Search results for " math"
showing 10 items of 11183 documents
I poligoni stellati: origini storiche ed implicazioni didattiche
2019
The genesis of mathematical concepts in the evolutionary line of human thought in the long story and the genesis in individual optics possess evident analogies. Starting from this assumption, we describe an activity presented to 15-year-old students; the aim was to consolidate fundamental concepts of Euclidean geometry related to regular polygons. The experimentation has used a didactic approach based on the historical evolution of the formal definition of regular star polygon through the centuries. The activity and the results obtained in terms of internalization of the concepts in the students are showed.
Students' usage patterns of video recorded lectures in an undergraduate mathematics course
2018
International audience; It is customary for some universities to offer recordings of live lectures to students. Whether this improves learning and academic performance is debated in the literature. As with most technology, correct usage can lead to increased academic performance, but there are also usage patterns that can be considered counter productive, especially for learning mathematics. In order to investigate patterns in students' usage of such online recorded live lectures, we analyze log files from a server holding the recordings of an undergraduate mathematics course. This poster presents results from the statistical analysis and discusses some of the usage patterns found in light …
Engineering students' engagement with resources in an online learning environment
2018
International audience; This study explores engineering students' interactions with different resources in an online learning environment. The constituent resources of this environment involve MyMathLab which is an online interactive system for practicing mathematics, the tutorial videos, and the textbook. We conducted a qualitative case study to observe a small group of undergraduate engineering students interacting with the resources in a Calculus course. Employing the documentational approach to didactics, we identified several techniques while participants used resources to practice mathematics in MyMathLab environment. We discuss the pragmatic and epistemic value of the identified tech…
Predictors of performance in engineering mathematics
2018
International audience; Mathematics in university courses was identified as a main obstacle for engineering students in the beginning of their study. Since difficulties with mathematics could lead to a dropout, our research aims to analyse students' profiles referring to individual characteristics that allow identifying possible risks for students' achievement or success in the first year of study. As a first step to identify possibly risky profiles, we started to find possible predictors of students' performance. For this, we give a short overview of the research state and our derived research interest. We discuss theoretical constructs that are possibly crucial characteristics of students…
A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence
2020
The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions.
Regular solutions for nonlinear elliptic equations, with convective terms, in Orlicz spaces
2022
We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in the Orlicz-Sobolev spaces and under general growth conditions on the convection term. The sub- and supersolutions method is a key tool in the proof of the existence results.
The Radó–Kneser–Choquet theorem for $p$-harmonic mappings between Riemannian surfaces
2020
In the planar setting the Rad\'o-Kneser-Choquet theorem states that a harmonic map from the unit disk onto a Jordan domain bounded by a convex curve is a diffeomorphism provided that the boundary mapping is a homeomorphism. We prove the injectivity criterion of Rad\'o-Kneser-Choquet for $p$-harmonic mappings between Riemannian surfaces. In our proof of the injecticity criterion we approximate the $p$-harmonic map with auxiliary mappings that solve uniformly elliptic systems. We prove that each auxiliary mapping has a positive Jacobian by a homotopy argument. We keep the maps injective all the way through the homotopy with the help of the minimum principle for a certain subharmonic expressio…
Discussing Mathematical Learning and Mathematical Praxeologies from a Subject Scientific Perspective
2018
International audience; This programmatic contribution discusses the link between concepts from Anthropological Theory of Didactics (ATD) and the “subject-scientific point of view” according to Holzkamp (1985, 1993). The main common concern of ATD and the subject-scientific approach is to conceptualize and analyse “objects” like “institutionalized mathematical knowledge” and “university” not as conditions that cause reactions but essentially as meanings in the sense of generalized societal reified action possibilities. The link of both approaches is illustrated by the issue of “real numbers” in the transition from school to university: Hypotheses are derived for further actual-empirical res…
Location of solutions for quasi-linear elliptic equations with general gradient dependence
2017
Existence and location of solutions to a Dirichlet problem driven by $(p,q)$-Laplacian and containing a (convection) term fully depending on the solution and its gradient are established through the method of subsolution-supersolution. Here we substantially improve the growth condition used in preceding works. The abstract theorem is applied to get a new result for existence of positive solutions with a priori estimates.
Attacking TrustZone on devices lacking memory protection
2021
AbstractARM TrustZone offers a Trusted Execution Environment (TEE) embedded into the processor cores. Some vendors offer ARM modules that do not fully comply with TrustZone specifications, which may lead to vulnerabilities in the system. In this paper, we present a DMA attack tutorial from the insecure world onto the secure world, and the design and implementation of this attack in a real insecure hardware.