Related papers: Using math in physics -- 4. Toy models
Given a physics scenario, different problem types presenting that scenario in various ways can emphasize different instructional goals. In this investigation, we examined the views of physics graduate teaching assistants (TAs) about the…
A central goal of Introductory Physics for the Life Sciences (IPLS) is to prepare students to use physics to model and analyze biological situations, a skill of increasing importance for their future studies and careers. Here we report our…
We investigate studnets' use of words used in everyday language as well as in physics. We find students are more likely to identify and explain the meaning of the word as it is used in physics when they have become familiar with the…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can…
We developed a two-day physics class that uses a nearby forest as a teaching location. Using low-cost material, students design and carry out physics projects outside of the usual controlled environment that is a classroom. In this way they…
Scientists do not merely choose to accept fully formed theories, they also have to decide which models to work on before they are fully developed and tested. Since decisive empirical evidence in favour of a model will not yet have been…
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…
Humans have a remarkable ability to use physical commonsense and predict the effect of collisions. But do they understand the underlying factors? Can they predict if the underlying factors have changed? Interestingly, in most cases humans…
We argue that most advances in science and technology during the past and the present centuries rely on modern physics concepts developed in the early $20$th century. The reliance is so profound that any improvement of literacy of science…
Expressing physics problems in the form of a mathematical model is one of the most important stages in the problem-solving process. Particularly in algebraic symbolization, understanding the meanings of signs and being able to manipulate…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
In this review we argue for the creation of a physics of moving systems -- a locomotion "robophysics" -- which we define as the pursuit of the discovery of principles of self generated motion. Robophysics can provide an important…
Experimental activities are an essential part of physics education. In addition to conveying scientific knowledge, they play a significant role in developing scientific literacy, inquiry skills, and critical thinking. In today's world,…
Computer-based modelling and simulation have become useful tools to facilitate humans to understand systems in different domains, such as physics, astrophysics, chemistry, biology, economics, engineering and social science. A complex system…
Information is physical, and for a physical theory to be universal, it should model observers as physical systems, with concrete memories where they store the information acquired through experiments and reasoning. Here we address these…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…
Mathematical modelling and ethics have more touching points than most of us would like to admit. Everyday decisions are often reasoned by mathematical arguments. Mathematics teachers belong to those mathematically literate, who must point…
Modeling is a central concern in both science and engineering. However, we need a new fundamental theory to address the challenges of the digital age. In this paper, we first explain why modeling is fundamental and which challenges must be…