Number of found documents: 369
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On the Friedmann equation for the three-dimensional hypersphere
Křížek, Michal; Mészáros, A.
2016 - English
The present standard cosmological model of the evolution of our universe, is based on the Friedmann equation, which was published by Alexander Friedmann in 1922. He applied Einstein’s equations to an expanding threedimensional sphere which enabled him to avoid boundary conditions. However, his description was very brief. Therefore, the main objective of this article is to detailed a derivation of the Friedmann equation for an unknown expansion function a = a(t) representing the radius of the universe. Furthermore, we present serious arguments showing why the validity of Einstein’s equations should not be extrapolated to the entire universe. Keywords: Einstein's equations; standard cosmological model; dark matter; dark energy Available in digital repository of the ASCR
On the Friedmann equation for the three-dimensional hypersphere

The present standard cosmological model of the evolution of our universe, is based on the Friedmann equation, which was published by Alexander Friedmann in 1922. He applied Einstein’s equations to an ...

Křížek, Michal; Mészáros, A.
Matematický ústav, 2016

Developing open approach to mathematics in future primary school teachers
Samková, L.; Tichá, Marie
2016 - English
In our contribution we focus on the possibility to develop open approach to mathematics in future primary school teachers during a university course on mathematics conducted in inquiry-based manner. We analyse data obtained in the beginning and in the end of the course with respect to two main aspects related to open approach to mathematics: searching for all solutions of a task, and acceptance of different forms of notation of a given solution. Data analysis revealed in the participants three different shifts towards open approach to mathematics, and showed that after the active participation in the course each of the participants improved at least in one of the monitored aspects, and that none of the participants got worse in any of the aspects. Keywords: argumentaion; concept Cartoons; future primary school teachers; inquiry-based Fulltext is available at external website.
Developing open approach to mathematics in future primary school teachers

In our contribution we focus on the possibility to develop open approach to mathematics in future primary school teachers during a university course on mathematics conducted in inquiry-based manner. ...

Samková, L.; Tichá, Marie
Matematický ústav, 2016

O některých miskoncepcích souvisejících se schopností argumentovat
Samková, L.; Tichá, Marie
2016 - Czech
Příspěvek se zaměřuje na různé způsoby prokazování pravdivosti obecných tvrzení (odkazy na autoritu, různé typy empirických argumentů, deduktivní argumenty). Podrobně sleduje argumentační schopnosti budoucích učitelů 1. Stupně ZŠ, zmiňuje často se vyskytující miskoncepce. Jako možnou cestu ke zlepšení argumentačních schopností nabízí badatelsky orientované vyučování. The contribution focuses on various ways of proving general statements (external convictions, various types of empirical arguments, deductive arguments). We observe in details argumentation skills of future primary school teachers, and mention often occurring misconceptions. We offer inquiry-based education as a possible way to development of argumentation skills. Keywords: general statements; argumentation skills; inqiry-based education Fulltext is available at external website.
O některých miskoncepcích souvisejících se schopností argumentovat

Příspěvek se zaměřuje na různé způsoby prokazování pravdivosti obecných tvrzení (odkazy na autoritu, různé typy empirických argumentů, deduktivní argumenty). Podrobně sleduje argumentační schopnosti ...

Samková, L.; Tichá, Marie
Matematický ústav, 2016

Badatelské aktivity s geometrickým obsahem v přípravě studentů učitelství
Roubíček, Filip
2016 - Czech
Příspěvek je věnován otázkám uplatnění badatelského přístupu v semináři z didaktiky matematiky určených budoucím učitelům prvního stupně základní školy. Studentům byly předkládány badatelské výukové situace, jejichž základem bylo specifické geometrické prostředí. Studenti se zabývali řešením neurčitých geometrických úloh, které umožňovalo uplatnění badatelských postupů, jako jsou kladení otázek, navrhování postupů, experimentování, usuzování, ověřování, diskutování závěrů aj. V příspěvku jsou prezentovány tři ukázky badatelských aktivit realizovaných se studenty a jejich reflexe bádání. The paper deals with the issue of implementation of inquiry-based approach into seminars of didactics of mathematics for future primary school teachers. Inquiry -stimulating teaching situations based on specific geometrical environments were presented to students. Students engaged in the solving of undefined geometrical problems that enables application od inquiry procedures, such as posing of questions, designing of solving processes, making experiments, reasoning, verification, discussion of findings and others. Three illustrations of inquiry activities realised with students and their reflection of inquiry are presented in the paper. Keywords: inquiry activities; geometrical problems; preservice teacher education Available at various institutes of the ASCR
Badatelské aktivity s geometrickým obsahem v přípravě studentů učitelství

Příspěvek je věnován otázkám uplatnění badatelského přístupu v semináři z didaktiky matematiky určených budoucím učitelům prvního stupně základní školy. Studentům byly předkládány badatelské výukové ...

Roubíček, Filip
Matematický ústav, 2016

Numerical modeling of magnetostrictive materials
Kholmetska, I.; Chleboun, J.; Krejčí, Pavel
2016 - English
An operator-differential model for magnetostrictive energy harvesting proposed in the literature is used to calculate the amount of harvested energy under some uncertainty in the Preisach density function. The uncertainty is modeled through a fuzzy set approach. In galfenol, an alloy of gallium and iron, however, the hysteresis phenomenon is present only weakly. This allows to propose a simpler, but computationally faster model without hysteresis. The new, simpler model has been identified from the measured magnetic and magnetostrictive cycles. The amount of harvested energy is of the same order in both models. Again, an uncertainty in the identified model can be considered and its impact on the amount of the harvested energy calculated. Keywords: magnetostrictive materials; hysteresis; energy harvesting Available in digital repository of the ASCR
Numerical modeling of magnetostrictive materials

An operator-differential model for magnetostrictive energy harvesting proposed in the literature is used to calculate the amount of harvested energy under some uncertainty in the Preisach density ...

