Perhaps reconsider the self study question 2.6.1(f)

[DorusKeijzer]

I don't know if these types of issues are welcomed, but I believe that self study queston 2.6.1 (f) is flawed in the sense that it fails to serve it's intended didactic purpose for some people.

in 2.6.1 (f) students have to evaluate the succesfulness of a (flawed) definition of the imaginary constant i.

From my experience in the work groups, quite a few people are unfamiliar with complex numbers and that distracts from the actual intended purpose of the exercise. Those people see the question, think the notion of an imaginary number is absurd (after all, that's kind of what they learned in high school; you can't take the square root of a negative number (complex numbers are only taught to high school students who take extra math courses)) and conclude that that's why the definition is unsuccesful.

I know that there's a brief explanation at the end of the chapter but I find that it doesn't clear it up for some people since they're still stuck on believing there is no such thing as a complex number.

I think complex numbers are really neat and math curious people should be introduced to them but this is not the time and place. I'd rather see the example be reworked to a (similarly flawed) definition of the square root of 2. That definition will be wrong for the same reasons, but there's no added confusion from introducing a concept that might be foreign to some people's ears

[jkorb]

Thanks @DorusKeijzer I'm surprised to hear that people don't learn about imaginary numbers in high-school (anymore?) but that's good feedback. I'll adjust but only push for next year

[DorusKeijzer]

@jkorb RE: your question "(anymore?)", I quickly skimmed a couple of the VWO national exam syllabusses for maths from the last 20 years and I don't think complex numbers have ever been a part of the dutch national exam (and therefore not a mandatory part of the syllabus at the majority of schools). The only place where a student could have run into them in a formal school setting is when they took an extra math subject (known as Math D), which — from what I read online — only 1% of students do (as this option is only available to a relatively small part of students and it can only be taken on top of the normal workload and not to replace another subject).

Incidentally, when trying to research which percentage of students took extra math courses, I ran into a research paper where they compared total math workload between the Dutch, Belgian and German school system and they concluded that Dutch math students who take the subject that includes geometry, algebra and (pre)calculus (VWO wiskunde B) spend significantly less time per week on mahts than german students who do take the equivalent course (Leistungskurs Mathematik), so that might explain the disconnect between your expeirence with high school maths and ours: there is simply less time to go through everything, so things like complex numbers are left out.

[jkorb]

Interesting. I remember being told about imaginary numbers already when we were first introduced to square roots. Like in the context of "Don't take square roots of negative numbers, they're not defined in the reals. For that you have to go to complex numbers, then you can define `\sqrt{-1}=i." But anyways, point taken, will be adjusted in the future. I'll leave the issue open for now to remind me.

PS: I'm thinking of opening a branch with changes for next year. Perhaps I'll reference this issue there...

[DorusKeijzer]

Hi Johannes, I was looking through the latest iteration of the lecture notes, and this question has not been updated. Was this a deliberate choice or did you forget?