• Title, Summary, Keyword: Mathematica

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Development of a Web-based Calculus module using Mathematica (Mathematica를 이용한 웹기반 미적분 모듈의 개발)

  • Jun, Youngcook
    • The Journal of Korean Association of Computer Education
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    • v.4 no.2
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    • pp.105-114
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    • 2001
  • This paper illustrates a calculus module which generates step-by-step solutions using J/Link that connects Java and Mathematica. Such a module provides intermediate and low level students with a practical environment where they can easily follow the solution paths on their own paces. The extra feature of this module depicts graphical images for a given function and its differentiated result to enhance the visual understandings of calculus concepts. Mathematica as a mathematical expert system that provides systematic mathematical knowledge to students with step-by-step solutions will be possibly extended to the tutorial or CMI development. The proposed module is implemented in a Java servlet that links to Mathematica FrontEnd. This approach results in adopting font systems to express two dimensional mathematical expressions in web documents as an alternative typesetting tool.

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Mathematica 소개

  • 민경원
    • Computational Structural Engineering
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    • v.5 no.3
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    • pp.52-55
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    • 1992
  • 이 글에서는 Mathematica의 고유한 특징과 많은 기능 중의 일부분만을 예를 들어 설명을 하였다. 그러나 Mathematica의 피할 수 없는 단점은 많은 수학적 기능이 포함되어 있기 때문에 처리속도가 늦다는 점이다. 예를 들면 많은 량의 반복작업이나 차수가 큰 매트릭스의 연산작업은 다소 속도가 늦어 PC기종에서는 곤란을 겪을 때가 많다. 따라서 PC대신 workstation 같은 상위기종의 컴퓨터를 이용한다면 처리속도가 빨라져 진행에 문제점이 없다. 한 예로 workstation에서는 차수가 30개인 고유치 해석도 내장함수인 명령어만으로 단지 몇초만에 할 수 있는 데 비하여 PC에서는 기종에 따라 몇배, 몇백배의 시간이 요구되는 것이다. 그리고 또 하나의 단점으로는 방대한 프로그램을 운용하기 위한 비용(ram)이 많이 든다는 점이다. 한 예로 PC에서는 기본적으로 Mathematica를 작동하기 위해 최소한 4 mega ram이 필요하며 여러 수학적 기능을 충분히 이용하기 위해 많은 량의 ram이 필요하다는 점이다. 그러나 위의 단점은 Mathematica가 지니고 있는 고유한 장점을 생각한다면 매우 미미한 것이라 여겨진다. 수학의 대부분의 기능을 포함하고 있으며 기호처리가 가능하고 프로그래밍 기법이 다양하기 때문에 수학을 이용하여 연구를 하는 사람에게는 훌륭한 도구가 생긴 것이라 할 수 있다.

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Electromagnetic Vector Fields Simulation with Mathematica (전자기 벡터장 시각화를 위한 Mathematica 시뮬레이션)

  • Choi, Yong-Dae;Yun, Hee-Joong
    • Journal of the Korean Vacuum Society
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    • v.21 no.2
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    • pp.69-77
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    • 2012
  • Visualization of the electromagnetic vector fields are presented and examined with Mathematica. Vector fields may be used to represent a great of many physical quantities in various area of physics, including electromagnetism with vector differential operators. Because they deal with abstract, three-dimensional fields that are some times very difficult to visualize, electromagnetism can be conceptually rather difficult. Visual representation of such an abstract vector fields is invaluable to student or researchers working in this field and also helps teaching electromagnetism to physics or engineering students. Mathematica provides a wider range of graphical tools including plot of vector fields and vector analysis, which can be applied to visualization of electromagnetic system. We have visualized the most fundamental concepts of the electromagnetic vector $\vec{E}=-\vec{\nabla}_{\varphi}$, $\vec{D}={\epsilon}\vec{E}$, $\vec{\nabla}{\times}\vec{A}$, $\vec{B}={\mu}\vec{H}$, $\vec{B}={\mu}_0(\vec{H}+\vec{M})$, which are confirmed with vector calculations and valid graphically with some presentations.

