Re: motivating a kid into analysis

On 5 Oct 2005 09:12:38 -0700, "Amanda" <sca18@xxxxxxxxxxx> wrote:

>Hello
>
>I'd like some hints from the experienced mathematicians on how I can
>motivate my 14-year-old son into Analysis. I'm an engineer and like
>Math, especially Analysis, and whenever I can I try to study in on my
>own. My boy loves math, but he's into number theory. He loves those
>problems like proving an integer number is prime, for example. He likes
>to deal with things like congruences, Fermat's Little Theorem and
>groups (according to his age, of course).
>I tried to introduce him to Analysis, but I noticed he had some
>difficulty to understand the epsilon-delta definitions of limit and
>continuity. He also showed some difficulty with the concepts of infimum
>and supremum.
>
>I'm not sure, but I think people who specializes in Number Theory are
>not into Analysis that much and vice versa. I've noticed that
>mathematicians that post about Analysis usually don't post about number
>theory, and the converse seems to be true.
>
>Amanda

I recommend these topics:

(1) inequalities -- algebraic methods

(2) geometry -- convexity, geometric inequalities, geometric limits

(3) sequences and series (arithmetic, geometric, limits of sequences,
infinite series)

(4) limits -- algebraic (no epsilon-delta)

Only after the victim is captured by the fascination of the limit
concept, perhaps then try again with epsilon-delta. But I would still
wait. My feeling is, first do sets, logic, proofs, so the student
understands that there is a need for rigor to actually prove something
and gets comfortable with logical statements -- especially statements
with quantifiers.

quasi
.

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