Related papers: Using math in physics -- 1. Dimensional analysis
Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with…
Differentiation is a mathematical skill applied throughout science in order to describe the change of a function with respect to a dependent variable. Thus, an intuitive understanding of differentiation is necessary to work with the…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students' and physicists' talking and writing about the subject of quantum mechanics. We found that physicists'…
The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…
Quantum theory is often regarded as challenging to learn and teach, with advanced mathematical prerequisites ranging from complex numbers and probability theory to matrix multiplication, vector space algebra and symbolic manipulation within…
Dimensionality reduction is used as an important tool for unraveling the complexities of high-dimensional datasets in many fields of science, such as cell biology, chemical informatics, and physics. Visualizations of the dimensionally…
Writing and argumentation are critical to both professional physics and physics education. However, the skill of making an extended argument in writing is often overlooked in physics classrooms, apart from certain practices like lab…
In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that…
This paper re-centres the discussion of student learning in physics to focus on context. In order to do so, a theoretically-motivated understanding of context is developed. Given a well-defined notion of context, data from a novel…
In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
It is becoming common to hear teaching advice about spending more time on the "physics of the problem" so that students will get more physical insight and develop a stronger intuition that can be very helpful when thinking about physics…
When faced with a mathematical model, often the first step is to reduce the complexity of the model by turning variables and parameters into dimensionless quantities. This process is often performed by hand, relying on a skill practiced…
Covariational reasoning -- how one thinks about the way changes in one quantity affect another quantity -- is essential to calculus and physics instruction alike. As physics is often centered on understanding and predicting changes in…
Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the…
What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence…
This paper summarizes some challenges encountered and best practices established in several years of teaching Machine Learning for the Physical Sciences at the undergraduate and graduate level. I discuss motivations for teaching ML to…