![]() Visualization materials are confirmed by the presented computational calculations. Similar objects are built to find the critical points of the Himmelblau’s special test function. Graphical and animated objects are presented that clearly demonstrate the areas of the location of initial approximations, allowing you to numerically obtain all the real roots of systems of trigonometric and nonlinear equations. The method is considered through the example of the process of solving systems of equations using the mathematical package Mathcad and the WolframAlpha online resource. Such objects allow, initially without going into the intricacies of the functioning of the package and the mathematical apparatus used, to competently describe a complete picture of a difficult situation for students and indicate ways to resolve it. Depending on the complexity of the problem being solved, either the teacher or the students themselves can create special visual graphic (animation) objects. Results indicate that math software should be implemented in calculus courses during online education.Ī method has been obtained for the use of visualization in computer mathematical packages, which is an effective means of overcoming difficult situations that arise for students when mastering such packages and solving computational problems. Students from experimental group answered a survey to evaluate in more detail the experience. Experimental group scored significantly better than control group demonstrating the positive effect this software had on multivariate calculus learning. Two-sample t-test was used to determine how similar the means of the control and experimental groups were for pre and post-tests’ scores. Pre-tests were carried out to evaluate the similarity of groups prior treatment and post-tests to assess scores after students learnt derivatives in multivariable calculus. A quasi-experiment was conducted with control and experimental groups. Math software Wolfram Mathematica under its cloud version was studied for learning second semester multivariate calculus online. The use of computer algebra systems (CAS) may improve students’ perception about online learning as it offers an interactive environment where academic achievement could increase. Technological tools, teaching materials and students’ acceptance are key aspects for online education at current times. The assumed simulation study could be useful for statistics teachers to motivate their students for lectures in computational statistics and fundamentals of probability. All computer code used in this article is provided on GitHub. For this application we obtained as a solution, an average number of 950 packages needed to complete the album, at an average cost of 3,800 reals (Brazilian currency), assuming that the collector does not exchange any of its repetitions with nobody. ![]() The simulation was based on a computational code written in R. In this case, the complete album has N = 670 stickers, which are sold in packages containing n = 5 stickers each. In addition, we propose a simulation algorithm to find the solution to the problem, where we present as a numerical illustration an album of stickers related to the Qatar 2022 Official Football World Cup, which is being sold in Brazilian newsstands. This paper considers some computational issues related to the problem of the coupon collector behavior.
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