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Matemática
AFM
[Annals of Formalized Mathematics]
AFM
Annals of Formalized Mathematics
Fundada em 2024, a revista Annals of Formalized Mathematics, apoiada pela MathOA, publica artigos originais sobre matemática formalizada e aplicações matemáticas de assistentes de prova. A revista aceita artigos em inglês que são normalmente acompanhados por um artefacto de código.
- Diretor de publicação: Jos Baeten
- Editores-gerais: Robert Y. Lewis ; Filippo A. E. Nuccio Mortarino Majno di Capriglio
- Tipo de suporte: digital
- Periodicidade: gradual
- Ano de criação: 2024
- Data de disponibilização online na Episciences: 2024
- eISSN: 3117-4604
- Disciplinas: matemática formalizada
- Idiomas da publicação: inglês
- Processo de avaliação: estudo cego
- Licença CC BY 4.0
- Editor: MathOA
- Endereço postal: Centrum Wiskunde & Informatica, P.O. Box 94079, 1090 GB Amsterdam
- País: Países Baixos
- Contacto: afm AT episciences.org
Últimos artigos
Formalising the Bruhat-Tits Tree
In this article we describe the formalisation of the Bruhat-Tits tree - an important tool in modern number theory - in the Lean Theorem Prover. Motivated by the goal of connecting to ongoing research, we apply our formalisation to verify a result about harmonic cochains on the tree.
Ludwig, Judith
April 21, 2026
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A formalization of Borel determinacy in Lean
We present a formalization of Borel determinacy in the Lean 4 theorem prover. The formalization includes a definition of Gale-Stewart games and a proof of Martin's theorem stating that Borel games are determined. The proof closely follows Martin's "A purely inductive proof of Borel determinacy".
Manthe, Sven
March 13, 2026
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Matemática
CM
[Communications in Mathematics]
CM
Communications in Mathematics
Existente desde 2009, a Communications in Mathematics é a continuação da revista Acta Mathematica et Informatica Universitatis Ostraviensis, fundada em 1993, que se tornou a Acta Mathematica Universitatis Ostraviensis em 2003. A Communications in Mathematics publica em inglês artigos de investigação e de estudo em todas as áreas da matemática pura e aplicada, da física matemática e da informática.
- Diretor de publicação: Jan Lata
- Redator responsável: Ivan Kaygorodov
- Tipo de suporte: digital
- Periodicidade: anual
- Ano de criação: 2009
- Data de disponibilização online na Episciences: 2021
- eISSN: 2336-1298
- Disciplinas: matemática
- Idiomas da publicação: inglês
- Processo de avaliação: estudo cego
- CC BY-SA 4.0 licence
- Editor: University of Ostrava
- Endereço postal: Dvořákova 7, 701 03 Ostrava
- País: República Checa
- Contacto: cm AT episciences.org
Últimos artigos
Cup product of inhomogeneous Tate cochains, and Galois cohomology of tori over local fields that split over cyclic extensions
In this note we give formulas for cup product in Tate cohomology in terms of inhomogeneous cochains. Using one of these formulas, for a torus T defined over a non-archimedean local field K and splitting over a cyclic extension of K, we compute explicit cocycles representing all cohomology classes in H^1(K,T).
Borovoi, Mikhail
July 08, 2026
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On the sizes of the maximal prime powers divisors of factorials
Let p be any prime, and $p^(ν_p(n!))$ the maximal power of $p$ dividing $n!$. It is proved that there exists a positive integer $n_0$, which depends only on $p$, such that $q^(ν_q(n!)) < p^(ν_p(n!))$ for all $n \ge n_0$ and all primes $q > p$. For twin primes $p$ and $q = p + 2$ it is proved that the minimal $n_0$ satisfying $q^(ν_q(n!)) < p^(ν_p(n!))$ for all $n \ge n_0$ is given by $n_0 = (p^2+p)/2$.
Levy, Dan
July 07, 2026
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Matemática
EpiDEMES
[Épijournal de Didactique et Epistémologie des Mathématiques pour l’Enseignement Supérieur]
EpiDEMES
Épijournal de Didactique et Epistémologie des Mathématiques pour l’Enseignement Supérieur
A Epijournal de Didactique et Epistémologie des Mathématiques pour l’Enseignement Supérieur (EpiDEMES) é uma revista especializada fundada em 2019 que publica artigos em francês ou em inglês. A EpiDEMES tem como objetivo a criação de uma base documental para a formação inicial e contínua dos docentes do ensino superior. As áreas abrangidas são a didática e a epistemologia da matemática (classificação AMS 97-XX Mathematics Education) tendo como objetivo a matemática do ensino superior e os fenómenos associados ao seu ensino-aprendizagem.
