相关论文: Mathematics and group theory in music

The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…

The isotropic harmonic oscillator in N dimensions is shown to have an underlying symmetry group O(2,1)X O(N)which implies a unique result for the energy spectrum of the system. Raising and lowering operators analogous to those of the…

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…

This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…

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…

We introduce the classical theory of the interplay between group theory and topology into the context of operads and explore some applications to homotopy theory. We first propose a notion of a group operad and then develop a theory of…

Politics today is largely about the art of messaging to influence the public, but the mathematical theory of messaging -- information and communication theory -- can turn this art into a precise analysis, both qualitative and quantitative,…

Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…

Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real,…

Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…

We consider a specific scenario of text aggregation, in the realm of musical harmonization. Musical harmonization shares similarities with text aggregation, however the language of harmony is more structured than general text. Concretely,…

Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mirror symmetry} or \emph{Homological mirror symmetry} can be…

Apart from a few remarks on lattice systems with global or gauge symmetries, most of this talk is devoted to some interesting ancient examples of symmetries and their breakdowns in elasticity theory and hydrodynamics. Since Galois Theory is…

We will discuss how certain group theory structures are found in music theory. Western music splits the octave into 12 equal tones called half-steps. We can take this division further and split the octave into 24 equal tones by splitting…

This article introduces into the whole section on Social Sciences, edited by A. Nowak for this Encyclopedia, concentrating on the applications of mathematics and physics. Here under "mathematics" we include also all computer simulations if…

We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a…

The mathematical analysis was conceived in XVII century in Newton and Leibniz works. The problem of logical rigor in definitions was considered by Arnauld and Nicole in "Logique ou l'art de penser". They were the first, who distinguished…

We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynamical systems, and in particular, on the theory of chaos. On…

Participation of mathematicians in the implementation of economic projects in Poland, in which mathematics-based methods played an important role, happened sporadically in the past. Usually methods known from publications and verified were…

The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…