One. I, being educated as a computer scientist, often cannot help thinking, upon reading papers from Pure Topology, as for how concepts mentioned there can be implemented using computer programming languages. For example, how do we implement the concept of vertex neighbourhood in C++? Whereas Computational Geometry was inaugurated in 1970s by Shannon and Chazelle (despite some earlier papers), probably Computational Topology had not seen as much attention until 1990s, and this sometimes makes me wonder whether implementations of topological concepts are harder to find. Either way, comparison between Pure Geometry, whose life spans across over 5000 years, and Computational Geometry (and Topology) is just like comparing an old, wise sage and a newborn baby.
Two. This semester, I am assigned as an example class assistant in Discrete Mathematics. While re-familiarising myself with concepts in it, an old thought emerges again, that Discrete Mathematics is considerably easier to grasp, let’s say if compared to Calculus, and we can see many applications of it in our daily lives. Some theories on propositional and predicate logic, for example, can help us to prevent ourselves from having fallacious thoughts
and eventually making a cleaner blogosphere. Why is it then only taught in high schools (or equivalent levels)? Why is it not introduced earlier, let’s say in primary schools or secondary schools?