- Diretor de publicação: Nicolas Grenier-Boley
- Redators responsáveis: Nicolas Grenier-Boley e Hussein Sabra
- Tipo de suporte: digital
- Periodicidade: semestral
- Ano de criação: 2019
- Data de disponibilização online na Episciences: 2019
- eISSN: 2970-166X
- Disciplinas: matemática, didática da matemática
- Idiomas da publicação: inglês, francês
- Processo de avaliação: estudo cego
- CC BY-SA 4.0 licence
- País: França
- Contacto: epidemes AT episciences.org
Últimos artigos
Des croquis comme support de raisonnement et de changement de registres
We are convinced of the usefulness of sketches and diagrams during mathematical work but the observation is made in our practices that they are not spontaneously used by students. In order to study the understanding and use of sketches by mathematics students, we designed and then proposed a test at different university levels. The test consists of five exercises.The first concerns different representation registers of a set of numbers, the second on a graphic proof of an implicative algebraic proposition and the last three on the graphic approch to the notions of injectivity, surjectivity, bijectivity in the context of the analysis. The sketches, proposed or requested in each exercise, are intended to be aids to changes of register and reasoning. We present what motivated the choices and developments of the exercises then we analyze the results of these tests. In each case, we see difficulties in understanding and the sketches proposed, which leads to think that the sketch must be the subject of specific work at the university level.
Grenier, D
July 09, 2026
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Peer assessment in mathematics: activity of students evaluating proofs
This article deals with peer-assessment in the context of higher education teaching in mathematics, and examines the nature of student activity when assessing work,more precisely proofs, produced by peers. After an overview of research on peer assessment, we propose an experiment with students in a specific post-secondary scientific class, and analyze the activity of the students involved. Our analyses are based on a priori analyses of the proposed tasks and tools from research on students personal mathematical work. We base on written notes of assessments, observations of pairs in assessment situations, and answers to a questionnaire on the perception of their activity. We have identified some specific student activities during the peer assessment process, in particular related to the analysis and correction of proofs, but also to the awareness of the issues associated with evaluation. This enables us to argue for the potential of peer assessment in higher mathematics education.
Veuillez--Mainard, Juliette
July 09, 2026
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Matemática
Epiga
[Épijournal de Géométrie Algébrique]
Epiga
Épijournal de Géométrie Algébrique
A Epijournal de Géométrie Algébrique (Epiga) é uma revista de matemática especializada criada em 2016. Apoiada pela Associação Épiga, publica anualmente artigos em francês ou em inglês. As áreas abrangidas são a geometria algébrica no sentido mais amplo, incluindo a geometria complexa e aritmética, a teoria dos grupos algébricos e das representações.
- Diretor de publicação: Gianluca Pacienza
- Editor coordenador: Daniel Greb
- Tipo de suporte: digital
- Periodicidade: anual
- Ano de criação: 2016
- Data de disponibilização online na Episciences: 2016
- eISSN: 2491-6765
- Disciplinas: matemática, geometria algébrica
- Idiomas da publicação: inglês, francês
- Processo de avaliação: estudo cego
- CC BY-SA 4.0 licence
- Editor: Association Épiga
- Endereço postal: Institut Elie Cartan de Lorraine, Université de Lorraine, BP 70239, 54506 Vandœuvre-lès-Nancy Cedex
- País: França
- Contacto: epiga AT episciences.org
Últimos artigos
Uniform unlikely intersections for unicritical polynomials
Fix $d\geq2$, and consider the family $f_{t}(z)=z^{d}+t$ of polynomials parameterized by $t\in\mathbb{C}$. In this article, we will show that there exists a constant $C(d)$ such that for any $a,b\in\mathbb{C}$ with $a^{d}\neq b^{d}$, the number of $t\in\mathbb{C}$ such that $a$ and $b$ are both preperiodic for $f_{t}$ is at most $C(d)$.
