술어 논리를 중심으로 한 명제 함수의 논리계산에 대한 연구

천석현 공주교육대학교 초등연구원 1970 公州敎大論叢 Vol.7 No.1

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De Rham 理論

千錫鉉 공주대학교 사범대학 과학교육연구소 1990 과학교육연구 Vol.22 No.1

We have defined the De Rham cohomology groups H??(X,d) for a smooth manifold X. These groups came from a sequence of maps. C??(X,∧??(X))→C??(X∧??(X))→C??(X,∧??(X)) and H??(X,d)=Ker d/Im d. We saw that the dime,nsion of H??(X,d) measured the number of connected components of X,and we saw, at least for the circle X=S¹, that the dimension of H¹(X,d) measured the number of "holes" in X. We shall now develop similar groups for simplical complexes. We shall study a sequence of maps. C??→C??→C?? where each C?? is an abelian group and where ??=0. Then homology groups H?? will be difined by H??=Z??/B??, where Z??=Ker ??:C??→C?? and B??=I??:C??→C??. An element of Z?? will be geometrically a "chain" of ℓ-simplices without boundary. An element of B?? will be geometrically a boundary of a chain of (ℓ+1)-simplices. The boundary of a 1-simplex(v??,v??)will be the sum of the 0-simplices v?? and V₁ with appropriate signs attached. Similarly, the boundary of a 2-simplex(v??,v₁,v₂)will be an appropriate linear combination of its edges (v??.v₁), (v₁,v₂) and (v₂,v??). The goal of this paper is to show that for smoothly triangulated manifolds (X,K.h), the De Rham cohomology of X is isomorphic to the simplical cohomology of K. For this, we shall need the following facts about barycentric coordinates. Recall that we have previously discussed the barycentric coodinates of a point relative to the vertices of a simplex containing it. Now we extend this concept.

2차원 다양체에 대한 곡률의 해석

千奭鉉 公州大學校 基礎科學硏究所 1994 自然科學硏究 Vol.3 No.-

Riemann 2차원 다양체에 대한 Gauss-Bonnet의 정리를 2-Simplex의 경우를 통해서 고찰하였다. We now show that the curvature K of M measures the amount of rotation obtained in parallel translating vectors around small closed curve in M. Let M be an oriented Riemannian 2-manifold and let 〈s〉 be an oriented 2-simplex in R2, and let h: [s]→M be a map which has a smooth extension mapping a neighborhood of [s] into M, let α be the closed broken C∞ curve in M obtained by restricting h to ∂ 〈s〉. Then the rotation obtained by parallel translation around the closed carve α is ◁수식삽입▷ 원문을 참조하세요 so that the angle of rotation is ◁수식삽입▷ 원문을 참조하세요 In chapter II, We give the Gauss-Bonnet Theorem for 2-Simplex. In chapter III, We study Gauss-Bonnet Theorem using the lemma in chapter II.

學校幾何學에 있어서 結合의 理論에 對하여

千奭鉉 공주대학교 사범대학 과학교육연구소 1979 과학교육연구 Vol.11 No.1

In this paper we give concrete meaning to the theory of incidence studied abstractly in the axiom of connection by Hilbert. We exhibit models of the theory, that is, specific systems which exemplify the theory, which satisfy its postulates. Several important ideas such as isomorphism and automorphism of geometric systems and the use of models to prove consistency and independency fit naturally into the context.

수학과 현장교육연구에 대한 고찰

千奭鉉 공주대학교 사범대학 과학교육연구소 1992 과학교육연구 Vol.23 No.1

Through the classroom teaching research meeting, the Korean Teacher`s Association established the educational problem that our educational world is facing and intended to reform classroom teaching and education in quality. This study is to examine the actual condition of the research such as that in the center of classroom teaching research to mathematics sectional report of which the Korean Teacher`s Association have charge in the area of Chungnam in 1991.

