Abstract. Let X and Y be affine nonsingular real algebraic varieties. A general problem in Real Algebraic Geometry is to try to decide when a smooth map f : X → Y can be approximated by regular maps in the space of C ∞ mappings from X to Y , equipped with the C ∞ topology.In this paper we give a complete solution to this problem when the target space is the standard 2-dimensional sphere and the source space is a geometrically rational real algebraic surface. The approximation result for real algebraic surfaces rational over R is due to J. Bochnak and W. Kucharz.Here we give a detailed description of the more interesting case, namely real Del Pezzo surfaces of degree 2.
Let X and Y be affine nonsingular real algebraic varieties. A general problem in real algebraic geometry is to try to decide when a continuous map f : X → Y can be approximated by regular maps in the space of C 0 mappings from X to Y , equipped with the C 0 topology. This paper solves this problem when X is the connected component containing the origin of the real part of a complex Abelian variety and Y is the standard 2-dimensional sphere.
Let X and Y be affine nonsingular real algebraic varieties. A general problem in Real Algebraic Geometry is to try to decide when a C ∞ mapping, f : X → Y , can be approximated by regular mappings in the space of C ∞ mappings, C ∞ (X, Y ), equipped with the C ∞ topology. In this paper, we obtain some results concerning this problem when the target space is the 2-dimensional standard sphere and X has a complexification X C that is a rational (complex) surface. To get the results we study the subgroup H 2 C−alg (X, Z) of the second cohomology group of X with integer coefficients that consists of the cohomology classes that are pullbacks, via the inclusion mapping X → X C , of the cohomology classes in H 2 (X C , Z) represented by complex algebraic hypersurfaces.
In this article we aim to deepen our understanding of the content and nature of the early childhood teacher's knowledge, focusing on those aspects which might promote students' algebraic thinking. Approaching arithmetic from the viewpoint of algebra as an advanced perspective and considering the analytical model Mathematics Teachers' Specialised Knowledge, we analyse the specialised knowledge in a classroom of five-year-olds handled by an experienced teacher in a lesson on the decomposition of the number 6. Moreover, alternative management of the session is proposed in order to promote early algebraic thinking. In the domain of mathematical knowledge, this analysis has revealed the specificity of the knowledge that this professional must have of the natural number. In the domain of pedagogical content knowledge, it has highlighted the many elements of the knowledge of mathematics teaching that should be possessed to promote algebraic thinking at this educational stage. These elements appear to be more closely related to a profound knowledge of the mathematics taught than to pedagogical knowledge of a more general nature.
RESUMENEn este artículo tratamos de profundizar en nuestra comprensión sobre el contenido y naturaleza del conocimiento del profesor de Educación Infantil, centrándonos en aquellos aspectos que podrían fomentar el pensamiento algebraico de los alumnos. Enfocando la aritmética desde el punto de vista del álgebra como perspectiva avanzada y, considerando el modelo analítico Conocimiento especializado del profesor de matemáticas (Mathematics Teachers' Specialised Knowledge, MTSK), analizamos el conocimiento especializado en una clase de alumnos de cinco años en la que una profesora con experiencia imparte una lección sobre la descomposición del número 6.
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