We derive conservation laws from symmetry operations using the principle of least action. These derivations, which are examples Noether’s theorem, require only elementary calculus and suitable for introductory physics. extend these arguments to transformation coordinates due uniform motion show that a argument applies more elegantly Lorentz than Galilean transformation.

We outline a story line that introduces Newtonian mechanics by employing conservation of energy to predict the motion particle in one-dimensional potential. show incorporating constraints and constants into expression allows us analyze more complicated systems. A heuristic transition embeds kinetic potential still powerful principle least action.

We present a method for introducing students to the classical principle of least action, using novel approach based on ordinary calculus one variable. define action path and draw connection between it Newton’s laws free particle in conservative potential. The use software help visualize analyze rectilinear motion is discussed. also briefly discuss origin Feynman’s sum over paths formulation quantum mechanics.

We derive Lagrange’s equations of motion from the principle least action using elementary calculus rather than variations. also demonstrate conditions under which energy and momentum are constants motion.

Dynamic geometrical systems bring new tools for visualization and exploring mathematical ideas, structures relations in teaching of mathematics. Among this type the Geogebra is coming to fore these days, thanks its extensive options. In methodical textbooks teachers created within Slovak national project "Modernization education at primary secondary schools" has an important position among used projects. This article introduces main newest possibilities software environment which joins...

During the last ten years advances in open-source digital technology, used especially by data science, led to very accessible ways how obtain, store, process, analyze or share almost every human activity. Data science tools bring not only transparency, accessibility, and reproducibility open but also give benefits education as learning for improving effectiveness of instruction. Together with our pedagogical introduction review Jupyter an interactive multimedia tool, we present three-years...

The contribution provides a detailed exploration of the online platform Perusall as an advanced social annotation technology in teaching and learning STEM disciplines. This is based on authors' insights experiences from three years implementing at P.J. \v{S}af\'arik University Ko\v{s}ice, Slovakia. While concept its educational applications are not novel, Perusall's features, including AI data science reports, enable use both synchronous asynchronous blended flipped environments. In this...

In the book Surely You Are Joking, Mr. Feynman! Richard Feynman tells a story of Cornell cafeteria plate being tossed into air. As spun, it wobbled. noticed relation between two motions. He solved motion by using Lagrangian approach. This solution didn’t satisfy him. wanted to understand analyzing its individual particles and forces acting on them. was successful, but he tell us how did it. We provide an elementary explanation for two-to-one ratio wobble spin frequencies, based analysis also...

Nowadays interactive digital scientific environments have become an integral part of computing in solving various tasks research, but also STEM education. We introduce SageMath or shortly Sage -- a free open Python-based alternative to the well-known commercial software frame our course Methods Physical Problems Solving for future scientists and science teachers. Particularly, 1st illustrative example from Physics Olympiad, we present as data source, symbolic, numerical, visualization tool....

We develop heuristic derivations of two alternative principles least action. A particle moving in one dimension can reverse direction at will if energy conservation is the only criterion. Such arbitrary changes motion are eliminated by demanding that Maupertuis–Euler abbreviated action, equal to area under momentum versus position curve phase space, has smallest possible value consistent with energy. Minimizing action predicts trajectories and three dimensions leads more powerful Hamilton...

At present, there is still no officially accepted and extensively verified implementation of computing the gamma difference distribution allowing unequal shape parameters. We explore four computational ways with different parameters resulting from time series kriging, a forecasting approach based on best linear unbiased prediction mixed models. The results our numerical study, emphasis using open data science tools, demonstrate that algorithm implemented in high-performance Python(with...

Abstract The COVID-19 pandemic has underscored the importance of blended learning in contemporary physics and, more generally, STEM education. In this contribution, we summarize current pedagogical models learning, such as rotational and flexible non-rotational models, customizable configurations physical virtual spaces. With inevitable integration digital technology one pillars teachers find themselves an unprecedented position to not only obtain data frequently but also analyze it adjust...

Abstract High school physics competitions serve as a platform for talented students to showcase their skills, engage in challenging problems, and foster passion science. This paper explores innovative approaches enhance these by harnessing the power of open science artificial intelligence (AI) tools. Particularly we delve into capabilities state-of-the-art AI chatbots, i.e. ChatGPT, Bard, Claude, related problem solving physics. Together with tools like SageMath Jupyter AI, they have...

Ratio statistics and distributions play a crucial role in various fields, including linear regression, metrology, nuclear physics, operations research, econometrics, biostatistics, genetics, engineering. In this work, we examine the statistical properties probability calculations of Hake normalized gain as measure effect size educational effectiveness physics education. Leveraging existing knowledge about ratio normal variables utilizing open data science tools, developed two novel...

We present an example of active learning activity in modern physics at secondary school developed by us the framework flipped learning. The dealing with black-body radiation was a part our experimental course one Slovak grammar schools. Using inquiry-based form interactive demonstration as its introduction, students actively learned GeoGebra simulation fundamental tool visualization, experimentation and measurement. Our results show that thanks to simulations methods can be really viable,...

Abstract We consider elections where the set of candidates is split into parties and each party can nominate just one candidate. study computational complexity two problems. The Possible President problem asks whether a given candidate become unique winner election for some nominations from other parties. Necessary to decide will be any possible several different voting rules show that all them NP-complete, even if size at most two; we prove coNP-complete. Further, formulate integer programs...

In 2014, physicists and data scientists F. Perez B. Granger started an ambitious project Jupyter with goals of developing a powerful, universal open virtual interactive scientific environment. Today, is the most widely used technology for performing calculations, analysis, processing, reporting, but it has also become very important educational tool. Our article summarizes pedagogical technological aspects experience from using notebooks SageMath in our research teaching university courses...

We present our experience and preliminary results from teaching modern physics using smartphones at one of Slovak secondary schools. To be more specific, we developed materials in the framework flipped learning, applying Feynman's many-path quantum model together with current digital technologies - GeoGebra simulations (www.geogebra.org) designed for smartphones. Using theoretical mixed methods research, report progress answering following research questions: What impact do have on learning...

We present our ideas how to apply modern data science technology and methodology effectively prepare statistically analyze large educational datasets which in case map inquiry skills computational thinking developed by students primary secondary schools at the Slovak national scale, within project "IT Academy - Education for 21st Century". Combining top two open-source tools, Python (within Jupyter notebooks) R studio software), we illustrate some of results from preprocessing (cleaning,...

High school physics competitions serve as a platform for talented students to showcase their skills, engage in challenging problems, and foster passion science. This paper explores innovative approaches enhance these by harnessing the power of open science artificial intelligence (AI) tools. Particularly we delve into capabilities state-of-the-art AI chatbots, i.e. ChatGPT, Bard, Claude, related problem solving physics. Together with tools like SageMath Jupyter AI, they have potential...

The COVID-19 pandemic has underscored the importance of blended learning in contemporary physics and, more generally, STEM education. In this contribution, we summarize current pedagogical models learning, such as rotational and flexible non-rotational models, customizable configurations physical virtual spaces. With inevitable integration digital technology one pillars teachers find themselves an unprecedented position to not only obtain data frequently but also analyze it adjust...