Re: Programming skills required by mathematicians?

Nasser Abbasi wrote:
> "rAgAv" <ragav.payne@[EMAIL PROTECTED]
> wrote in message
>
news:7479d8a6-9aba-418f-9bb3-073fc3bd802e@[EMAIL PROTECTED]
>> Hello,
>>
>> I'm a highschool graduate and I'm going to major in Mathematics this
>> Fall. I would like to have a foundation in programming so that it
>> would be useful in my later career as a mathematician with interests
>> in logic, numerical analysis, formal systems and that sort.
>>
>> I don't know enough technicalities to seek the right sort of
>> programming that I should learn now. I wish to hear advice on what
>> sort of programming skills a pure mathematician would find useful.
>>
>> Regards.
>>
>> PS - At the moment, I know only the basics of C++.
>
> You probably need to learn how to use a CAS system and how to program 
in it.
> This could be a useful skill to have over the years.
>
> There are many CAS systems out there, find out you like, and learn its
> programming and commands.
>
> http://en.wikipedia.org/wiki/Computer_algebra_system

Good advice!

Could I raise a different twist on this question?

Over the years, starting almost at the beginning of the personal
computer revolution, I've seen (at least three) cases of
extremely bright kids, with the potential to become excellent
pure mathematicians or physicists, be seduced into programming,
to the point of not majoring in mathematics or physics, or
dropping out of university early because of high salaries
offered by recruiters or to start their own companies.

Now maybe that's not a bad thing, but it's my prejudice that it
is.

I think it would be good if those kids had their mind space
exposed to some real, pure mathematics to counterbalance the
siren call of programming, before it's too late.

How about reading some self-contained pure math over the summer,
like Landau's "Foundations of Analysis"*, or the appendix to
Kelley's "General Topology" on "Elementary Set Theory"?

I know for a fact that Landau is accessible to at least some
bright high school students, say, who have done AP calculus,
and believe Kelley's appendix to be so as well.

You can infer that there's some uncertainty about the
suitability of Landau for this purpose from these reviews:

rave:
http://www.amazon.com/review/R3R4YQOMY3ARJU/ref=cm_cr_rdp_perm

pan:
http://www.amazon.com/review/R3INMVDAQZODN2/ref=cm_cr_rdp_perm


But maybe something along that line would be a good idea.

Or maybe the OP is already resistant to premature seduction by
programming...

-- David