Search

Transfer of structural math knowledge to physics is difficult for students. While research suggests various improvement techniques, enhancing parallelism of algebraic structures used in physics to those studied in mathematics courses seems underrepresented. This paper proposes an alternative way of introducing wave functions as a set of parametric equations. Research shows that the mathematical underpinnings of the mechanical wave function are problematic for students. As seen from the math perspective, there can be several drawbacks that likely impede scientific analysis and interpretation of the wave function: y (x , t) = A cos ( 2 π λ x − 2 π T t). [ABSTRACT FROM AUTHOR]

I next enjoyed her charming "Bob Ross"-style ultramellow Zen-like introduction to imaginary numbers, logarithms, and calculus (imagine a yoga cooldown monologue from a mathematical physics professor). Https://www.youtube.com/@tibees https://tobyhendy.com/ https://en.wikipedia.org/wiki/Toby Hendy https://en.wikipedia.org/wiki/Flatland https://cdn.openai.com/papers/gpt-4.pdf I first became aware of mathematical physicist Toby Hendy's YouTube videos with her series of "Flatland"-like videos discussing 2D creatures living in a 2D world and how we 3D folk might mess with them, and how in turn we might be messed with by 4D creatures. [Extracted from the article]

When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (co-vary). How much a change in one variable or parameter is associated with a change in another depends on how they appear in the equation—their functional dependence. Understanding this sort of relationship is rarely emphasized in introductory mathematics classes, and students who have not yet learned to blend conceptual ideas with mathematical symbols may not see the relevance and power of this idea. We need to explicitly teach functional dependence as part of our effort to help students learn to use math productively in science. [ABSTRACT FROM AUTHOR]