Re: [quizbowl] Re: ICT Comments

William Paul Meyerson <*meyerson_at_mmailliw.yahoo.invalid*> · Sat, 12 Apr 2003 17:10:32 -0400 (EDT)

How about if we use an even more obscure formulation of the definition
(e.g. A function f is said to have this property if f of the closure of V
is contained in the closure of f of V for each set V) as the starting
clue?  This one requires senior year topology level knowledge... the open
set definition is probably junior level real analysis

William

On Sat, 12 Apr 2003, acfraud wrote:

> --- In quizbowl_at_yahoogroups.com, Alexander Richman <arichman_at_b...>
> wrote:
> > At 04:19 PM 4/12/2003 +0000, you wrote:
> > >Experts? Senior year as math majors? That's an exaggeration.
> >
> > Maybe this is the whole root of the disagreement.  I don't consider
> NAQT
> > (even ICT) to be a place where only grad students (or beyond)
> should be
> > "experts" in any field for the purpose of askability of
> > questions.  Certainly, I don't view an old fogey Ph.D. like me to be
> the
> > right audience. If we disagree at this stage, then I hope we can
> just agree
> > to disagree.
>
> I think I did not phrase this as I intended - I meant that it's an
> exaggeration to say that only experts, or senior year math majors,
> would know that definition of continuous, not that one need be more
> than a senior year math major to be an expert. I agree that questions
> should not be targetted only at grad students in a field.
>
> > Good for you.  VERY few people fit under your situation or used
> Spivak's
> > book in their regular calculus course.  Even in real analysis, it
> depends
> > whether it's done in one or several variables as to whether that
> definition
> > will be there.  Not many schools use Baby Rudin any more.
>
> I expect that among the teams at the ICT with better science and math
> players, however, most would have a person who would be familiar with
> this definition. The question was certainly answered quickly in the
> room I was in, and not by me; I believe 3 people were buzzing at the
> time. The average state of mathematical education is not relevant here
> so much as the average mathematical knowledge among the better teams
> at the ICT, as the goal of the ICT is to accurately discriminate among
> those teams.
>
> > So may I ask what you would prefer in this case?  An operator based
> > definition in which the most expert will be sitting asking
> themselves
> > whether they want continuous or bounded?  Or perhaps a list of
> functions
> > that might have to be quite long before only the only common
> > characteristic, and again the most expert will likely be sitting
> longer
> > than some who know less?  For many mathematical terms, an
> unfamiliar, or
> > unusually formulated definition is often the best way to get an
> unambiguous
> > clue quickly into the question.
>
> But I think this is problematic. If you're writing a question on a
> mathematical term for which you cannot find a better opening clue than
> the definition, it probably means that you should seek a different
> topic altogether for your question! I agree that it's hard to find
> good clues for continuous. But if one cannot do better than giving the
> definition first, one should find something else to ask about.
>
> But I'm not convinced "continuous" is impossible to write about. How
> about this for a question with the answer continuous (making use of
> one of your suggestions, but later in the question):
>
> Tossup:
> These maps are the morphisms in the category of topological spaces.
> The Weierstrass approximation theorem lets one approximate them by
> smooth functions on a closed interval. The absolute value function has
> this property, but the floor function does not. A function is this if
> the preimage of an open set is open. FTP, what is this property a
> function has at x when its limit at x is defined and the value of the
> function is equal to the limit?
> Answer: continuous
>
> It's not perfect, but I think it's significantly better than the
> question asked at the ICT. I don't know what the later clues in the
> ICT question were, either; perhaps some of them could reasonably have
> been given as the first clue, perhaps not.
>
> I still think my main point (previously made by naqtrauma), slightly
> modified, is true: a science or math question should not start with a
> definition of the term in question (or a statement of the theorem,
> etc.). If one cannot write a question on a topic without either
> beginning with a definition or with a clue that is not uniquely
> identifying, one should find another topic to write about.
>
>
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