• Communications of Mathematical Education
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• v.22 no.4
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• pp.515-531
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• 2008

The visual cryptography scheme is a simple method which can be decoded directly the secret information in human visual system without performing any cryptographic computations. For some secret of image type, we scatter them to random n images and if any threshold (or more) of them are stacked together then original image is visible. In this paper we consider (2,n) visual cryptography scheme and show a construction method of the sample matrix using the rule of binomial coefficients $_nC_2$. This scheme can contribute interesting and effectiveness to the study of mathematics.

• Journal of Korea Society of Industrial Information Systems
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• v.14 no.4
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• pp.198-204
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• 2009

It is one of important and interesting topics in mathematics education to study the process of the logical thinking and the intuitive thinking in mathematical problem-solving abilities from the viewpoint of mathematical thinking. The main purpose of the present paper is to investigate on this problem with reference to secondary talented students (students aged 16~17 years). In particular, we focus on the relationship between the preference of mathematical thinking and their problem-solving abilities for logical-type problems by applying logistic regression analysis.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1163-1184
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• 2007

In this presentation dedicated to the tricentennial birth anniversary of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707-1783), we begin by remarking about the so-called Basler problem of evaluating the Zeta function ${\zeta}(s)$ [in the much later notation of Georg Friedrich Bernhard Riemann (1826-1866)] when s=2, which was then of vital importance to Euler and to many other contemporary mathematicians including especially the Bernoulli brothers [Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)], and for which a fascinatingly large number of seemingly independent solutions have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. We then investigate various recent developments on the evaluations and representations of ${\zeta}(s)$ when $s{\in}{\mathbb{N}}{\backslash}\;[1],\;{\mathbb{N}}$ being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ${\zeta}(2n+1)(n{\in}{\mathbb{N}})$ which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ${\zeta}(3)$ can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger $Ap\'{e}ry$ (1916-1994) in his proof of the irrationality of ${\zeta}(3)$. Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.

• Journal of The Korean Association of Information Education
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• v.5 no.3
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• pp.321-328
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• 2001

Generally, a Learning Games made based on Off-line. But Today, Web based learning has been used for many educational system by aid of the development of internet technique. If Off-line learning game serviced by On-line learning game, can provide learner with interesting and growing learner's study will. In this paper, I design the Mathematical of Elementary school Roll playing game for learning based on On-line. This is matched the point of On-line game with the point of Learning. A Learner's mathematical technic will be improve by The Mathematical On-line Roll playing game for Elementary school student. A student's ability of self directed learning and solving problem is expended too.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1201-1208
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• 2010

In teaching probability and statistics classes, we should increase efforts to develop examples that enhance teaching methodology in delivering more meaningful knowledge to students. Sports is one field that provides a variety of examples and World Cup Soccer events are a treasure house of many interesting problems. Teaching, using examples from this field, is an effective way to enhance the interest of students in probability and statistics because World Cup Soccer is a matter of national interest. In this paper, we have suggested several examples pertaining to counting the number of cases and computing probabilities. These examples are related to many issues such as possible scenarios in the preliminary round, victory points necessary for each participant to advance to the second round, and the issue of grouping teams. Based on a simulation using a statistical model, we have proposed a logical method for computing the probabilities of proceeding to the second round and winning the championship for each participant in the 2010 South Africa World Cup.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.9
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• pp.3510-3516
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• 2010

In this paper to make young children to learn habits of the animals, crying, features, and English and Korean language, The system was developed to target the zoo various animals exist. If young child places a doll on the front of interesting animal, then young child can learn to look through the display connected to the model. The zoo is reducing the current appearance of the zoo, sensors that can recognize animals are attached to each cage. Attached to each sensor has a unique ID, If this approach recognizes a doll baby and will transmit a unique ID to the handler. Transmitted ID search the matched value sent from the database to retrieve the content and then the content is to be output through the output device. Also if the doll near the animal's room, young children find out animal sound and basic learning by multimedia effects. At the same time Korean, English, Mathematics are learned.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.

• Steel and Composite Structures
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• v.19 no.2
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• pp.369-384
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• 2015

This work presents a free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a simple displacement field based on higher order shear deformation theory is implemented. The proposed theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. In addition, it has strong similarities with Euler-Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. By employing the Hamilton's principle, governing equations of motion for coupled axial-shear-flexural response are determined. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Journal of the Korean School Mathematics Society
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• v.3 no.1
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• pp.189-200
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• 2000

The purpose of this thesis is that the students understand the sentence stated math problems closely related to the real life and adapted the right solving strategies try to find the solution to a problem. The following research problem were proposed. 1. How repeated thinking lessons develop the understanding of problems and influence the usage of correct problem solving strategies and extensions of problem solving. 2. There are how much differences of achievement for each type of sentence stated problems by using comparative analysis of upper class, intermediate class, and lower class for each level between the experimental and comparative classes. In order to conduct this research the classes were divided into three different level - upper class, intermediate class and lower class. Each level include an experimental class and a comparative class. The two classes (experimental class and comparative class) of the same level were tested on the basis of class division record with the experimental class repeated learning papers for two weeks were used to guide the fixed thinking algorism for each sentence stated math problems. Eight common problems were chosen from a variety of textbooks : number calculation problems, velocity-distance-time problems, the density of a mixture, benefit problems, distribution problems, problems about working, ratio problems, the length of a figure problems. After conducting this research experiment The differences in achievement level between the experimental class and comparative class, were compared and analyzed through achievement tests made from the achievement test papers with seven problems, which were worth seventy points (total score). The conclusions of this thesis are as follows: Firstly, leaning activities through the usage of repeated learning papers for each level class produce an even development of achievement level especially in the case of the upper class learners, they have particular differences (between experimental class and comparative class) compared to the intermediate level and lower classes. Secondly, according to the analysis about achievement development each problems, learners easily accept the strategies of solution through the formula setting up to the problem of velocity -distance-time, and to the density of the mixture they adapted the picture drawing strategies interestingly, However each situation requires a variety of appropriate solution strategies. Teachers will have to employ other interesting solution strategies which relate to real life.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.357-377
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• 2014

The purpose of this study is to identify whether math class with clip-type contents has a significant impacts on the academic achievement and attitude of students. To answer the questions, two classes of 4th graders at Sinlim Elementary School in Gwanak-gu, Seoul were selected as subjects; they were divided into experimental group and comparative group. They were confirmed as a homogeneous group at the significance level of 0.05 during a pre-test. The findings are as follows. First, math class with clip-type contents had positive influence on the academic achievement. Second, math class with clip-type contents had positive influence on the attitude towards learning. Furthermore, proper clip-type contents for class boost their understanding and enhance their mathematical thinking with multiple views. It led to their self-confidence in learning math, developing a positive attitude towards math. The benefits of the present research can be summarized as follows. First, the math class with clip-type contents benefited both teachers and students. For teachers, it helped them boost the quality of their teaching. For students, it helped them understand the class better, improving their academic achievement. Second, the diverse, interesting contents had a positive impact on the following of the students: self-concept of math; attitude towards math; learning habits.