Fu, Hang
September 09, 2026
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Lines, Twisted Cubics on Cubic Fourfolds, and the Monodromy of the Voisin Map
For a general cubic fourfold $Y$ with associated Fano variety of lines $ F $, we show that the monodromy group of the finite degree 16 rational Voisin self-map $ψ\colon F \dashrightarrow F$ is maximal. To achieve this, we investigate the intriguing interplay between $ ψ$ and the fixed locus of the antisymplectic involution on the LLSvS variety $ Z $, examined via the degree 6 Voisin map $F \times F \dashrightarrow Z $.
Giovenzana, Franco
September 03, 2026
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Matemática
HRJ
[Hardy-Ramanujan Journal]
HRJ
Hardy-Ramanujan Journal
Criada em 1978, a Hardy-Ramanujan Journal é uma revista especializada. Editada pela Hardy-Ramanujan Society, publica anualmente artigos em inglês de matemática fundamental, mais precisamente, de teoria dos números.
- Diretor de publicação: C.S. Aravinda
- Redators responsáveis: Atul Dixit, Saurabh Kumar Singh, Kotyada Srinivas
- Tipo de suporte: digital
- Periodicidade: anual
- Ano de criação: 1978
- Data de disponibilização online na Episciences: 2014
- eISSN: 2804-7370
- Disciplinas: matemática, teoria dos números
- Idiomas da publicação: inglês
- Processo de avaliação: estudo cego
- CC BY 4.0 licence
- Editor: Hardy-Ramanujan Society
- Endereço postal: Bhavana Trust, No.24, `Athreya’ 21st Main, 2nd Block, BSK I Stage BANGALORE — 560 050
- País: Índia
- Contacto: hrj AT episciences.org
Últimos artigos
Vanishing Coefficient Results in Three Families of Infinite q-products
In the recent past, the work in the area of vanishing coefficients of infinite $q$-products has been taken to the forefront. Weaving the same thread as Ramanujan, Richmond, Szekeres, Andrews, Alladi, Gordon, Mc Laughlin, Baruah, Kaur, Tang, we further prove vanishing coefficients in arithmetic progressions moduli 5, 7, 11, 13, 17, 19 and 29 of the following four families of infinite products, where $\{X_{a,b,sm,km,u,v}(n)\}_{n\geq n_0}$, $\{Y_{a,b,sm,km,u,v}(n)\}_{n\geq n_0}$ and $\{Z_{a,b,sm,km,u,v}(n)\}_{n\geq n_0}$ are defined by\begin{align*}\sum_{n\geq n_0}^{\infty}X_{a,b,sm,km,u,v}(n)q^n:=&\p(q^{a},q^{sm-a};q^{sm})^u\p(q^{b},q^{km-b};q^{km})^v, \\\sum_{n\geq n_0}^{\infty}Y_{a,b,sm,km,u,v}(n)q^n:=&\p(q^{a},q^{sm-a};q^{sm})^u\p(-q^{b},-q^{km-b};q^{km})^v, \\\sum_{n\geq n_0}^{\infty}Z_{a,b,sm,km,u,v}(n)q^n:=&\p(-q^{a},-q^{sm-a};q^{sm})^u\p(q^{b},q^{km-b};q^{km})^v,\end{align*}here $a, b, s, k, u$ and $v$ are chosen in such a way that the infinite products in the right-hand side of the above are convergent and $n_0$ is an integer (possibly negative or zero) depending on $a, b, s, k, u$ and $v$. The proof uses the Jacobi triple product identity and the properties of Ramanujan general theta function.
Ananya, S
April 27, 2026
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Modular transform of free fermion generalised Gibbs ensembles and generalised power partitions
In [1] a conjecture for the modular transformation of the free fermion generalised Gibbs ensemble (GGE) was given where only the KdV charge associated to the weight four quasi primary field was inserted. In this paper we first generalise this conjecture to the case with an arbitrary, finite collection of KdV charges in the GGE. These GGEs are generalisations of the generating function of power partitions. We prove the conjectured transformation for the case with a finite number of charges inserted and discuss the case with an infinite number of charges.
Downing, Max
April 27, 2026
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Matemática
jGCC
[journal of Groups, Complexity, Cryptology]
jGCC
journal of Groups, Complexity, Cryptology
A journal of Groups, Complexity, Cryptology (jGCC) é a continuação da revista Groups, Complexity, Cryptology criada em 2009. Revista semestral especializada, a jGCC publica em inglês artigos de investigação nas áreas da teoria combinatória e computacional dos grupos, da teoria da complexidade e da criptologia.