Kholmetska, I.; Chleboun, J.; Krejčí, Pavel
Matematický ústav, 2016

Anthropic principle and the local Hubble expansion
Křížek, Michal; Somer, L.
2016 - English
We claim that a local expansion of the universe, whose rate is comparable with the Hubble constant H0, had an essential influence on the development of intelligent life on the Earth. We present more than 10 examples showing that some antigravitational effects of the cosmological constant are observable locally in the Solar system. It is known that the luminosity of the Sun increased approximately linearly within the last 4.5Gyr starting at 70% of its present value. We give several independent arguments showing that the average Earth-Sun distance increases about 5m/yr due to antigravitational forces and such a large recession speed cannot be explained by solar wind, tidal forces, plasma outbursts from the Sun, or by the decrease of the Solar mass due to nuclear reactions. Models based on Newtonian mechanics can explain only a few cm per year. Keywords: antigravity; habitable zone; law of conservation of energy Available in digital repository of the ASCR
Anthropic principle and the local Hubble expansion

We claim that a local expansion of the universe, whose rate is comparable with the Hubble constant H0, had an essential influence on the development of intelligent life on the Earth. We present more ...

Křížek, Michal; Somer, L.
Matematický ústav, 2016

Error patterns in computation in concept cartoons
Samková, L.; Tichá, Marie; Hošpesová, A.
2015 - English
The paper focuses on an educational tool called Concept Cartoons, and its possible usage in primary school mathematics, especially in promoting discussion in the classroom. We show in detail how to prepare Concept Cartoons displaying various mental computation strategies and error patterns. Keywords: concept Cartoons; error patterns; mental computation strategies Available at various institutes of the ASCR
Error patterns in computation in concept cartoons

The paper focuses on an educational tool called Concept Cartoons, and its possible usage in primary school mathematics, especially in promoting discussion in the classroom. We show in detail how to ...

Samková, L.; Tichá, Marie; Hošpesová, A.
Matematický ústav, 2015

Programs and Algorithms of Numerical Mathematics 17 : Dolní Maxov, June 8-13, 2014 : Proceedings of Seminar
Chleboun, J.; Přikryl, Petr; Segeth, Karel; Šístek, Jakub; Vejchodský, Tomáš
2015 - English
This volume comprises peer-reviewed papers that are based on invited lectures, survey lectures, short communications, and posters presented at the 17th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in Dolní Maxov, Czech Republic, June 8–13, 2014. The seminar was organized by the Institute of Mathematics of the Academy of Sciences of the Czech Republic. It continued the previous seminars on mathematical software and numerical methods held (with only one exception) biannually in\nAlšovice, Bratříkov, Janov nad Nisou, Kořenov, Lázně Libverda, Dolní Maxov, and Prague in the period 1983–2012. The objective of this series of seminars is to provide a forum for presenting and discussing advanced topics in numerical analysis, singleor multi-processor applications of computational methods, and new approaches to mathematical modeling. Keywords: numerical mathematics Available in digital repository of the ASCR
Programs and Algorithms of Numerical Mathematics 17 : Dolní Maxov, June 8-13, 2014 : Proceedings of Seminar

This volume comprises peer-reviewed papers that are based on invited lectures, survey lectures, short communications, and posters presented at the 17th seminar Programs and Algorithms of Numerical ...

Chleboun, J.; Přikryl, Petr; Segeth, Karel; Šístek, Jakub; Vejchodský, Tomáš
Matematický ústav, 2015

Proceedings of the International Conference Applications of Mathematics 2015 : Prague, November 18-21, 2015
Brandts, J.; Korotov, S.; Křížek, Michal; Segeth, Karel; Šístek, Jakub; Vejchodský, Tomáš
2015 - English
Professors Ivo Babuška, Milan Práger, and Emil Vitásek are renowned experts in numerical analysis and computational methods. Their fruitful scientific careers started in Prague, at the Institute of Mathematics of the Czechoslovak Academy of Sciences (now Czech Academy of Sciences). They collaborated there on various projects including the computational analysis of the construction technology for Orlík Dam. In 1966 they published their joint book entitled Numerical Processes in Differential Equations. It is an honor for the Institute of Mathematics to host a conference on the occasion of their birthdays. Keywords: applications of mathematics Available in digital repository of the ASCR
Proceedings of the International Conference Applications of Mathematics 2015 : Prague, November 18-21, 2015

Professors Ivo Babuška, Milan Práger, and Emil Vitásek are renowned experts in numerical analysis and computational methods. Their fruitful scientific careers started in Prague, at the Institute of ...

Brandts, J.; Korotov, S.; Křížek, Michal; Segeth, Karel; Šístek, Jakub; Vejchodský, Tomáš
Matematický ústav, 2015

Reasoning of pupils in the solving process of a geometrical inquiry-stimulating task
Roubíček, Filip
2015 - English
The poster focuses on the issue of solving geometrical problems in the context of inquiry based education, namely on the use of inquiry by pupils and on classroom mathematics discourse. The poster describes communicative situations in solving of inquiry based problems and presents examples of pupils’ solutions and discussion in the classroom. Keywords: inquiry based education; teaching of geometry; problem solving; mathematical discourse Available at various institutes of the ASCR
Reasoning of pupils in the solving process of a geometrical inquiry-stimulating task

The poster focuses on the issue of solving geometrical problems in the context of inquiry based education, namely on the use of inquiry by pupils and on classroom mathematics discourse. The poster ...

Roubíček, Filip
Matematický ústav, 2015

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