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National and International standardized assessments have shown sharp differences between native and foreign students’ performance in both text comprehension and mathematics. Based on the data gathe...

Mathematical music theory helps us investigate musical compositions in mathematical terms. Some hints can be extended towards the visual arts. Mathematical approaches can also help formalize a "translation" from the visual domain to the auditory one and vice versa. Thus, a visual artwork can be mathematically investigated, then translated into music. The final, refined musical rendition can be compared to the initial visual idea. Can an artistic idea be preserved through these changes of media? Can a non-trivial pattern be envisaged in an artwork, and then still be identified after the change of medium? Here, we consider a contemporary installation and an ensemble musical piece derived from it. We first mathematically investigate the installation, finding its patterns and structure, and then we compare them with structure and patterns of the musical composition. In particular, we apply two concepts of mathematical music theory, the Quantum GestART and the gestural similarity conjecture, to the analysis of Qwalala, realized for the Venice Biennale by Pae White, comparing it to its musical rendition in the homonymous piece for harp and ensemble composed by Federico Favali. Some sketches of generalizations follow, with the "Souvenir Theorem" and the "Art Conjecture."

Research, at both national and international levels, has started to focus on the gender gap regarding student performances in technological/scientific topics. Fervent ideological and epistemological debates have sprung up, particularly concerning the differences in mathematics test results between males and females (with males outshining females in most countries). In this paper, we analyse some questions taken from the INVALSI mathematics tests administered at varying educational stages; emergent didactic phenomena are investigated via one of the key concepts of mathematics education, the didactic contract. From a quantitative analysis, based on the percentage of answers given and Rasch Model results, it is possible to identify the presence of significant gender differences between the performances which can be traced back to the effects of the didactic contract. Furthermore, study of the features which accompany these gender gaps in the case studies allows us to investigate the gender gap in mathematics via a new interpretative method which also takes into account student ability levels.

“The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry” (Bertrand Russel, Mysticism and Logic, 1910). This sentence, quoted by François Le Lionnais in his work La Beauté en Mathématiques in [1], reflects his conception of a deep bond between mathematics and literature. He had a multifaceted education and was an erudite and founder of the Oulipo with Raymond Queneau. Even though he was neither a “professional” mathematician nor a “professional” man of letters but only an épicurien passionné as he defined himself [2],1 while alive, he channelled his interests in the theorisation of the so-called littérature potentielle (potential literature) “pour exciter les curieux d’insolite et faire réfléchir les passionnés de littérature aussi bien que le fanatiques de mathématiques” [3]. The purpose of this chapter is outline the figure of François Le Lionnais (who we will refer to from here on as FLL as he himself liked to do [4]) through the analysis of his most meaningfulworks,2 which, in the current literature, appear as subordinated to the works of the more famous and researched Queneau.

It is with great pleasure that we dedicate the special issue Functional Analytic Methods in Partial Differential Equations of Complex Variables and Elliptic Equations to the 60th birthday of Massim...

Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions. We propose a method based on diagrammatic thinking and quantum formalism. We exploit decompositions of complex forms into a set of simple shapes, discretization of complex images, and Dirac notation, imagining a world of "prototypes" that can be connected to obtain a fine or coarse-graining approximation of a given visual image. Visual prototypes are exchanged with auditory ones, and the information (position, size) characterizing visual prototypes is connected with the information (onset, duration, loudness, pitch range) characterizing auditory prototypes. The topic is contextualized within a philosophical debate (discreteness and comparison of apparently unrelated objects), it develops through mathematical formalism, and it leads to programming, to spark interdisciplinary thinking and ignite creativity within STEAM., Comment: Accepted for publication, Journal of Mathematics and Music. New references added in this version

If abstraction makes mathematics strong, it often makes it also hard to learn, if not discouraging. If math pedagogy suffers from the lack of engaging strategies, the pedagogy of mathematical music theory must deal with the additional difficulty of double fields and double vocabulary. However, games and interdisciplinary references in a STEAM framework can help the learner break down complex concepts into essential ideas, and gain interest and motivation to approach advanced topics. Here we present some general considerations, followed by two examples which may be applied in a high-school or early college level course. The first is a musical application of a Rubik’s cube, the CubeHarmonic, to approach group theory and combinatorics jointly with musical chords; the second is an application of category theory to investigate simple musical variations together with transformations on a visual shape.

