Related papers: Visualisation of matrix product: Using light to cl…
We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \times 8$ matrix…
Many Physics Education Researchers have discussed the positive correlation between students' incoming mathematics skills and performance in their physics classes. Thus, in order to strengthen their performance gains in their physics…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
We analyze the behavior of light as it passes through systems composed of polarizing filters at different angular orientations. The analysis is initially conducted in the context of classical optics, using Malus's Law to calculate the…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
In this work, I propose a way to help high school students and the general population understand quantum concepts by adopting a new inherently dual representation. Major difficulties in explaining to people the basic concepts of quantum…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…
We present an approach to fully characterize the polarization of general vector light beams. When attempting to generalize the notion of Stokes parameters to nonparaxial light beams in momentum space, we find that the Jones function that…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
The paper describes methodology of math education for students interested in chemistry. Suppose we have mathematical circle 2 hours per week. What can be done? We can not provide any systematic study, but we can choose one subject and show…
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the…
By starting with the Maxwell theory of electromagnetism, we study the change of polarization state of light transmitting through optically anisotropic media. The basic idea is to reduce the Maxwell equation to the Schroedinger like equation…
We introduce a new matrix product, that we call the wreath product of matrices. The name is inspired by the analogous product for graphs, and the following important correspondence is proven: the wreath product of the adjacency matrices of…
Linear polarimetric transformations of light polarization states by the action of material media are fully characterized by the corresponding Mueller matrices, which contain in an implicit and intricate manner all measurable information on…
Polaritons are quasiparticles resulting from strong quantum coupling of light and matter. Peculiar properties of polaritons are a mixture of physics usually restricted to one of these realms, making them interesting for study not only from…
In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of…
Any rational number can be factored into a product of several rationals whose sum vanishes. This simple but nontrivial fact was suggested as a problem on a maths olympiad for high-school students. We completely solve similar questions in…