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Platforma Moodle wspomagana systemem algebry komputerowej

Kucharska Magdalena, Perl Monika

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

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2020

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Nr 71

41--44

PL

Niniejszy artykuł poświęcony jest możliwościom tworzenia randomizowanych zadań matematycznych, jakie daje zastosowanie systemu algebry komputerowej STACK (System for Teaching and Assessment using a Computer algebra Kernel). Przedstawione są w nim przykłady takich zadań, na bazie których autorki tego artykułu stworzyły na uczelnianej platformie Moodle kurs „Matematyka” dla wszystkich studentów pierwszego roku Zachodniopomorskiego Uniwersytetu Technologicznego w Szczecinie. W czasach pandemii wirusa SARS-CoV-2 okazał się on nieocenionym następcą tradycyjnych zbiorów zadań. System STACK umożliwia bowiem przekazanie studentowi pełnego rozwiązania wylosowanej przez niego wersji zadania, pobieranie wprowadzonego rozwiązania i dostosowanie do niego odpowiedzi zwrotnej. Daje zatem możliwość przeprowadzania bieżącej kontroli efektów kształcenia oraz rzetelnych egzaminów zdalnych kończących daną formę zajęć.

EN

This article focuses on the possibilities of creating randomized mathematical problems provided by the STACK system, which is an open source automatic assessment tool, which is based on the Maxima Computer Algebra System. This publication contains examples of the tasks used by the authors to create ‘Mathematics’ course on the university’s Moodle platform. The above mentioned course was aimed at first-year students of the West Pomeranian University of Technology in Szczecin. During the SARS-CoV-2 pandemic it proved to be the invaluable replacement for the traditional set of tasks. The STACK system enables students to transmit a complete solution of a randomly selected version of the task along with dynamic drawings made with GeoGebra. It is also possible to download the solution introduced by the student and adapt the feedback. In addition, there is also an option of a gradual construction of the exercise where the mistakes made by the student in each stage do not disqualify the entire task and allow to check whether it is consistently solved till the end. Attention will also be paid to the possibility of using the STACK system to monitor the effects of learning, as well as to perform reliable remote final examinations, which cannot even be provided by multiple-choice test tasks.

2

Complexity of the Inversion Algorithm of Polynomial Mappings

Bogdan P.

Schedae Informaticae

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2016

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Vol. 25

209--225

EN

In this paper we will recall the inversion algorithm described in [1]. The algorithm classifies polynomial automorphisms into two sets: Pascal finite and Pascal infinite. In this article the complexity of the inversion algorithm will be estimated. To do so, we will present two popular ways how Computer Algebra Systems (CASes) keep the information about multivariate polynomials. We will define the complexity as the amount of simple operations performed by the algorithm as a function of the size of the input. We will define simple operations of the algorithm. Then we will estimate complexity of checking that the polynomial map is not a polynomial automorphism. To do so we will use theorem 3.1 from [1].

3

Using a CAS to visualize some images of lines mapped via the harmonic cross-ratio

Korczak E., Marlewski A.

Journal Biuletyn of Polish Society for Geometry and Engineering Graphics

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2012

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Vol. 23

11--19

EN

Let K be a cubic curve in the projective space P 3 and let T1 and T2 be points determining a bisecant T1T2 of K. We fix a point A on K and a point B≠A which does not lay on K, and such that T1T2 ≠AB. We are interested in the set of points X generated by the equation (T1, T1; M, X) = –1 where M denotes the point at which AB meets the bisecant T1T2. So we consider the line congruence of order 1 and of class 3 in the aspect of the harmonic cross-ratio. We derive theoretic formulas for the set of X ‘s and we go on in the harmonic case– then the set of X ’s is a conic. We use the computer algebra system Derive 5 from Texas Instruments, Inc., USA, to produce visualizations of the images of resulting curves.

PL

Niech K będzie krzywą przestrzenną rzędu trzeciego w przestrzeni rzutowej P 3 i niech M będzie dowolnym punktem tej przestrzeni nieleżącym na K. W wiązce prostych, której wierzchołkiem jest M, znajduje się dokładnie jedna bisekanta. Punkty, w których przecina ona krzywą K, oznaczamy przez T1 i T2. Tematem pracy jest zbadanie miejsc geometrycznych punktów X i T1T2, dla których dwustosunek (T1, T2; M, X) = –1, gdy punkt M przebiega prostą, którą wyznaczają ustalone punkt krzywej K i punkt, który na K nie leży. Badanie to przeprowadzamy przy użyciu programu Derive 5 for Windows (Texas Instruments, Inc.).

4

Reaction-diffusion problems with Random parameters using the generalized stochastic finite difference method

Kamiński M.

Journal of Applied Computer Science

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2011

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Vol. 19, nr 2

31-45

EN

The main idea here is to demonstrate the new stochastic discrete computational approach consisting of the generalized stochastic perturbation technique based on the Taylor expansions of the random variables and, at the same time, classical Finite Difference Method on the regular grids. As it is documented by the computational illustrations, it is possible to determine using this approach also higher probabilistic moments and to provide full hybrid analytical-discrete analysis for any random dispersion of input variables unlike in the second order second moment technique worked out before. A numerical algorithm is implemented here using the straightforward partial differentiation of the reaction-diffusion equation with respect to the random input quantity; all symbolic computations of probabilistic moments and characteristics are completed by the computer algebra system MAPLE.