Mathematics can help investigate hidden patterns and structures in music and visual arts. Also, math in and of itself possesses an intrinsic beauty. We can explore such a specific beauty through the comparison of objects and processes in math with objects and processes in the arts. Recent experimental studies investigate the aesthetics of mathematical proofs compared to those of music. We can contextualize these studies within the framework of category theory applied to the arts (cARTegory theory), thanks to the helpfulness of categories for the analysis of transformations and transformations of transformations. This approach can be effective for the pedagogy of mathematics, mathematical music theory, and STEAM.

This paper examines an annotation in Newton’s hand found by H. W. Turnbull in David Gregory’s papers in the Library of the Royal Society (London). It will be shown that Gregory asked Newton to explain to him how the trajectories of a body accelerated by an inverse-cube force are determined in a corollary in the Principia: an important topic for gravitation theory, since tidal forces are inverse cube. This annotation opens a window on the more hidden mathematical methods which Newton deployed in his magnum opus. The received view according to which the Principia are written in a geometric style with no help from calculus techniques must be revised.

The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of music theory and performance strengthen the relationship between music and images: in this way, we can connect a theremin or violin performance with a study on perspective, always through mathematical ideas and paradigms. So can math explain musical concepts, and, on the contrary, can music explain mathematical concepts? Can music and math together give rise to visual arts in ever more innovative ways? In this paper, we try to connect different topics such as musical performance on instruments with continuous pitch, and the paradigm of geometry and continuity.

In this paper we describe how, starting from our experience of Geometry's teaching in two different academic contexts (mathematic and drawing), we identified together common didactics tools in order to educate the reading of the geometric shapes and their properties with particular attention to the architectural cases. To do this we use 3D models (for example origami models) and gaming activities, both with students and with trainers and our lessons are held not only in the classroom but in public places such squares or cultural sites. Today, we use our teaching idea to train the trainers to understand how to teach geometry in each kind of school level in a new way, using a tangible geometry.

The analysis of the housing market of a city requires suitable approaches and tools, such as data mining models, to represent its complexity which derives on many elements, e.g. the type of capital asset-house is a common good and an investment good as well, the heterogeneity of the urban areas—each of them has own historical and representative values and different urban functions—and the variability of building quality. The housing market of the most densely populated area of Palermo (Italy), corresponding to ten districts, is analyzed to verify the degree of its inner homogeneity and the relations between the quality of the characteristics and the price of the properties. Five hundred sets of housing data have been collected and elaborated by cluster analysis with the aim of describing the structure of the housing market in each district and developing operational tools for the implementation of urban policies and public-private investments.

Brigaglia Aldo, Gaino Bruna, Radelet-de-Grave Patricia. Saccheri vu par Corrado Segre en Italie et par Mansion et Bosmans en Belgique. In: Bulletin de la Classe des sciences, tome 21, 2010. Le Père Henri Bosmans SJ (1852-1928) historien des mathématiques. pp. 83-104.

A General Framework and Theoretical References.- The Chinese Written Language as Tool for a Possible Historical and Epistemological Reflections on the Mathematics and the Impact of Teaching/Learning of Mathematics.- The Meta-rules between Natural Language and History of Mathematics.- Common Sense and Fuzzy Logic.- The Experimental Epistemology as a Tool to Observe and Preview Teaching/Learning Phenomena.- Strategy and Tactics in the Chinese and European Culture: Chess and Weich'i.- Rhythm and Natural Language in the Chinese and European Culture.- Conclusions.