Computational Relativistic Astrophysics With Adaptive Mesh Refinement: Testbeds

We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS binary inspiral and coalescence carried out on a workstation having an accuracy equivalent to that of a $1025^3$ regular unigrid simulation, which is, to the best of our knowledge, larger than all previous simulations of similar NS systems on supercomputers. We believe the capability opens new possibilities in general relativistic simulations.Comment: 7 pages, 16 figure

Developing technologically enhanced mathematics pedagogical content knowledge in initial teacher education

© Springer Nature Switzerland AG 2019. Nowadays perspectives on mathematics education argue for student-centred maths teaching that enables students to engage into learning activities and to play an active role in learning. Information and communication technological evolution provides teachers with an ever-increasing diversity of digital and smart tools that may successfully promote students’ deep engagement with the learning tasks. However, mathematics teachers need to learn how to integrate mathematics pedagogical content knowledge with technological knowledge so that they can develop technologically enhanced mathematics pedagogical content knowledge (TEMPCK). TEMPCK is required for teachers to select the best technological tool to teach a given content in the best way to a certain group of students in a specific social and cultural context. Initial mathematics teacher education has a key responsibility on this issue as it is expected to form updated teachers, able to effectively cope with the technological challenges of the moment as well as with the unanticipated challenges of future technology advancements. This chapter presents a few attempts of prospective mathematics teachers to use digital tools to teach different mathematics topics to secondary school students. Suggestions are made to increase the smartness of the learning environments used by the prospective teachers.(undefined)info:eu-repo/semantics/publishedVersio