• 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 the Korean Society for Aviation and Aeronautics
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• v.23 no.2
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• pp.69-74
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• 2015

We propose a rigorous and practical methodology to evaluate the performance of symbolic manipulation program such as Mathematica, Maple, and Maxima. First, we demonstrate an inverse method to construct the benchmark problems of an initial value problems. The benchmark problems associated with the discrete version of the Chebyshev polynomials provide a rigorous and objective measure to evaluate the performance of symbolic manipulation programs. We compare three symbolic manipulation programs, which are Mathematica, Maple and Maxima, using this methodology. The computation time, the used memory and the perturbation terms are chosen for comparison parameters.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.39-48
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• 2009

Fisher information matrix plays an important role in statistical inference of unknown parameters. Especially, it is used in objective Bayesian inference which derives to the posterior distribution using a noninformative prior distribution and is an example of metric functions in geometry. The more parameters for estimating in a distribution are, the more complicate derivation of the Fisher information matrix for the distribution is. In this paper, we derive to the Fisher information matrix for 3-parameters Weibull distribution which is used in reliability theory using Mathematica programs.

• 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.

• Communications of Mathematical Education
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• v.26 no.2
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• pp.155-176
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• 2012

In this paper, we present a practical and essential method of using team projects for calculus. We, specifically, take into account the team project that calculate the volume of lung represented on CT scan images. We have demonstrated that the process of analyzing the images in a team project encourage studying numerical methods of integration for calculus. Also, we have used various technological programs(MATLAB, MATHEMATICA, MS Excel) to solve the team project.

• Journal of Integrative Natural Science
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• v.7 no.2
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• pp.138-144
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• 2014

Fisher information matrix plays an important role in statistical inference of unknown parameters. Especially, it is used in objective Bayesian inference where we calculate the posterior distribution using a noninformative prior distribution, and also in an example of metric functions in geometry. To estimate parameters in a distribution, we can use the Fisher information matrix. The more the number of parameters increases, the more its matrix form gets complicated. In this paper, by using Mathematica programs we derive the Fisher information matrix for 4-parameter generalized gamma distribution which is used in reliability theory.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.401-413
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• 2002

In this paper, we consider hyperstructures (H,.) defined on the set H = {e, a, b}. We study the hyperstructure of H when every element is one of a scalar unit, a unit or a weak scalar. On those conditions the $H_{\upsilon}$-quasigroups are classified. And we obtain the 15 minimal $H_{\upsilon}$-groups and 2 non-quasi $H_{\upsilon}$-semigroups For these we use the Mathematica 3.0 computer programs.

• Research in Mathematical Education
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• v.11 no.2
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• pp.143-151
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• 2007

Nowadays there are practically no mathematical courses in which Computer Algebra Systems (CAS) programs, such as MATHEMATlCA, Maple, and TI-89/92, are not used to some extent. However, generally the usage of these programs is reduced to illustration of computing processes: calculation of integrals, differentiation, solution of various equations, etc. This is obtained by usage of standard command of type: Solve [...] in MATHEMATICA. At the same time the main difficulties arise at teaching nonconventional mathematical courses such as coding theory, discrete mathematics, cryptography, Scientific computing, which are gaining the increasing popularity now. Now it is impossible to imagine a modern engineer not having basic knowledge in discrete mathematics, Cryptography, coding theory. Digital processing of signals (digital sound, digital TV) has been introduced in our lives.

• Steel and Composite Structures
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• v.12 no.4
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• pp.303-324
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• 2012

This paper presents the mode-shape analysis of the cross-ply laminated composite cylindrical shallow shells. First, the kinematic relations of strains and deformation are given. Then, using Hamilton's principle, governing differential equations are developed for a general curved shell. Finally, the stress-strain relation for the laminated, cross-ply composite shells are obtained. By using some simplifications and assuming Fourier series as a displacement field, the governed differential equations are solved by the matrix algebra for shallow shells. Employing the computer algebra system called MATHEMATICA; a computer program has been prepared for the solution. The results obtained by this solution are compared with the results obtained by (ANSYS and SAP2000) programs, in order to verify the accuracy and reliability of the solution presented.

• Investigative Magnetic Resonance Imaging
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• v.4 no.1
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• pp.20-26
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• 2000

Gradient moment nulling techniques require the introduction of an additional gradient on each axis for each order of motion correction to be applied. The additional gradients introduce new constraints on the sequence design and increase the demands on the gradient system. The purpose of this paper is to demonstrate techniques for optimization of gradient echo gradient moment nulling sequences within the constraints of the gradient hardware. Flow compensated pulse sequences were designed and implemented on a clinical magnetic resonance imaging system. The design of the gradient moment nulling sequences requires the solution of a linear system of equations. A Mathematica package was developed that interactively solves the gradient moment nulling problem. The package allows the physicist to specify the desired order of motion compensation and the duration of the gradients in the sequence with different gradient envelopes. The gradient echo sequences with first, second, and third order motion compensation were implemented with minimum echo time. The sequences were optimized to take full advantage of the capabilities of the gradient hardware. The sequences were used to generate images of phantoms and human brains. The optimized sequences were found to have better motion compensation than comparable standard sequences.