• Journal of the Korean School Mathematics Society
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• v.18 no.2
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• pp.223-240
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• 2015

This paper deals with how to design and develop white-box based e-learning contents which are equipped with conceptual understanding and step-by-step computational procedures for studying vector calculus for science-engineering majors who might need supplementary mathematics learning. Noting that rewriting rules are often used in school mathematics for students' problem solving, the theoretical aspects of rewriting rules are reviewed for developing supplementary e-learning contents for them. The software design of step-by-step problem solving requires careful arrangement of rewriting rules and pattern matching techniques for white-box procedures using a computer algebra system such as Mathematica. Several modules for step-by-step problem solving as well as producing dynamic display of e-learning contents was coded by Mathematica in order to find the length of a curve in vector calculus after implementing several rules for differentiation and integration. The developed contents are equipped with diagnostic modules and immediate feedback for supplementary learning in terms of a tutorial. At the end, this paper indicates the strengths and features of the developed contents for college students who need to increase math learning capabilities, and suggests future research directions.

• Communications of Mathematical Education
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• v.35 no.1
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• pp.119-136
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• 2021

We performed the research and education programs using engineering tools such as Mathematica, Microsoft Excel and GeoGebra for the students in mathematics mentorship program of the institute of science education for the gifted. We used the engineering tools to solve the problems and found the rules by observing the solutions. Then we generalized the rules to theorems by proving the rules. Mathematica, the professional mathematical computation program, was used to calculate and find the length of the repeating portion of the repeating decimal. Microsoft Excel, the spreadsheet software, was used to investigate the Beatty sequences. Also GeoGebra, the dynamic geometric software, was used to investigate the Voronoi diagram and develop the Voronoi game. Using GeoGebra, we designed the Voronoi game plate for the game. In this program, using engineering tools improved the mathematical creativity and the logical thinking of the gifted students in mathematics mentorship program.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.269-278
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• 1998

This paper is composed of computer programs and practical examples for the education of mathematics. The Animation package in the Mathematica standard packages is the Graphics Animation. Animations are the ways which produce a sequence of different pictures by rapid succession. The command Animate has a number of options such as Animate, SpinShow and ShowAnimation. Mathematica is available for a large variety of practical education of mathematics. The method in this report are familiar with the general principles of operating the computer in Mathematica 3.0. In this paper there a set of useful examples of mathematical education and we discusses some of the advanced technique for the Input-Output systems.

• Journal of Astronomy and Space Sciences
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• v.37 no.2
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• pp.131-142
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• 2020

As the laws of physics are expressed in a manner that makes their invariance under coordinate transformations manifest, they should be written in terms of tensors. Furthermore, tensors make manifest the characteristics and behaviors of electromagnetic fields through inhomogeneous, anisotropic, and compressible media. Electromagnetic fields are expressed completely in tensor form, F^αβ, which implies both electric field ${\overrightarrow{E}}$ and magnetic field ${\overrightarrow{B}}$ rather than separately in the vector fields. This study presents the Mathematica platform that generates and transforms a second-rank antisymmetric field-strength tensor F^αβ and whiskbroom pattern in Minkowski space. The platforms enhance the capabilities of students and researchers in tensor analysis and improves comprehension of the elegant features of complete structure in physics.

• Journal of Astronomy and Space Sciences
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• v.31 no.1
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• pp.91-99
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• 2014

The atmospheric flow in the 3-Cell model of global atmosphere circulation is described by the Lagrange's equation of the non-inertial frame where pressure force, frictional force and fictitious force are mixed in complex form. The Coriolis force is an important factor which requires calculation of fictitious force effects on atmospheric flow viewed from the rotating Earth. We make new Mathematica platform to solve Lagrange's equation by numerical analysis in order to analyze dynamics of atmospheric general circulation in the non-inertial frame. It can simulate atmospheric circulation process anywhere on the earth. It is expected that this pedagogical platform can be utilized to help students studying the atmospheric flow understand the mechanisms of atmospheric global circulation.

• The Journal of Korean Association of Computer Education
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• v.5 no.3
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• pp.79-87
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• 2002

Theorema system is built on top of Mathematica to automate deductive reasoning processes as the combination of computer algebra system and deductive system. Theorema system that was developed at RISC in Austria provides three modes based on rewriting techniques; computation, problem solving and proving. This paper shows how the computation mode of Theorema can simulate Derive part for TI-92 graphic calculators to produce TI-92 manuals. Moreover, it also describes how such manuals can be converted to web-based learning materials via Java servlet.

• Research in Mathematical Education
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• v.7 no.2
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• pp.101-117
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• 2003

In this paper, we give examples of models we have created for use in university mathematics courses. We explain the concept of linear transformation, investigate the roles of each component of 2 ${\times}$ 2 and 3 ${\times}$ 3 transformation matrices, consider the relation between sound and trigonometry, visualize the Riemann sum, the volume of surfaces of revolution and the area of unit circle. This paper illustrates how one can use Mathematica to visualize abstract mathematical concepts, thus enabling students to understand mathematics problems effectively in class. Development of these kinds of teaching and learning models can stimulate the students' curiosity about mathematics and increase their interest.

• The Mathematical Education
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• v.40 no.1
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• pp.93-102
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• 2001

The world we live in is called the age of information. Thus communication and computers are doing the central role in it. When one studies the mathematical problem, the use of tools such as computers, calculators and technology is available for all students, and then students are actively engaged in reasoning, communicating, problem solving, and making connections with mathematics, between mathematics and other disciplines. The use of technology extends to include computer algebra systems, spreadsheets, dynamic geometry software and the Internet and help active learning of students by analyzing data and realizing mathematical models visually. In this paper, we explain concepts of transformation, linear transformation, congruence transformation and homothety, and introduce interesting, meaningful and visual models for teaching of a plane transformation geomeoy which are obtained by using Mathematica. Moreover, this study will show how to visualize linear transformation for student's better understanding in teaching a plane transformation geometry in classroom. New development of these kinds of teaching-learning methods can simulate student's curiosity about mathematics and their interest. Therefore these models will give teachers the active teaching and also give students the successful loaming for obtaining the concept of linear transformation.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.133-142
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• 1998

A simple mathematical theory is developed on the periodicity of elementary polar functions. The periodicity plays an important role in efficient plotting of some closed polar curves, without the excessive use of plotting devices and materials. An efficient plotting algorithm utilizing the periodicity is proposed and its implementation by a Mathematica program is introduced for a family of closed polar functions.

• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.121-129
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• 1994

Using the software named MATHEMATICA which can evaluate symbolic operation, it is demonstrated to obtain the maximum likelihood estimation form. A sample from Multivariate Normal distribution is adopted to show the process of obtaining the maximum likelihood estimator.