• Korean Journal of Computational Design and Engineering
• /
• v.20 no.2
• /
• pp.93-103
• /
• 2015

In this study, we organize and explain various ways to construct 3D models in the 2D plane using Geogebra, mathematical education software that enables us to visualize dynamically the interaction between algebra and geometry. In these ways, we construct three unit vectors for 3 dimensions at a point on the Cartesian coordinates, on the basis of which we can build up the 3D models by putting together basic mathematical objects like points, lines or planes. We can apply the ways of constructing the 3 dimensions on the Cartesian coordinates to modeling of various structures in the real world, and have chances to translate, rotate, zoom, and even animate the structures by means of slider, one of the very important functions in Geogebra features. This study suggests that the visualizing and dynamic features of Geogebra help for sure to make understood and maximize learning effectiveness on mechanical modeling or the 3D CAD.

• Research in Mathematical Education
• /
• v.17 no.4
• /
• pp.279-290
• /
• 2013

Presently, there has been growing interests in using mathematics' history in teaching mathematics [Katz, V. & Tzanakis, C. (Eds.) (2011). Recent Developments on Introducing a Historical Dimension in Mathematics Education. Washington, DC: Mathematical Association of America]. Thus, this article introduces some work of scholars from ancient East Indian culture like Bhaskara (AD 1114-1185) and Arabic culture such as Ibn Qurrah (AD 9th c) that are related to Pythagoras Theorem. In addition, some Babylonian creative works related to Pythagorean triples found in a tablet known as 'Plimpton 322', and an application of the Pythagorean Theorem found in another tablet named 'Yale Tablet' are presented. Applications of computer animation of dissection Motion Operations concept in 2D and 3D using dynamic software like Geometer's-Sketchpad and Cabri-II-and-3D. Nowadays, creative minds are attracted by the recent stampede in the advances of technological applications in visual literacy; consequently, innovative environments that would help young students, gifted or not, acquiring meaningful conceptual understanding would immerge.

• The Mathematical Education
• /
• v.48 no.3
• /
• pp.213-234
• /
• 2009

College students have a diverse educational background with the recent multiplicity in university admissions standards and procedures. As a result, their mathematical preparation and performance varies widely. Teaching calculus to such a diverse student group is a demanding task. Differentiated curriculum has been conducted for the university calculus course in Yonsei university for the past five years. A case study on the differentiated curriculum in Yonsei university is presented for the curriculum improvement. With its ideal purpose, the differentiated curriculum has created issues and problems in practice. As an alternative to the ideal differentiated curriculum, this study shows that a computer-based approach using a numerical software could give aids to overcoming the difficulty of inadequately prepared students in the learning process while mathematically sophisticated students could keep interested in the course. This study also presents the useful topics in calculus that can be implemented for computer-based calculus education and provides guidelines for the effective usage.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.15 no.3
• /
• pp.1015-1029
• /
• 2021

Modern technology offers many ways to enhance teaching and learning that in turn promote the development of tools for educational activities both inside and outside the classroom. Many educational programs using the augmented reality (AR) technology are being widely used to provide supplementary learning materials for students. This paper describes the potential and challenges of using GeoGebra AR in mathematical studies, whereby students can view 3D geometric objects for a better understanding of their structure, and verifies the feasibility of its use based on experimental results. The GeoGebra software can be used to draw geometric objects, and 3D geometric objects can be viewed using AR software or AR applications on mobile phones or computer tablets. These could provide some of the required materials for mathematical education at high schools or universities. The use of the GeoGebra application for education in Laos will be particularly discussed in this paper.

• Education of Primary School Mathematics
• /
• v.3 no.1
• /
• pp.47-54
• /
• 1999

The development of computer software accelerates the change of teaching-learning method in primary school mathematics. In this paper, we discuss how to apply the software GSP to teach mathematics in primary school and suggest some examples fur the creative and active loaming. Moreover, we give the efficient teaching method for the primary school mathematics.

• Journal of the Chungcheong Mathematical Society
• /
• v.15 no.2
• /
• pp.97-107
• /
• 2003

An efficient algorithm for the multiplication in a binary finite filed using a normal basis representation of $F_{2^m}$ is discussed and proposed for software implementation of elliptic curve cryptography. The algorithm is developed by using the storage scheme of sparse matrices.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.475-483
• /
• 2013

We give some characterizations of injective modules over ${\omega}$-Noetherian rings. It is also shown that each localization of a GV-torsion-free injective module over a ${\omega}$-Noetherian ring is injective.

• Journal of the Chungcheong Mathematical Society
• /
• v.36 no.3
• /
• pp.155-162
• /
• 2023

We study permutatons that satisfy a necessary and sufficient condition for the equality of Fulton's essential set and the maximal-inversion-descent(MID) set.

• Nuclear Engineering and Technology
• /
• v.31 no.2
• /
• pp.157-171
• /
• 1999

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri Net (CPN) for system modeling and Prototype Verification System (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, an information extractor from CPN models has been developed in this work. In order to convert the extracted information to the PVS specification language, a translator also has been developed. ML that is a higher-order functional language programs the information extractor and translator. This combined method has been applied to a protection system function of Wolsong NPP SDS2(Steam Generator Low Level Trip). As a result of this application, we could prove completeness and consistency of the requirement logically. Through this work, in short, an axiom or lemma based-analysis method for CPN models is newly suggested in order to complement CPN analysis methods and a guideline for the use of formal methods is proposed in order to apply them to NPP Software Verification and Validation.

• The Journal of Asian Finance, Economics and Business
• /
• v.7 no.11
• /
• pp.83-93
• /
• 2020

This empirical research aims to modeling and improving the forecasting accuracy of the volatility pattern by employing the Saudi Arabia stock market (Tadawul)by studying daily closed price index data from October 2011 to December 2019 with a number of observations being 2048. In order to achieve significant results, this study employs many mathematical functions which are non-linear spectral model Maximum overlapping Discrete Wavelet Transform (MODWT) based on the best localized function (Bl14), autoregressive integrated moving average (ARIMA) model and generalized autoregressive conditional heteroskedasticity (GARCH) models. Therefore, the major findings of this study show that all the previous events during the mentioned period of time will be explained and a new forecasting model will be suggested by combining the best MODWT function (Bl14 function) and the fitted GARCH model. Therefore, the results show that the ability of MODWT in decomposition the stock market data, highlighting the significant events which have the most highly volatile data and improving the forecasting accuracy will be showed based on some mathematical criteria such as Mean Absolute Percentage Error (MAPE), Mean Absolute Scaled Error (MASE), Root Means Squared Error (RMSE), Akaike information criterion. These results will be implemented using MATLAB software and R- software.