2843 research outputs found
Sort by
Les mathématiques sont-elles là dehors ou en dedans?
No full textDepuis l’Antiquité, les mathématiques suscitent une question qui dépasse les équations : décrivent-elles une réalité indépendante de nous ou ne sont-elles qu’un produit de l’esprit humain? Cette présentation propose un survol historique et critique des principales postures ontologiques et épistémologiques à ce sujet.
Nous évoquerons les grands courants, certes. Et au fil du parcours, nous soulignerons le contexte historique et les débats qui ont façonné ces positions. Mais nous ouvrirons aussi la discussion vers des perspectives plus récentes, souvent en marge des canons philosophiques, qui renouvellent la réflexion sur la nature et la portée des mathématiques
Lu pour vous : Discrete and Computational Geometry, 2nd Edition
Get PDFLa géométrie classique est morte et sa dépouille s’est fossilisée. Telle était l’opinion largement partagée au cours la majeure partie du XXe siècle. Qualifié de miraculeux, l’étonnant théorème du trisecteur, obtenu par le mathématicien anglo-américain Frank Morley en 1899, faisait figure d’ultime sursaut d’orgueil avant l’agonie. Le regard déjà porté vers d’autres horizons, le mathématicien professionnel type, ce chasseur de trésors, n’avait guère besoin d’être convaincu pour qu’il envisage la possibilité de céder la géométrie classique aux architectes, aux arpenteurs, aux charpentiers, aux ingénieurs, aux opticiens et aux urbanistes. En somme, considéré comme pleinement explorée, ce champ du savoir avait décidément perdu son prestige des temps passés.
C’est en tout cas l’impression qui se dégage des propos tenus par Eric Temple Bell (1883-1960), ce mathématicien écossais qui connut un certain succès populaire lorsqu’il s’adonna à la chronique sur l’histoire des mathématiques, dans The Development of Mathematics :
The geometers of the 20th century have long since piously removed all these treasures to the museum of geometry where the dust of history quickly dimmed their luster [Les géomètres du XXe siècle ont depuis longtemps pieusement transféré tous ces trésors au musée de la géométrie, où la poussière de l'histoire a rapidement terni leur éclat].
Le topologiste juif allemand Hans Freudenthal (1905-1990) pointait sensiblement dans la même direction lorsqu’il affirma ce qui suit dans un texte intitulé Geometry Between the Devil an the Deep Sea :
For long times mathematics has been synonymous with geometry. In fact, there existed other branches, too, algebra, trigonometry, calculus, which, however, were not much more than collections of haphazard, badly founded rules, whereas geometry was a perfect logical system, where everything rigorously followed from definitions and axioms. You know that things have changed; today mathematicians are prone to reject traditional geometry, because it is not a rigorously deductive system. [Pendant longtemps, les mathématiques ont été synonymes de géométrie. En réalité, il existait d'autres branches, telles que l'algèbre, la trigonométrie et le calcul, qui n'étaient toutefois guère plus que des recueils de règles aléatoires et mal fondées, alors que la géométrie était un système logique parfait, où tout découlait rigoureusement de définitions et d'axiomes. Vous savez que les choses ont changé ; aujourd'hui, les mathématiciens ont tendance à rejeter la géométrie traditionnelle, car elle n'est pas un système rigoureusement déductif.].
Et que dire de la formule-choc assénée par Jean Dieudonné (1906-1992) – le grand mathématicien lillois comptant parmi les membres fondateurs, mais aussi parmi les plus prolifiques, de l’influent groupe Bourbaki qui s’était positionné comme fer de lance du formalisme et de la hiérarchisation des structures abstraites – lors d’un séminaire, en 1969 : « À bas Euclide! Mort aux triangles! ».
