Related papers: Using math in physics -- 3. Anchor equations
A priority of physics instruction is to help students make the connection between the formulae they think they are required to memorize and the real world in which they interact every day. If you ask students to describe a situation in real…
The CODATA recommended values of the fundamental constants are widely applied in particle, nuclear and atomic physics. They are a result of a complicated evaluation (adjustment) of numerous correlated data of different nature. Their…
We believe that economists have much to learn from educational research practices and related pedagogical innovations in other disciplines, in particular physics education. In this paper we identify three key features of physics education…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
Very little is known about how the nature of expertise in introductory and advanced courses compares in knowledge-rich domains such as physics. We develop a framework to compare the similarities and differences between learning and patterns…
From industry to government to academia, attracting and retaining science, technology, engineering, and mathematics majors is recognized as a key element of the 21$^{\text{st}}$ century knowledge economy. The ability to retain students…
"Is math useful?" might sound as a trick question. And it is. Of course math is useful, we live in a data-filled world and every aspect of life is totally entwined with math applications, both trivial and subtle applications, of both basic…
This Thesis is devoted to the analysis of entanglement in relevant physical systems. Entanglement is the conducting theme of this research, though I do not dedicate to a single topic, but consider a wide scope of physical situations. I have…
Incorporating computer programming exercises into introductory physics is a delicate task that involves a number of choices that may have an effect on student learning. We present a "hybrid" approach that speaks to a number of common…
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
There is a substantial curricular overlap between calculus and physics, yet introductory physics students often struggle to connect the two. We introduce a quantity-based framing of the Fundamental Theorem of Calculus (FTC) to help unify…
Science has traditionally played an important role in sharing knowledge among people. Particle Physics, with its large experiments, has shown that one not only can share the knowledge among different cultures, but that one can also work…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
Infographics are a form of data visualization combining data, information, and statistics. Over the last ten years, infographics have become a popular method for displaying concise information, where infographics are a useful tool for…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
Analysis of institutional data for physics majors showing predictive relationships between required mathematics and physics courses in various years is important for contemplating how the courses build on each other and whether there is…
Experiments performed in the Physics Laboratory play a significant role in understanding the concepts taught in the theory. A good accompanying laboratory manual serves as a concise guideline which students can use to complete the…