- Diretor de publicação: Murray Elder
- Redators responsáveis: Murray Elder e Vladimir Shpilrain
- Tipo de suporte: digital
- Periodicidade: semestral
- Ano de criação: 2009
- Data de disponibilização online na Episciences: 2020
- eISSN: 1869-6104
- Disciplinas: teoria dos grupos combinatório e computacional, teoria da complexidade, criptologia
- Idiomas da publicação: inglês
- Processo de avaliação: estudo cego
- CC BY 4.0 licence
- Contacto: gcc-contact AT episciences.org
Últimos artigos
On the Hausdorff dimension and attracting laminations for fully irreducible automorphisms of free groups
Motivated by a classic theorem of Birman and Series about the set of complete simple geodesics on a hyperbolic surface, we study the Hausdorff dimension of the set of endpoints in $\partial F_r$ of some abstract algebraic laminations associated with free group automorphisms. For an exponentially growing outer automorphism $ϕ\in Out(F_r)$ we show that the set of endpoints $\mathcal E_{L}\subseteq \partial F_r$ of any of the \emph{attracting laminations} $L$ of $ϕ$ has Hausdorff and packing dimension $0$ for any visual metric on the boundary $\partial F_r$. Similarly that $L\subseteq \partial^2 F_r$ (where $\partial^2 F_r$ is equipped with the product metric of a visual metric) has Hausdorff dimension $0$ and packing dimension $0$. If $ϕ\in Out(F_r)$ is an atoroidal and fully irreducible, we deduce the same conclusion for the set of endpoints of the ending lamination $Λ_ϕ$ of $ϕ$ that gets collapsed by the Cannon-Thurston map $\partial F_r\to \partial G_ϕ$ for the associated free-by-cyclic group $G_ϕ=F_r\rtimes_ϕ\mathbb Z$. By contrast, the set of endpoints of any of these laminations has upper box dimension $>0$ for any visual metric on $\partial F_r$.
Kapovich, Ilya
July 08, 2026
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The group identification problem for $p$-groups of small order
We investigate which group-theoretic invariants are powerful in distinguishing among non-isomorphic p-groups. Based on this, we devise an effective algorithm to solve the group identification problem for the $10,494,213$ groups of order $2^9$. We exhibit 56 pairs of groups of order $2^9$ which are difficult to distinguish by invariants.
Eick, Bettina
July 07, 2026
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Matemática
JNSAO
[Journal of Nonsmooth Analysis and Optimization]
JNSAO
Journal of Nonsmooth Analysis and Optimization
Criada em 2019, a Journal of Nonsmooth Analysis and Optimization (JNSAO) publica gradualmente artigos em inglês sobre todos os aspetos da análise não lisa relacionada com a otimização e os problemas de equilíbrio.
- Diretor de publicação: Christian Clason
- Redators responsáveis: Christian Clason e Tuomo Valkonen
- Tipo de suporte: digital
- Periodicidade: gradual
- Ano de criação: 2019
- Data de disponibilização online na Episciences: 2019
- eISSN: 2700-7448
- Disciplinas: análise variacional, teoria e algoritmos
- Idiomas da publicação: inglês
- Processo de avaliação: estudo cego
- CC BY 4.0 licence
- Contacto: jnsao AT episciences.org
Últimos artigos
A trust-region method for optimal control of ODEs with continuous-or-off controls and TV regularization
A solution algorithm for a special class of optimal control problems subject to an ordinary differential equation is proposed. The controls possess a continuous-or-off structure and are priced by a convex function. Additionally, a total variation regularization is applied to penalize switches. Our solution method combines a trust-region method and a proximal gradient method. The subproblems are solved via Bellman's optimality principle. Convergence with respect to a criticality measure is proven. As a numerical example, we solve a simple optimal control problem involving an SIR model.
Friedemann, Markus
August 31, 2026
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A constructive approach to strengthen algebraic descriptions of function and operator classes
It is well known that functions (resp. operators) satisfying a property~$p$ on a subset $Q\subset \mathbb{R}^d$ cannot necessarily be extended to a function (resp. operator) satisfying~$p$ on the whole of~$\mathbb{R}^d$. Given $Q \subseteq \mathbb{R}^d$, this work considers the problem of obtaining necessary and ideally sufficient conditions to be satisfied by a function (resp. operator) on $Q$, ensuring the existence of an extension of this function (resp. operator) satisfying $p$ on $\mathbb{R}^d$. More precisely, given some property $p$, we present a refinement procedure to obtain stronger necessary conditions to be imposed on $Q$. This procedure can be applied iteratively until the stronger conditions are also sufficient. We illustrate the procedure on a few examples, including the strengthening of existing descriptions for the classes of smooth functions satisfying a Łojasiewicz condition, convex blockwise smooth functions, Lipschitz monotone operators, strongly monotone cocoercive operators, and uniformly convex functions. In most cases, these strengthened descriptions can be represented, or relaxed, to semi-definite constraints, which can be used to formulate tractable optimization problems on functions (resp. operators) within those classes.
