so i finally have something ready to write about [1]: i'm advising a former calculus student of mine on a summer (undergraduate) research project .. and (for me, anyway) it's a scary thing.

many of my colleagues are old hands at this, i know;

so if i seem naive, it's because this is the first go and i don't know any better.

so if i seem naive, it's because this is the first go and i don't know any better.

i worry, for good reason: he's studying a topic i know little to nothing about. in particular, it's not clear to me how easy or hard the problems i pose to him really are .. and as a result, i don't know how much frustration i'm throwing his way.

it depends, of course, how much the student is willing to work. if i give him a badly-posed problem, then a good work ethick can actually be

it depends, of course, how much the student is willing to work. if i give him a badly-posed problem, then a good work ethick can actually be

*bad*.. in the sense that, by working with abandon for too long a time, he burns out and gets turned off by pure maths in the future.
in case it's not clear, i'm encouraging the student to make his own conjectures;

of the established theorems whose proofs he can easily understand,

i'm suggesting him to try his own variants.

in other words .. and for better or worse ..

i'm insisting that i don't give him orders;

he'll have to train himself to think like a pure mathematician,

but i'll be there if he needs advice or guidance.

of the established theorems whose proofs he can easily understand,

i'm suggesting him to try his own variants.

in other words .. and for better or worse ..

i'm insisting that i don't give him orders;

he'll have to train himself to think like a pure mathematician,

but i'll be there if he needs advice or guidance.

i was worried about his technical chops before .. until i realise that if his proof-writing skills require work, then this is potentially the best way that he can practice them: by working with a topic that interests him.

let's hope these aren't another example of famous last words ..!

let's hope these aren't another example of famous last words ..!

[1]

*as you can see at the end of this post, i'll be tagging these thoughts with the handle "Σ:nextgeneration" .. and the usual disclaimer follows: unlike other maths blogs out there, i'm not out to train or educate maths-inclined people out there, at least not directly. instead, i'm going to show you, through my mistakes, what*__not__to do.
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