formalized by Noether for the structural research.

• 대한수학회논문집
• /
• 제22권1호
• /
• pp.91-109
• /
• 2007

In this paper, we derive a change of scale formula for conditional Wiener integrals, as integral transforms, of possibly unbounded functions over Wiener paths in abstract Wiener space. In fact, we derive the change of scale formula for the product of the functions in a Banach algebra which is equivalent to both the Fresnel class and the space of measures of bounded variation over a real separable Hilbert space, and the $L_p-type$cylinder functions over Wiener paths in abstract Wiener space. As an application of the result, we obtain a change of scale formula for the conditional analytic Fourier-Feynman transform of the product of the functions.

• 충청수학회지
• /
• 제22권3호
• /
• pp.481-495
• /
• 2009

Huffman, Park and Skoug introduced various results for the $L_{p}$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra $\mathcal{S}$ introduced by Cameron and Storvick. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class $\mathcal{F}(B)$ which corresponds to $\mathcal{S}$. Moreover they introduced the $L_{p}$ analytic Fourier-Feynman transform for functionals on a product abstract Wiener space and then established the above results for functionals in the generalized Fresnel class $\mathcal{F}_{A1,A2}$ containing $\mathcal{F}(B)$. In this paper, we investigate more generalized relationships, between the Fourier-Feynman transform and the convolution product for functionals in $\mathcal{F}_{A1,A2}$, than the above results.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제45권1호
• /
• pp.61-74
• /
• 2006

The ability of understanding the number and number systems, grasping the properties of number systems, and manipulating number systems is the foundation to understand algebra. It is useful to deepen students' mathematical understanding of number systems and operations. The authentic understanding of numbers and operations can make it possible for the students to manipulate algebraic symbols, to represent relationship among sets of numbers, and to use variables to investigate the properties of sets of numbers. The high school students need to understand the number systems from more abstract perspective. The purpose of this study is to study on understanding and application ability of eleventh graders of basic properties of operations with real numbers.

• 대한수학회지
• /
• 제55권4호
• /
• pp.809-832
• /
• 2018

In this paper, we form the basis of the abstract theory for constructing the $K{\ddot{u}}nneth$ spectral sequence for a complex of Banach spaces. As the category of Banach spaces is not abelian, several difficulties occur and hinder us from applying the usual method of homological algebra directly. The most notable facts are the image of a morphism of Banach spaces is not necessarily a Banach space, and also the closed summand of a Banach space need not be a topological direct summand. So, we consider some conditions and categorical terms that fit the category of Banach spaces to modify the familiar method of homological algebra.