Rubbens, Anne
July 13, 2026
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Matemática
JoNAS
[JoNAS - Journal of Non-Associative Structures]
JoNAS
JoNAS - Journal of Non-Associative Structures
JoNAS, the Journal of Non-Associative Structures, is a diamond open-access, electronic, international research journal that publishes research and survey articles in mathematics since 2026. It is dedicated to publishing high-quality original research articles in non-associative algebra and its applications to geometry, combinatorics, mathematical analysis, mathematical physics, and other areas of pure and applied mathematics.
- Director of publication: Jos Baeten
- Editor in chief: Ivan Kaygorodov (University of Beira Interior, Portugal)
- Medium: electronic
- Frequency: continuous
- Date created: 2025
- Date of publication on Episciences: 2026
- eISSN: pending
- Subjects: non-associative algebra
- Language of publication: English
- Review process: single blind peer review
- CC BY 4.0 licence
- Publisher: MathOA
- Address: Centrum Wiskunde & Informatica, P.O. Box 94079, 1090 GB Amsterdam
- Country: The Netherlands
- Contact: jonas AT episciences.org
Últimos artigos
Construction of pre-and post-Lie algebras for stochastic PDEs
We give and study a construction of pre-Lie algebra structures on rooted trees whose edges and vertices are decorated, with a grafting product acting, through a map $ϕ$, both on the decoration of the created edge and on the vertex that holds the grafting. We show that this construction gives a pre-Lie algebra if, and only if, the map $ϕ$ satisfies a commutation relation, called tree-compatibility. We show how to extend this pre-Lie algebra structure to a post-Lie one by a semi-direct extension with another post-Lie algebra. We also define several constructions to obtain tree-compatible maps, and give examples, including a description of all tree-admissible maps when the space of decorations of the vertices is $2$-dimensional and the space of decorations of the edges is finite-dimensional. A particular example of such a construction is used by Bruned, Hairer and Zambotti for the study of stochastic partial differential equations: when no noise is involved, we show that the underlying tree-compatible map is the exponential of a simpler one and deduce an explicit isomorphism with a classical pre-Lie algebra of rooted trees; when a noise is involved, we obtain the underlying tree-compatible map as a direct sum. We also obtain with our formalism the post-Lie algebras described by Bruned and Katsetsiadis.
Foissy, Loïc
August 13, 2026
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Central Products of Cayley-Dickson Loops
This paper studies the triviality of commutators in central products of Cayley-Dickson loops. Two immediate outcomes of this study are (1) the construction of a sequence of non-commutative di-associative loops in which the probability that a random commutator is trivial approaches 1, and (2) an easy proof that if two central products of $n$-fold Cayley-Dickson loops are isomorphic for $n\geq 3$, then the loops in the first product are term-wise isomorphic to the loops in the second product.
Chapman, Adam
June 29, 2026
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Matemática
OCNMP
[Open Communications in Nonlinear Mathematical Physics]
OCNMP
Open Communications in Nonlinear Mathematical Physics
Criada em 2020, a Open Communications in Nonlinear Mathematical Physics (OCNMP) é uma revista de matemática centrada nos problemas não lineares da física matemática. Insere-se na continuidade do Journal of Nonlinear Mathematical Physics (1994-2020) e publica anualmente artigos em inglês.