曲面의 寫像에 對한 硏究

千奭鉉 공주대학교 사범대학 과학교육연구소 1978 과학교육연구 Vol.10 No.1

An important aspect of geometry is the study of the properties of a surfaces which remain invariant under a given class of 1-1 mapping. Thus this research shows the following; (1) We recall that our definition for some mappings of surfaces. (2) A regular differentiable mapping f of a surface S into a surface ?? is a continuous mapping of S into ??. (3) If f is a regular differentiable mapping of S into ?? and g is a regular differentiable mapping of ?? into ??, then the composite mapping g of is a regular differentiable mapping of S into ??. (4) If f is a 1-1 regular differentiable mapping of a surface S onto a surface ??, then ?? is a regular differentiable mapping of ?? onto S. (5) If f is a mapping of S into ?? such that for every coordinate patch X=X(u,v) of a basis of patches for S the mapping ?? is a regular parametric representation of class ??, then ?? is a regular parametric representation of class ?? for all coordinate patches X=X(u,v) on S. (6) If f is an isometry of a S onto a surface ??, then f-1 is an isometry of ?? onto S. (7) The first fundamental coefficients is invariant under an isometric mapping.

中等學校 數學科 實驗實習敎材의 開發硏究(Ⅲ) : 實物透視圖를 中心으로 On the basis of Stereo-graph

千奭鉉 공주대학교 사범대학 과학교육연구소 1983 과학교육연구 Vol.15 No.1

A projection can be used as one of the methods representing the solid ge-ometric figures on the paper-plane. But it is difficult to conceive exactly the sense of solid body, position relat-ion between the lines and which line is larger. So, I have studied teaching material(Stereo-graph) which can show a posit-ion, shape, bigness of figures and give the real sense of soild body : (1) To find the principle of the stereo-graph. (2) How to make the Stereo-graph. (3) How to use the Stereo-graph. (4) To find the considerations in using the Stereo-graph. (5) To find the teaching case using the stereo-graph.

Cusp Catastrophe Manifold에 關한 硏究

千奭鉉 공주대학교 사범대학 과학교육연구소 1985 과학교육연구 Vol.17 No.1

This paper explains some of the basic mathematical ideas involved in Rene Thom's catastrophic Theory. in the simplest and most accessible case: the ele-mentary catastrophes. Topics discussed include the classification of local behavior of smooth functions, determinancy (how much of a Taylor series is adequate to capture the function's behavior). These and other concepts are exemplified using simple models from science: the buckling of an arch. This model has been selected to act as illustrative exemple, and no attempt is made here to survey the applications of the theory since this has already been done in Stewart (1981, 1982).

수학과 현장 교육 연구의 실태에 관한 조사 연구

천석현 공주대학교 사범대학 과학교육연구소 1996 과학교육연구 Vol.27 No.1

The teaching is highly specialized and skillful work which required a teacher to possess a specialized knowledge and skill of those obtained through continual and intensive research activities. In order to survive and enjoy prosperity, especially under the flooded circumstance of new datum of informations, knowledges and infinity brain competitive status between one nation to the other, the education is the mastery and key power to overcome, or at lesat withstand, such tense of international relationship. To contribute toward betterment of mathematic education as well as promote scientifical technology fully based on the research report from the mathematic teams set forced on Chungnam by on the Spot Education Research Institute of Korean Federation of Teacher`s Association during the year between 1992 to 1995, the following result were discovered. 1. The forms and substances and method of education shall be based and accorded on the circumstance of the actuallity of the spot because on the spot education is the key to renovates the actual spot education. 2. Noticeablly incleased in research work toward problem solving, however, the result was too far to reach of adequate generalization. 3. There were numbers of displayment, highly computerized, however, they are way too far to reach toward CAI staneard. 4. The result of the researches were too coarsness to apply in practical use in compare to the substances of the subject. 5. The teaching materials must be prepared(manufactured) upon completion of sufficient study on theoretical foundations. 6. The educators must be fully possessed the knowledge of concreteness and should be developed under the ample consideration of multishape of educationl environment. 7. Despit the intensive statement from research team there seems lack of result from comparative equitability dispotion. 8. Felt at loss without having a statistical disposition in obtaining the result of research. 9. Insufficient in detailization of main cause of making error and method of correction. 10. The research work must be fully refrlected and based on the creative power of originality.

내함명제를 중심으로 한 명제변수의 논리치에 대한 연구

천석현 공주교육대학교 초등연구원 1969 公州敎大論叢 Vol.6 No.-

The original contact between logic and mathematics can be traced as far back as the days of Leibniz. It has, thenceforth, been developed into Symbolic Logic, enhanced and enriched by such great scholars as Morgan, Peirce, Boole, Schroder, Frege, Russel, Whitehead. This treatise has dealt with the variation of logical truth value and basic argument forms of implication which serves as the basis of argument. The findings, if the antecedent is falsehood, implication must necessarity be true, regardless °f whether the consequent is “truth” or “falsehood"