• Journal for History of Mathematics
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• v.24 no.2
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• pp.71-89
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• 2011

This article discusses and reviews the mathematics education of F. Klein who had a leading role in the reform movement of mathematics education from the late 19th century. We are mainly investigated the 'Erlanger Antrittsrede' in 1872 that showed Klein's view on early mathematics education and the 'Meraner Lehrplan f$\"{u}$r Mathematik' in 1905 that Widely known, the basis of the curriculum of modern mathematics education. Based on this, We discusses the educational implications-the purpose and methods of mathematics education, teacher education and so on.

• The Journal of Natural Sciences
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• v.17 no.1
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• pp.1-12
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• 2006

The main results in this paper concern the set of natural numbers correrponding to the least period of periodic orbits of a map on the Klein bottle K.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1483-1503
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• 2008

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.333-357
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• 2007

One of the most important issues in mathematics education is to restore the educational foundation of school mathematics, which requires fundamental discussions about 'What are the reasons for teaching mathematics?'. This study begins with the problematic that mathematics education is generally pursued as an instrumental know-ledge, which is useful to solve everyday problems or develop scientific technology. This common notion cannot be overcome as long as the mathematics education is viewed as bringing up the learners' ability to work out practical problems. In this paper we discuss the value of mathematics education reflecting on the theory of 'two fold structure of mind'. And we examine the ideas pursued by mathematics educators analyzing the educational theory of Plato and Froebel. Furthermore, we review the mathematics educational theory of F. Klein, an educator who led the reformation of mathematics education in the early 20th century and established the basic modern philosophy and curriculum of mathematics education. In particular, reflecting on the 'two fold structure of mind,' we reexamine his mathematics educational theory in the aspect of the mind cultivation so as to elucidate his ideas more clearly. Moreover, for the more deep discussion about Klein's thoughts on the mathematics education, his viewpoint on tile teaching of 'functional thinking' for the mind cultivation is reexamined based on the research results found in the developments of mathematics education after Klein. As the result we show that under the current mathematics education, which regards mathematics as a practical tools for solving everyday problems and an essential device for developing science and technology, there is a more important value for cultivating the human mind, and argue that mathematics education should contribute to the mind cultivation by emphasizing such an educational value.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1447-1465
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• 2019

In this paper, the relativistic Vlasov-Klein-Gordon system in one dimension is investigated. This non-linear dynamics system consists of a transport equation for the distribution function combined with Klein-Gordon equation. Without any assumption of continuity or compact support of any initial particle density $f_0$, we prove the existence and uniqueness of the mild solution via the iteration method.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.541-551
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• 1995

The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.1015-1030
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• 2017

This paper is concerned with the following Klein-Gordon-Maxwell system: $$\{-{\Delta}u+{\lambda}V(x)u-(2{\omega}+{\phi}){\phi}u=f(x,u),\;x{\in}\mathbb{R}^3,\\{\Delta}{\phi}=({\omega}+{\phi})u^2,\;x{\in}\mathbb{R}^3$$ where ${\omega}$ > 0 is a constant and ${\lambda}$ is the parameter. Under some suitable assumptions on V (x) and f(x, u), we establish the existence and multiplicity of nontrivial solutions of the above system via variational methods. Our conditions weaken the Ambrosetti Rabinowitz type condition.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.77-88
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• 2006

In 1876, America's first Jewish math professor J. J. Sylvester took a department head position at the first research university in USA at the age of 61. He launched the America's first research journal of mathematics in 1877. We study the role and meaning of J. J. Sylvester, F. Klein and E. H. Moore in late 19th century of American mathematics from Korean's perspective.

• The KIPS Transactions:PartA
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• v.11A no.7 s.91
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• pp.571-576
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• 2004

In this paper, by using Lagrange polynomial interpolation with a trick such that for $f(x)^{3}$ we shall use $f(x_i)^{3}I_i(x)^{3}$ instead of $I(x)^{3}$ where $I{x}{\;}={\;}\sum_{i}^{f}(x_i)I_i(x)$. We show the convergence and stability and calculate errors. These errors are approximately less than $C(\frac{1}{N})^{N-1} hN(N-1)(\frac{N}{2})^{N-1} /(\frac{N}{2})!$ where N is a polynomial degree.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.621-633
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• 2002

This paper provides some functional equations and parametric expressions of f-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.