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Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
The increasing availability of digital tools for education offers significant opportunities to enhance teaching practices and student engagement. This study presents a structured categorization of online educational tools based on their…
We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
The objective of this paper is to describe a development of an innovative approach to enable students studying science, technology, engineering, and mathematics (STEM) to apply the concepts learned in physics and mathematics to engineering…
An important step in learning to use math in science is learning to see physics equations as not just calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and…
An elementary understanding of the relevant length, mass and energy scales at the molecular level can be used to explain the order of magnitude of material properties such as mass density, latent heat, surface tension, elastic moduli and…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
The purpose of this paper is to show the magic of physics by showing the physics of magic. What usually makes magic tricks interesting is that something unexpected occurs. Similarly, demonstrations are interesting inasmuch as they produce…
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…
We describe the problems of quantum chemistry, the intuition behind classical heuristic methods used to solve them, a conjectured form of the classical complexity of quantum chemistry problems, and the subsequent opportunities for quantum…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Students' answers to tasks provide a valuable source of information in teaching as they result from applying cognitive processes to a learning content addressed in the task. Due to steadily increasing course sizes, analyzing student answers…
The paper presents a teaching module about liquid crystals. Since liquid crystals are linked to everyday student experiences and are also a topic of a current scientific research, they are an excellent candidate of a modern topic to be…
Student performance of virtual introductory physics class (calculus-based mechanics) is analyzed. A fully web-enhanced class was done synchronously. The analysis is done in two categories, averaging all mid-exams (or chapter exams) and…
The University of Maryland (UMD) Biology Education and Physics Education Research Groups are investigating students' views on the role of physics in introductory biology courses. This paper presents data from an introductory course that…
Problems for the graduate students who want to improve problem-solving skills in geometry. Every problem has a short elegant solution -- this gives a hint which was not available when the problem was discovered.
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
In this article we present and discuss a didactic activity that combines epistemic aspects of the nature of science (NOS) and a simple, relatively low-cost experiment on electromagnetic induction. The aim of the activity is for students to…