Sous l’impulsion imprimée par Bourbaki, la géométrie – déjà en voie de se dissoudre dans l’algèbre et l’analyse – était en train de se redéfinir en une discipline sans diagrammes ni représentations visuelles, où tous les résultats ne devaient être obtenus que par le raisonnement. Indigne de confiance, car elle nous abandonnait à la subjectivité et à l’erreur, la perception visuelle du réel devait être expurgée des mathématiques.
Fort heureusement, il s’en trouva – comme Harold Scott MacDonald Coxeter – pour s’opposer à cet effort de raréfaction de l’atmosphère dans laquelle s’effectuent les mathématiques et pour tenter de réhabiliter l’indispensable imagerie interne dans un premier temps, puis l’utilisation de supports visuels pour favoriser, sinon la compréhension, du moins l’apprentissage, dans un deuxième temps.
Satyan L. Devadoss et Joseph O’Rourke, respectivement professeurs au Williams College et au Smith College, appartiennent au courant alimenté par Coxeter. Ils nous proposent, dans la seconde édition de Discrete and Comptutational Geometry, publiée aux presses de l’Université Princeton, un remarquable ouvrage d’introduction à une branche relativement récente des mathématiques dont les racines puisent à des sources remontant à l’Antiquité grecque et dont les fruits sont résolument ancrés dans le XXIe siècle
Digital competence in Quebec’s teacher education programs: Toward a critical perspective
Get PDFDigital competence, beyond core content knowledge, is a key skill for many teachers in this day and age, and several frameworks for this have been proposed internationally. In Canada, some provinces and territories are currently implementing rules and guidelines regarding the digital competencies of teachers. However, only Quebec has an actual one that is linked to teachers, with specific dimensions integrating critical knowledge and attitudes. This interpretive study examines Quebec’s teacher reference and digital-competency frameworks by exploring their integration into teacher-education programs. Two qualitative data-collection methods, namely, semi-structured interviews and document analysis, were used in this study. The sample included seven university professors from the education departments at different Quebec universities and 34 descriptions of digital technologies courses in Quebec’s teacher-education programs. The main results indicate that digital competence is included in at least one course in teacher-education programs, and that instrumental elements are prioritized over critical and ethical digital dimensions. The findings also highlight professors’ awareness of the importance of further developing these less prominent dimensions. The challenges associated with this integration are acknowledged, and the need for future research to develop pedagogical strategies that promote the acquisition of these competencies is emphasized
Mastering Programming: From Testing to Performance in Go
Get PDFThis book is tailored for programmers eager to elevate their software development expertise beyond foundational skills, empowering them to craft code that is not only correct and efficient but also aligned with organizational goals. With a deep dive into unit testing, concurrency management using Go’s goroutines, and performance optimization, the author bridges the gap between low-level technical details—like memory and processor mechanics—and high-level algorithm design principles. Through hands-on examples in Go and Python, alongside advanced techniques such as fuzzing, mutexes, and atomic operations, this book delivers a practical, no-nonsense approach to organizing workflows, ensuring robust code quality, and preventing regressions. It tackles the intricacies of parallelism and synchronization in complex projects head-on, offering solutions to real-world challenges. Each chapter concludes with targeted exercises to solidify understanding, making this an indispensable, all-in-one resource for driven developers aiming to excel in modern programmin
Paley inequality for the Weyl transform and its applications
Get PDFThe Hausdorff-Young inequality is a foundational result in Fourier analysis which admits several generalizations.
The main aim of the paper under consideration is to study Paley’s extension of the Hausdorff-Young
inequality and to establish variants for the Weyl transform associated to locally compact abelian groups.
Following a presentation of the historical and conceptual context (Section 1), and a detailed presentation
of the results on which the proofs of the main theorems are based (Section 2), two generalizations of
the Hausdorff-Young theorem are obtained. The first extends the Hausdorff-Young theorem to Lorentz
spaces while the second (a version of the Paley inequality) is a more generalized result that extends
the Hausdorff-Young theorem to non-commutative Lorentz spaces on the Banach algebra of all bounded
operators on L2(G) where G is a locally compact abelian group.
