i was just informed that modular arithmetic is not taught in school (here) at all. like at any stage. IS THIS REALLY TRUE????
that is quite astounding. why is it not taught?
i mean it’s not say very difficult, especially if you couch it as “clock arithmetic”, which is america’s (dumbed down but no less accurate) take on it. And from there it’s very easy to progress to finite fields.
also i realised learning induction in secondary school is also not the norm. (my colleagues were trying to educate me about normal school education at lunch today). that’s another thing that i also think is not difficult to pick up, especially if you are taught properly. i mean it’s so rule-oriented it’s perfect for singaporean math students. It’s like teaching BODMAS or like models or algorithms. Just follow the steps. Let Pk be the statement we are trying to prove. Show P0 is true. Show if Pk is true, then Pk+1 is true. So Pk is true for all k > -1. So simple. And useful for math later on (especially in combi)
at the same time there is no real hurry to learn it. It’s just surprising, coming from the view point of someone who has seen a pretty broad reach of simple math, for someone not to know any of this by 16. But it could be worse. There are americans who haven’t dealt with complex numbers and calculus by uni. All in all I would venture to say that the singapore education system is definitely one of the best for math. If you are interested, you will get to prove things in secondary sch/jc. And if you’re not, you’ll still be pretty adept at calculus and other useful mathematical concepts for engineering and physics. And math professors in the states are well aware of its superiority.
We only got to talking about it because an arrow was randomly flying for someone from the lab to coach the next batch of interested kids from NUS high on crypto (we do it every year apparently). And the first lesson was on modular arithmetic. (which was when I got really surprised and everyone kindly and collectively informed me that i didn’t know squat about our public school system). K and I were informed of the arrow but we didn’t agree to it or anything. She sounds quite amenable to it and I… shall niftily step out of the arrow’s parabola the next time it is shot. I don’t really see the point, i mean the amount we can teach them, they can also learn by themselves if they are interested/motivated enough. And after that a subsequent (connected) arrow will be shot to supervise YDSP projects by the same students. yuck. I am not particularly interested in supervising some young over-ambitious schmuck’s project for him to include in his resume for uni. In all I don’t really see the point of the whole thing. Is this some charitable corporate outreach thing where we teach kids who will never get such lessons otherwise? What is in it for the company? Publicity, I guess. But there is no guarantee that they will apply for a job after attending our (free) lessons that will take up lots of my time to plan and assign homework, nor that they will take it seriously. Couldn’t they just do the coursera course? Forgive me for being an idealist, but I think any lesson that is conducted ought to be conducted by a teacher who really wants to share his/her knowledge and attended by a student whose primary goal is to learn more about the subject matter that is being taught (as opposed to attending to bolster his resume). Same as how if any child is to be had the parents should REALLY want a child and the child should REALLY want to be born. To care less would be to shortchange the student/child.
See if you can translate the logic statement in the title. All the chineseness is really getting to me.