- Diretor de publicação: Norbert Euler
- Redator responsável: Norbert Euler
- Tipo de suporte: digital
- Periodicidade: anual
- Ano de criação: 2020
- Data de disponibilização online na Episciences: 2021
- eISSN: 2802-9356
- Disciplinas: matemática, física matemática, ciências não lineares
- Idiomas da publicação: inglês, francês
- Processo de avaliação: estudo cego
- CC BY 4.0 licence
- Editor: International Society of Nonlinear Mathematical Physics
- Endereço postal: Auf der Hardt 27, 56130 Bad Ems
- País: Alemanha
- Contacto: ocnmp AT episciences.org
Últimos artigos
Symmetries of the Generalized Yang--Baxter Equations
The generalized Yang-Baxter equations are multi-site versions of the standard Yang-Baxter equation. When spectral parameters are included, such equations are expected to lead to integrable Hamiltonians with local interactions involving multiple degrees of freedom. In this work we characterize both the continuous and discrete symmetries of these equations required to establish an equivalence class of solutions. We find that the set of such symmetries depends on the number of sites on which the equation is supported. In several cases there are more symmetries than the standard Yang-Baxter equation, thus placing heavy constraints on the number of inequivalent solutions and the associated integrable models. As an application we show how to restrict the generic $16\times16$ ansatz to the 30-dimensional subspace invariant under a chosen discrete symmetry subgroup. An explicit $16\times 16$ solution is also written down.
Padmanabhan, Pramod
September 10, 2026
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Co-primeness preserving higher dimensional extension of $q$-discrete Painlevé I, II equations
We construct the $q$-discrete Painlevé I and II equations and their higher order analogues by virtue of periodic cluster algebras. Using particular $k \times k$ exchange matrices, we show that the cluster algebras corresponding to $k=4$ and $5$ give the $q$-discrete Painlevé I and II equations respectively. For $k \ge 6$, we obtain higher-order discrete equations that satisfy an integrability criterion, namely, the co-primeness property.
Okubo, Naoto
August 18, 2026
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Matemática
RDM
[Recherches en didactique des mathématiques]
RDM
Recherches en didactique des mathématiques
Fundada em 1980, Recherches en Didactique des Mathématiques é uma revista internacional que relata a investigação fundamental na didática da matemática. Editada pela Association pour la Recherche en Didactique des Mathématiques, publica artigos em inglês, francês e espanhol três vezes por ano.
- Diretora de publicação: Marie-Line Gardes
- Directora editorial: Cécile Ouvrier-Buffet
- Redatoras responsáveis: Mariam Haspekian y Elisabetta Robotti
- Tipo de suporte: digital
- Periodicidade: três vezes por ano
- Ano de criação: 1980
- Data de disponibilização online na Episciences: 2023
- eISSN: 2728-2422
- Disciplinas: matemática aplicada, didática da matemática
- Idiomas da publicação: francês, inglês, espanhol
- Processo de avaliação: estudo cego
- Licença CC BY 4.0
- Editor: Association pour la Recherche en Didactique des Mathématiques (ARDM)
- Endereço postal: Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75005 Paris
- País: França
- Contacto: rdm AT episciences.org
Últimos artigos
Epistemologische Anforderungen der Zweiten Diskontinuität
Die Hochschulmathematik vermittelt ein stark verdichtetes Wissen, das sich auf mengentheoretische Definitionen und formale Beweise stützt und weitgehend von Kontextbezügen befreit ist. Dies ist die letzte Stufe einer langfristigen Entwicklung des mathematischen Denkens, die mit der physischen Wahrnehmung und dem Handeln in konkreten Situationen beginnt und in einem langen Prozess der Reformulierung und Verfeinerung wächst. Wenn ein junger Student/eine Studentin als Lehrkraft in die Schule zurückkehrt, muss er oder sie zu den Wurzeln zurückkehren und seine oder ihre Schülerinnen und Schüler in diesem Prozess begleiten und unterstützen. Diese Aufgabe ist mit vielfältigen erkenntnistheoretischen Anforderungen verbunden, auf die im folgenden Beitrag eingegangen wird.
Hefendehl-Hebeker, Lisa
April 23, 2026
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Specificity of the knowledge in logic and its consequences on Klein's double discontinuity
In mathematics, logic is a field with a specific and transversal status. Indeed, it allows us to describe, control and validate mathematical activity. Therefore, it seems relevant to teach it in mathematics' classes.First, we present some research results from the DEMIPS’ « Logic and Proof » group. Based on interviews with university teachers, we will show different choices made for these kinds of courses and the different epistemologies relating to the proof that underlie them.Furthermore, since 2009, logic is faintly coming back in the french high school curriculum. Then, how can pre-service teachers rely on their university knowledges and transpose them to teach at high school level? We are going to answer this question of Klein's second discontinuity by presenting results from research in mathematics education about students’ difficulties and by explaining training situations we suggest.
Gandit, Michèle
April 08, 2026
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