Some Thoughts on Math

God uses geometry as a mean for creation, scholars of the Middle Age believed (picture from Wikipedia)

God uses geometry as a mean for creation, scholars of the Middle Age believed (picture from Wikipedia)

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?

2 Responses to “Some Thoughts on Math”


  1. 1 Akiko 26/08/2011 at 6:54 PM

    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 —-. 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?

    Do they teach Calculus in Primary school? If you speak about education, you should consider what country you referring to… AFAIK, the term Primary and Secondary school has completely different meaning in different country. Let’s say Indonesia vs Germany. I don’t know how they do it in Singapore.

    Then, if it’s in Indonesia, if you want to propose new curriculum, you should tell it to ‘person in charge’ of curriculum in Education Office or above. Then, he/she must really understand the important of Discrete Maths for Primary and Secondary school level… (if not, s/he will definitely reject your proposal) then, School for teacher should do sort of additional “micro teaching” for this subject or government do such training for math teacher. Because, teaching is not only about transferring knowledge. The way you deliver it gives so much effect to students. Well, something like that.

  2. 2 lambrtz 27/08/2011 at 12:39 AM

    Do they teach Calculus in Primary school?

    Not there, but secondary school, if my memory is still correct.

    I was not referring to any particular country’s education system, on the basis that Math curricula in different countries do not diverge very much; only the implementation is different. I found that materials in Math textbooks here is not that different from those in Indonesia. But please CMIIW.

    I notice that if there is a significant curriculum change, certain adaptations must be made, like micro-teaching, as you mentioned. Nevertheless, what I was wondering here is actually the particular reason, as for why DiscretaeMathematics (actually I was particularly thinking of Mathematical logic in particular, instead of the general issue) is commonly deferred until the last high school year in many countries.

    BTW, by primary and secondary schools, I was referring to schools attended by kids whose ages range from 6 to 15.


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