It was in this context that the French mathematician Louis Gérard defended, in 1892 at the Faculty of
Sciences in Paris, a thesis titled Sur la géométrie non euclidienne [On Non-Euclidean Geometry]. Gérard’s
thesis – the most significant work specifically on this subject published in French-speaking countries since
the Memoirs of Joseph-Marie De Tilly [1870] and Camille Flye Sainte-Marie [1871] – has not yet been
the subject of an in-depth study, and this gap is what the article under review seeks to address.
First, a word about Louis Gérard. Born in 1859 in Grand, in the historical region of Lorraine, in eastern
France, Gérard spent his entire career in secondary education. His thesis on non-Euclidean geometry thus
represents his main contribution to mathematical research. The date of his death is unknown but is after
1939.
As this article demonstrates, Gérard’s thesis serves as a transitional work between the contributions of
the inventors of non-Euclidean geometry and the purely axiomatic research of the late 19th and early
20th centuries. For this reason, it deserves our attention
AI & XR Explorations to Support Social Interactions: Speculative Design for Ubiquitous Workplace Space by and for Neurodivergent Employees
Get PDFThis study explores the potential of interdisciplinary theories and advanced technologies, such as augmented realities and artificial intelligence, to address the socio-professional integration challenges faced by neurodivergent individuals, particularly those on the autism spectrum. It investigates the design of personalized, functional spaces that integrate interconnected living environments and intelligent systems tailored to support communication needs.
Using speculative design methodology, the research adopts an experiential framework to examine alternative solutions, starting with a central hypothesis and testing it through debates with researchers, experts, neurodivergent individuals, and knowledge users. The premise is rooted in the recognition that neurodivergent individuals encounter significant barriers to social interaction and communication, limiting their integration into professional and social
environments. This project envisions leveraging Internet of Things devices and immersive extended reality systems to create accessible, personalized spaces where individuals can reflect, feel secure, and engage in meaningful interactions. These spaces aim to foster confidence, well-being, and adaptability while addressing the limitations of existing tools. Hypotheses are informed by frameworks addressing autistic experiences and studies on self-narratives, proposing innovative applications of AI and immersive technologies. A diegetic device illustrates an augmented reality environment allowing users to practice social scenarios, engage in interest-based interactions, and participate freely, while preserving the emotional safety of a personalized setting. The research highlights the potential for such environments to transform social and workplace adaptation, fostering inclusion and employability
amongeurodivergent individuals. Results and discussions delve into emerging ideas, providing a foundation for advancing adaptive strategies that meet the specific needs of this population. By bridging theoretical and technological innovations, this work seeks to open new possibilities for integrating neurodivergent individuals into society while enhancing their quality of life through tailored, intelligent, and interactive solutions
Digital disruption or union neutralization? A diachronic history of tensions between the figures of the professional and the worker in the history of a Canadian newspaper
No full textIn this chapter, I propose a genealogy of the tensions between the figures of the professional and the worker in the history of journalistic labor in Canada. By examining the case of the newspaper Le Devoir in Quebec (Canada), I first look back at the historical tensions between the typographers’ pressroom and the journalists’ newsroom. In the mid-20th century, a porous line separated manual workers from journalists with relative autonomy in newsrooms. However, digital transformation since the 1990s has brought major changes. The pressroom has been computerized, and journalists have been forced to accept the rhetoric of permanent innovation. In the end, it is now journalists who do repetitive, alienating work. A class recomposition is at the heart of this mutation
L’analyse en classe latente et de profil
Get PDFLes analyses en classes latentes permettent d’identifier des sous-groupes d’individus normalement inobservables à partir de variables ayant une échelle nominale ou ordinale. Les fondements de base, les méthodes de détermination du nombre de classes ainsi que les analyses posthoc seront présentés. Ce cours couvrira comment réaliser ces analyses avec R en recourant au package poLCAExtra. Les avantages et inconvénients de ce progiciel comparativement à d’autres seront discutés