Re: Sectionals questions

• From: nate_1729 <no_reply_at_yahoogroups.com>
• Date: Thu, 13 Feb 2003 16:18:01 -0000
• Message-ID: <b2ggfp+aidl_at_...>

I think Jordan's right here.  Given the set-theoretic underpinnings 
of, well, just about everything, the concept of surjectivity has to 
be one of the N most important concepts in math.

Indeed, surjectivity is an excellent example of an important concept 
that is highly accessible to those without specialized training -- 
look at various pigeon-hole arguments for examples of elementary and 
elegant proofs that use only basic (and intuitive) set theory.

It's laughable to suggest that surjectivity is too specialized, when 
Zorn's lemma and Russell's paradox, just to name two, are asked 
frequently -- both of those are (when studied rigorously) 
exponentially less accessible to the non-specialist.  (One might 
defend these on the grounds that they're more interesting in a purely 
philosophical sense -- I would disagree, but my point here is to note 
that any 'accessibilty' or 'specialization' argument is without 
basis.)

I applaud efforts to ask about surjectivity and other important and 
accessible concepts, in mathematics and elsewhere in academia.  I 
hope that we can eliminate the bias toward things named after people -
- I believe that this at least partially accounts for the popularity 
of Zorn's lemma and Russell's paradox.  Among other things, the fact 
that "Zorn's lemma" comes up more than the "axiom of choice" [they're 
equivalent], to me, provides rather compelling evidence for this 
stance.  (More easily checked, lots of math answers start with 
capital letters.)

--Nate 

--- In quizbowl_at_yahoogroups.com, "Jordan Boyd-Graber <jordanbg_at_y...>" 
<jordanbg_at_y...> wrote:
> 
> > it's a point to be made.  The rough equivalent in my field would
> > be discussing the differences between spectra expected from
> > bremsstrahlung and synchrotron emissions from an astrophysical 
plasma,
> > which I learned (though don't necessarily remember) in an astro. 
class 
> 
> I dunno.  I think that set theory has wider applications than that. 
> Everybody in my frosh math course learned the definitions of closed,
> compact, and open sets.  It's fresher in my mind after taking 
analysis
> (and perhaps I'm just saying this to convince myself that it's 
useful
> for a CS major to take this course).  I would think that any
> mathematically rigorous education (regardless of the eventual major)
> would talk about these things at some point because of their
> importance in probability and the philisophical underpinnings of 
math.
> 
> While I don't know enough about astronomy to make an analogy, I 
think
> it would be more like asking a question (perhaps slightly hard-core)
> about relativity, which is like a basement level for physics.  It
> might be hard, but it's important because everything else is built
> upon that.
> 
> -Jordan