Related papers: Problem Solving and the Use of Math in Physics Cou…
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…
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…
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
Computation is a central aspect of modern science and engineering work, and yet, computational instruction has yet to fully pervade university STEM curricula. In physics, we have begun to integrate computation into our courses in a variety…
Computation is intertwined with essentially all aspects of physics research and is invaluable for physicists' careers. Despite its disciplinary importance, integration of computation into physics education remains a challenge and, moreover,…
Without a doubt many problems in physics arise as a consequence of our philosophical conception of the world. In this contribution however we endeavor to alleviate this scenario by putting forward a philosophical approach under which some…
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students…
The large number of published articles in physics journals under the title "Comments on ..." and "Reply to ..." is indicative that the conceptual understanding of physical phenomena is very elusive and hard to grasp even to experts, but it…
While philosophy of science is the study of problems of knowledge concerning science in general, there also exists - or should exist - a '' philosophy in science'' directed at finding out in what ways our actual scientific knowledge may…
This book is devoted to an informal discussion of patterns constructed for treating physical problems. Such patterns, when sufficiently formalized, are usually referred as "models", and tents to be applied not only in physics, but conquer…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a given problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem…
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…
Paradoxes are a very frequent phenomenon in processes of thought which strive towards the intelectual and cognitive shifts. They occur in all areas of human spiritual activites. What we are interested here in, are the paradoxes in physics.…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Human languages employ constructions that tacitly assume specific properties of the limited range of phenomena they evolved to describe. These assumed properties are true features of that limited context, but may not be general or precise…
Developing expertise in physics requires appropriate integration and assimilation of physics and mathematics. Instructors and students often describe physics courses in terms of their emphasis on conceptual and quantitative problem-solving.…