A Web Manual Generator for Courseware Development using CAS and Web Connectivity Technology (컴퓨터 대수 시스템과 웹 연동 기술을 활용한 코스웨어 개발용 웹 매뉴얼 생성기)

  • Park, Hong-Joon;Jun, Young-Cook;Jang, Moon-Suk
    • The Journal of Korean Association of Computer Education
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    • v.8 no.5
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    • pp.97-108
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    • 2005
  • In this paper, we present our prototype of a web manual creator that is based on MSP technology embedded in webMathematica. This tool gives courseware authors more simple ways to make their own mathematical web contents. We first classified authoring models for creating mathematical content development and proposed an advanced model. The final application called phpMath can generate MSP-driven documents automatically using Mathematica commands typed by users. In other words, phpMath users can make interactive dynamic mathematical web contents even though they do not know anything about web server, HTML, and webMathematica. We illustrated the details of the prototype from the user's perspectives followed by comments on usefulness.

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Teaching Mathematics using Mathematica (Mathematica를 활용한 수학 지도)

  • 허혜자
    • Journal of Educational Research in Mathematics
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    • v.8 no.2
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    • pp.541-551
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    • 1998
  • Recently, the importance of participating in classes activity and cultivating student's thinking ability is emphasized in the mathematics education society. Teachers are demanded to change their teaching style centered pencile-and paper into using the variety instructional aids, such as calculator, video tape, computer, ohp, and projector, etc. In this paper, we search for the mathematica's function and the method that apply mathematical to the secondary school mathematics. Mathematical has many functions: calculator, algebra, graphics, animations, programing, notebook. We find that mathematica can be applied to the graph of function, the understand of simultaneous equations, the graph of trigonometry function, the calculation of limit, the computation of areas as limits, the derivative of a function and tangent line, a solid figure, and others in secondary school mathematics.

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Implementation of an Algorithm that Generates Minimal Spanning Ladders and Exploration on its relevance with Computational Thinking (최소생성사다리를 생성하는 알고리즘 구현 및 컴퓨팅 사고력과의 관련성 탐구)

  • Jun, Youngcook
    • The Journal of Korean Association of Computer Education
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    • v.21 no.6
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    • pp.39-47
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    • 2018
  • This paper dealt with investigating the number of minimal spanning ladders originated from ladder game and their properties as well as the related computational thinking aspects. The author modified the filtering techniques to enhance Mathematica project where a new type of graph was generated based on the algorithm using a generator of firstly found minimal spanning graph by repeatedly applying independent ladder operator to a subsequence of ladder sequence. The newly produced YC graphs had recursive and hierarchical graph structures and showed the properties of edge-symmetric. As the computational complexity increased the author divided the whole search space into the each floor of the newly generated minimal spanning graphs for the (5, 10) YC graph and the higher (6, 15) YC graph. It turned out that the computational thinking capabilities such as data visualization, abstraction, and parallel computing with Mathematica contributed to enumerating the new YC graphs in order to investigate their structures and properties.

대학수학에서 Mathematica를 이용한 ${\pi}$의 계산

  • Kim, Byeong-Mu
    • Communications of Mathematical Education
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    • v.11
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    • pp.307-319
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    • 2001
  • 대학수학에서, 멱급수의 전개를 배우는 단원에서 관심을 끄는 수 ${\pi}$에 대하여 고찰함으로써, ${\pi}$값의 계산 과정에 있어서의 발달을 이해하고, Mathematica를 이용하여 수학자들이 만든 공식을 통해 ${\pi}$값을 구체적으로 계산하여 보며, 또한 수학에 흥미를 느끼도록 하여 학생들 스스로가 ${\pi}$값을 계산해 볼 수 있는 기회를 갖도록 유도한다.

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Design and Development of White-box e-Learning Contents for Science-Engineering Majors using Mathematica (이공계 대학생을 위한 Mathematica 기반의 화이트박스 이러닝 콘텐츠 설계 및 개발)

  • Jun, Youngcook
    • 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.

Teaching-Learning Method for Plane Transformation Geometry with Mathematica (평면변환기하에 있어서 Mathematica를 이용한 교수-학습방법)

  • 김향숙
    • 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.

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