• Korean Journal of Mathematics
• /
• v.5 no.2
• /
• pp.119-125
• /
• 1997

We show that there exists an isomorphism between the basic construction $(M_f)_1$ for $N_f{\subset}M_f$ and the reduction $(M_1)_f$ of the basic construction $M_1$ for $N{\subset}M$, where $f$ is a nontrivial projection in N. For a nontrivial projection $f{\in}N^{\prime}{\cap}M$ we give the basic construction $(M_f)_1$ for $N_f{\subset}M_f$ and compare it with $(M_1)_f$.

• Communications of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.885-898
• /
• 2017

The Bailey lemma has been a powerful tool in the discovery of identities of Rogers-Ramanujan type and also ordinary and basic hyper-geometric series identities. The mechanism of Bailey lemma has also led to the concepts of Bailey pair and Bailey chain. In the present work certain new WP-Bailey pairs have been established. We also have deduced a number of basic hypergeometric series identities as an application of new WP-Bailey pairs.

• Kyungpook Mathematical Journal
• /
• v.53 no.3
• /
• pp.333-340
• /
• 2013

In this paper, we prove that on a K$\ddot{a}$hler spin foliatoin of codimension $q=2n$, any eigenvalue ${\lambda}$ of type $r(r{\in}\{1,{\cdots},[\frac{n+1}{2}]\})$ of the basic Dirac operator $D_b$ satisfies the inequality ${\lambda}^2{\geq}\frac{r}{4r-2}\;{\inf}_M{\sigma}^{\nabla}$, where ${\sigma}^{\nabla}$ is the transversal scalar curvature of $\mathcal{F}$.

• Journal of Engineering Education Research
• /
• v.20 no.6
• /
• pp.3-11
• /
• 2017

The purpose of this study is to investigate the variables that learners should consider for learning persistence when applying blended learning to mathematics class which is a basic curriculum of engineering college. For this purpose, this study compared the basic mathematics class with the blended learning and the class without it. In addition, this study analyzed the influence of the learning outcomes of the blended learning on the willingness to learning persistence by using the self-efficacy and self-regulated learning variables that can predict it. As a result, it was found that the blended learning applied mathematics class of K university which is the subject of analysis in this study has higher self - efficacy, self - regulated learning, and learning persistence intention than general classroom. Finally, the results of this study are meaningful to provide the points to be considered for improving the learning performance when applying the blended learning to the subject class in the future.

• The Mathematical Education
• /
• v.40 no.2
• /
• pp.291-315
• /
• 2001

There are some problems in the introduction of proof in middle school mathematics. Among the problems, one is the use of postulates and the another is the methods of proof how to connect a statement with others. The first case has been treated mainly in this note. Since proof means to state the reason logically why the statement is true on the basis of others which have already been known as true and basic properties, in order to prove logically, it is necessary to take the basic properties and the statement known already as true. But the students don't know well what are the basic properties and the statement known already as true for proving. No use of the term postulation(or axiom) cause the confusion to distinguish postulation and theorem. So they don't know which statements are accepted without proof or not accepted without proof, To solve this problems, it is necessary to use the term postulate in middle school mathematics. In middle school mathematics, we present same model of the introduction of proof which are used the postulates needed for the proof.

• Education of Primary School Mathematics
• /
• v.27 no.2
• /
• pp.173-185
• /
• 2024

Mathematics is a subject that is closely related to ensuring basic academic abilities. As the importance of basic academic abilities has emerged recently, various policies and programs have been implemented to ensure basic academic abilities in mathematics. In this study, we extracted the programs related to mathematics from the Implementation Plans of the Basic Academic Abilities Guarantee of 17 city and provincial education departments and analyzed the actual status of the programs. We divided the programs into diagnosis and support. Regarding diagnosis, we analyzed what types of diagnostic tools are used, who chooses diagnostic tools, who is diagnosed, and when students are diagnosed. Regarding support, we classified it as in-class, in-school, and out-of-school support, and further analyzed the type of the learning support program and the expertise of the instructor. The results of this study showed that there was room for improvement in the timing of diagnosis and diagnostic expertise. This study also found the problems with the lack of preventive programs, ensuring teacher expertise, and support for dyscalculia. This study is expected to contribute to the implementation of programs to ensure basic academic abilities in mathematics and to promote research on basic academic abilities in mathematics education.

• Journal of the Korean School Mathematics Society
• /
• v.14 no.3
• /
• pp.339-354
• /
• 2011

The purpose of this paper is to find out the effective teaching method and improvement for managing the special lecture of basic mathematics which is grouped by the level of low achievement students who are matriculants. From the result, we want to know how the lecture with teaching method of differentiated learning affect on the students, especially who have under achievement, to be interested and confidential in mathematics.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2004.04a
• /
• pp.367-371
• /
• 2004

We study some properties of intuitionistic fuzzy normal subgroups of a group. In particular, we obtain two characterizations of intuitionistic fuzzy normal subgroups. Moreover, we introduce the concept of an intuitionistic fuzzy coset and obtain several results which are analogs of some basic theorems of group theory.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.2
• /
• pp.473-495
• /
• 2023

The use of mathematical modelling in the study of epidemiological disorders continues to grow substantially. In order to better support global policy initiatives and explain the possible consequence of an outbreak, mathematical models were constructed to forecast how epidemic illnesses spread. In this paper, fractional derivatives and (${\varpi}$ - F_𝓒)-contractions are used to explore the existence and uniqueness solutions of the novel coronavirus-19 model.

• Journal for History of Mathematics
• /
• v.14 no.2
• /
• pp.69-76
• /
• 2001

This paper aims to show an inner, basic harmony between metaphysics and current directions in mathematics and in the philosophy of mathematics. In this attempt, the general truths of metaphysics and the truths particularly relevant to the nature of mathematical abstraction serve as speculative guides in ordering the content and discussing the nature of the multiple questions lie between and disputed frontiers of metaphysics and mathematics.