GRAPH ISOMORPHISMS AND MATRIX SIMILARITY: SWITCHING BETWEEN REPRESENTATIONS

A proof whether two graphs (possibly oriented graphs or multigraphs, etc.) are isomorphic or not can be derived by various methods. Some of them are reasonable for small numbers of vertices and/or edges, but not for larger numbers. Switching from iconic representation to a matrix representation transforms the problem of Graph Theory into a problem in Linear Algebra. The support provided by a Computer Algebra System is analyzed, in particular with regard to the building of new mathematical knowledge through a transition from graphical to algebraic representation. Moreover two important issues are discussed: a. the need for more than one representation; b. the direction of the switch between representations, which is non standard, from graphical to algebraic

ChatGPT may excel in States Medical Licensing Examination but falters in basic Linear Algebra

The emergence of ChatGPT has been rapid, and although it has demonstrated positive impacts in certain domains, its influence is not universally advantageous. Our analysis focuses on ChatGPT's capabilities in Mathematics Education, particularly in teaching basic Linear Algebra. While there are instances where ChatGPT delivers accurate and well-motivated answers, it is crucial to recognize numerous cases where it makes significant mathematical errors and fails in logical inference. These occurrences raise concerns regarding the system's genuine understanding of mathematics, as it appears to rely more on visual patterns rather than true comprehension. Additionally, the suitability of ChatGPT as a teacher for students also warrants consideration

From conic intersections to toric intersections: The case of the isoptic curves of an ellipse

Starting from the study of the orthoptic curves of parabolas and ellipses, we generalize to the case of isoptic curves for any angle, i.e. the geometric locus of points from which a parabola or an ellipse are viewed under a given angle. This leads to the investigation of spiric curves and to the construction of these curves as an actual intersection of a self-intersecting torus with a plane. The usage of a Computer Algebra System facilitated this investigation

Dynamic construction of a family of octic curves as geometric loci

We explore the construction of curves of degree 8 (octics) appearing as geometric loci of points defined by moving points on an ellipse and its director circle. To achieve this goal we develop different computer algebra methods, dealing with trigonometric or with rational parametric representations, as well as through implicit polynomial equations, of the given curves. Finally, we highlight the involved mathematical or computational issues arising when reflecting on the outputs obtained in each case

ARIA digital anamorphosis : Digital transformation of health and care in airway diseases from research to practice

Digital anamorphosis is used to define a distorted image of health and care that may be viewed correctly using digital tools and strategies. MASK digital anamorphosis represents the process used by MASK to develop the digital transformation of health and care in rhinitis. It strengthens the ARIA change management strategy in the prevention and management of airway disease. The MASK strategy is based on validated digital tools. Using the MASK digital tool and the CARAT online enhanced clinical framework, solutions for practical steps of digital enhancement of care are proposed.Peer reviewe

ARIA digital anamorphosis: Digital transformation of health and care in airway diseases from research to practice

Digital anamorphosis is used to define a distorted image of health and care that may be viewed correctly using digital tools and strategies. MASK digital anamorphosis represents the process used by MASK to develop the digital transformation of health and care in rhinitis. It strengthens the ARIA change management strategy in the prevention and management of airway disease. The MASK strategy is based on validated digital tools. Using the MASK digital tool and the CARAT online enhanced clinical framework, solutions for practical steps of digital enhancement of care are proposed

STEAM Education: Technological Skills, Students’ Cultural Background and Covid-19 Crisis

We present an initial description of an ongoing research project. Students are attracted to learn mathematics, not only for its application but also for their cultural interest. The students’ cultural backgrounds are used, and situations are analyzed and modeled using technology. This first step has been instrumental in making the transition to distance learning necessary due to the Covid-19 crisis. We focus on a specific population of students who had to overcome, within a short time, two important transitions in the learning processes