What kind of maths should be taught in high-schools?

This is an apparently simple question, but the answer is not always obvious.

BUT there are things a teacher (or a problem books writer, etc.) should not ask 16 years old kids in regular schools to solve. One example is Exercise 28, on page 55 from the book by Burtea et al. “Matematica: Culegere de probleme, Clasa X, Trunchi comun si diferentiat”, Ed. Carminis, Pitesti, 2005. The exercise asks: “Show that there are no surjective functions between a set A and the set of all its subsets (ususally denoted by P(A)). ” This exercise is nothing else than what 1st year (university) students in mathematics meet in their mathematical analysis course as “Cantor Theorem”, whose proof is based on a not really intuitive contradiction argument. Kids and trainers preparing themselves for the mathematics olympiad may want to prove Cantor’s result by themselves, but all the others should pick other nicer and more accessible math exercises involving surjective functions…

Author: multiscale

Adrian Muntean obtained his MSc in mathematics from Babes-Bolyai University, Cluj-Napoca, Romania, in 1999. He received his Dr. rer. nat. in 2006 at Bremen University, Germany, where he worked as Wissentschaftlicher Mitarbeiter (researcher) at the Zentrum fuer Technomathematik (Centre for Industrial Mathmeatics) during the period from 2001 to 2007. He continued to work as assitant professor in Applied Analysis with the Eindhoven University of Technology, the Netherlands (2007-2015). His main activities were connected to two institutes CASA (Center for Analysis, Scientific Computing and Applications) and ICMS (Institute for Complex Molecular Systems), before becoming a full professor in mathematics at the Karlstad University in 2015. His research interest focuses on mathematical modeling with differential equations and interacting-particle systems and their applications to the "real world". His work spans the spectrum from fundamental to applied, with mathematical contributions to civil engineering, logistics, combustion engineering, soft matter and complexity, and contributions to asymptotic methods for differential equations with a particular focus on the theory of homogenization. Muntean received his Venia legendi in mathematics with a Habilitationsschrift at the University of Bremen (2011). In 2014 he was visiting professor with the University of La Sapienza in Rome, Italy. He serves on the editorial board of the international journal Advances in Mathematical Sciences and Applications.