• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.247-263
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• 2009

In this paper we use degree and index theory to present new applicable fixed point theory for permissible maps.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.693-708
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• 2002

We generalize algebraic results of Nielsen fixed point theory to Nielsen coincidence theory. We use the algebraic methods of D. Ferrario in Nielsen fixed point theory.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.419-428
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• 2000

This work presents a new construction of Mayer-Vietoris sequence using techniques from torsion theory and including the classical case as an example.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.79-92
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• 2005

It is shown that the K-theory of the $C^{\ast}$-algebras of continuous fields on locally compact Hausdorff spaces with fibers elementary $C^{\ast}$-algebras is the same as the K-theory of the base spaces. We also consider the slightly generalized case. Furthermore, we give some applications of these results.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.563-571
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• 1995

The recent work of Hopkins, Kuhn and Ravenel [H-K-R] indicates the Morava K-theory, $K(n)^*(-)$, occupy an important and fundamental place in homology theory. In particular $K(n)^*(BG)$ for classifying spaces of finite groups are studied by many authors [H-K-R], [R], [T-Y 1, 2] and [Hu].

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.585-593
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• 1996

We make the definition of hermitian K-theory for nonunital rings which makes as many senses as possible. We next show that the excision property in rational hermitian K-theory implies the nullity of rational $H B^-$-homology which is the antisymmetric part of Bar homology.

• East Asian mathematical journal
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• v.29 no.2
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• pp.137-168
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• 2013

In this paper we study activity theory and Davydov's learning activity theory. We analyze brief history of activity theory in Russia, structure of human activity, and Davydov's studies in activity theory. Especially we analyze Davydov's 1st grade mathematics textbook, and try to investigate embodiment of Davydov's learning activity theory in his mathematics textbook.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.1-24
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• 2008

The purpose of this study is to uncover weaknesses in the constructivism in mathematics education and to search for ways to complement these deficiencies. We contemplate the relationship between the capability of construction and the performance of it, with the view of the 'Twofold-Structure of Mind.' From this, it is claimed that the construction of mathematical knowledge should be to experience and reveal the upper layer of Mind, the Reality. Based on the examination on the conflict and relation between the structuralism and the constructivism, with reference to the 'theory of principle' and the 'theory of material force' in Neo-Confucianist theory, it is asserted that the construction of mathematical knowledge must be the construction of the structure of mathematical knowledge. To comprehend the processes involved in the construction of the structure of mathematical knowledge, the epistemology of Michael Polanyi is studied. And also, the theory of mathematization, the historico-genetic principle, and the theory on the levels of mathematical thinking are reinterpreted. Finally, on the basis of the theory of twofold-structure, the roles and attitudes of teachers and students are discussed.

• Journal of Educational Research in Mathematics
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• v.12 no.3
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• pp.331-351
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• 2002

It is widely recommended that teachers should actively mediate students' engagement with tools such as manipulative materials. This paper is to help to parse classroom life so that both social and psychological aspects are accounted for and coordinated. Building on the theory of affordances from ecological psychology and the activity theory from sociocultural perspectives, the main strategy of this paper is to view manipulative materials as simultaneously participating in social and psychological activity systems. Within these activity systems it is charted how both mathematical affordances related to the structure of mathematical concepts and ecological affordances related to socially situated classroom practices need to be considered by teachers in effective mediation of mathematical manipulatives. This paper has three major sections. The first section develops a theoretical extension of Gibson's theory of affordances from natural to social environments. The second section introduces mathematical and ecological affordances using empirical data from a grade two elementary school classroom. The third section illustrates the need of coordinating the two affordances as embedded in different activity systems.

• East Asian mathematical journal
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• v.24 no.1
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• pp.11-20
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• 2008

We survey recent results and some conjectures in analytical fixed point theory. We list the known fixed point theorems for Kakutani maps, Fan-Browder maps, locally selectionable maps, approximable maps, admissible maps, and the better admissible class $\cal{B}$ of maps. We also give 16 conjectures related to that theory.