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Re: Re: Re: algebraic numbers
*To*: mathgroup at smc.vnet.net
*Subject*: [mg106321] Re: [mg106263] Re: [mg106206] Re: algebraic numbers
*From*: DrMajorBob <btreat1 at austin.rr.com>
*Date*: Fri, 8 Jan 2010 04:16:20 -0500 (EST)
*References*: <hhc7a1$2o2$1@smc.vnet.net> <200912300912.EAA17052@smc.vnet.net>
*Reply-to*: drmajorbob at yahoo.com
Agreed. In the US at least, the safest reason an employer can use for
hiring or firing is "no reason".
They can't be sued unless they tell you (or record somewhere, discuss in
front of witnesses, etc.) the reason they didn't hire (or admit) you.
That flexibility is lost with a rule like Texas has, where the top 10% of
high school students MUST be accepted to state schools. If I'm not
mistaken, though, it seems I heard students are only guaranteed admission
to SOME state school... not necessarily the one they want.
Bobby
On Wed, 06 Jan 2010 18:00:45 -0600, Andrzej Kozlowski <akoz at mimuw.edu.pl>
wrote:
> Well, I can't tell much about SATs and SAT II as I never had to take
> them, but from my perspective I see quite a different problem
>
> My daughter, who was educated in Japan and the UK, took the SAT and SAT
> II's while attending an international school in Britain. She got the
> maximum possible scores on all of them. (Later she also got a maximum
> possible score on GRE).
>
> Although we did not really want her to go to a US university she wanted
> to see if she could get in, so she applied to 3 of the top Ivy League
> schools and was turned down by all three, in spite of her perfect scores
> (and a record high score in the European International Baccalaureate
> examinations).
>
> So she went to Cambridge University in the UK (which accepted her on the
> basis of her IB results) and then did a doctorate in Germany and
> published a paper in the top ranked journal in her field. She then
> applied for post-doc position to one of the places that turned her down
> as an undergraduate, and they accepted her this time giving her at least
> the satisfaction of being able to turn down an offer from a famous Ivy
> League university.
>
> We have a pretty good idea why she was turned down as an undergraduate
> in spite of having as good an academic record as one could possibly
> have - but this it not the right place to write about that. But, at
> least from my perspective, the problem with these SATs, SAT IIs, GREs
> etc., is that the supposedly best institution ignore them and make
> selectons on the basis of their own highly dubious (and secret)
> criteria. However bad these exams are, they are better than that.
>
> Andrzej Kozlowski
>
> On 6 Jan 2010, at 20:02, DrMajorBob wrote:
>
>> I've always told people, "I test smarter than I really am," and now I
>> see... I was right!
>>
>> But not because I worked hard or my parents got involved in my
>> schoolwork,
>> as the New Yorker article suggests.
>>
>> At least, I didn't think so, until I thought about it some more and came
>> up with some factoids:
>>
>> a) My grandmother bought me comic books... and I READ them.
>>
>> b) I participated in summer reading programs at the local library
>> (voluntarily).
>>
>> c) My mother coached me for spelling bees, twice.
>>
>> d) She took dictation for my history notebook one summer when I
>> (voluntarily) went to summer school.
>>
>> e) Nobody told me math was hard, that I can remember.
>>
>> f) Comics led me to science fiction, which I read like a house on fire.
>>
>> So the article makes more sense than I originally thought.
>>
>> Highly recommended. Thanks for the link!
>>
>> Bobby
>>
>> On Tue, 05 Jan 2010 00:44:27 -0600, Noqsi <jpd at noqsi.com> wrote:
>>
>>> On Jan 4, 4:00 am, DrMajorBob <btre... at austin.rr.com> wrote:
>>>>> The issue here is
>>>>> whether the student has enough common culture with the test writer to
>>>>> find the same answer. And that's *always* an issue.
>>>>
>>>> So those are cultural conformity questions?!?
>>>
>>> One might not need to conform, but one must at least understand the
>>> culture. Mathematics is a human cultural artifact, and students are
>>> going to need to understand some things about that artifact and its
>>> expression to be successful in college.
>>>
>>> Specifically in this case series are often presented as specific terms
>>> and ellipsis, judged to be easier to comprehend in some ways than a
>>> formula, so the student should be able to comprehend that form.
>>>
>>> And this continues into professional life. Today I'm looking over the
>>> specs of a megapixel image sensor. The drawings that document its
>>> structure contain "..." in a number of places: it's not practical to
>>> show every pixel! I can, of course, think of all kinds of perverse and
>>> stupid ways to misunderstand what's omitted, but that wouldn't be
>>> helpful in any way.
>>>
>>>>
>>>> That's even worse than I thought!
>>>
>>> It's still worse. The intentions behind the widespread adoption of the
>>> SAT didn't really address the need to establish that the student could
>>> comprehend the academic cultural context: instead, they were
>>> consciously bigoted.
>>>
>>> http://www.newyorker.com/archive/2001/12/17/011217crat_atlarge
>>>
>>>>
>>>> Bobby
>>>>
>>>>
>>>>
>>>> On Sun, 03 Jan 2010 02:40:36 -0600, Noqsi <j... at noqsi.com> wrote:
>>>>> On Jan 2, 3:05 am, DrMajorBob <btre... at austin.rr.com> wrote:
>>>>>> When I clicked on the link below, the search field was already
>>>> filled =
>>>
>>>>>> with
>>>>>> the sequence
>>>>
>>>>>> target = {1, 2, 3, 6, 11, 23, 47, 106, 235};
>>>>
>>>>>> Searching yielded "A000055 Number of trees with n unla=
>>> beled
>>>>>> nodes."
>>>>
>>>>>> I tried a few Mathematica functions on it:
>>>>
>>>>>> FindLinearRecurrence@target
>>>>
>>>>>> FindLinearRecurrence[{1, 2, 3, 6, 11, 23, 47, 106, 235}]
>>>>
>>>>>> (fail)
>>>>
>>>>>> FindSequenceFunction@target
>>>>
>>>>>> FindSequenceFunction[{1, 2, 3, 6, 11, 23, 47, 106, 235}]
>>>>
>>>>>> (fail)
>>>>
>>>>>> f[x_] = InterpolatingPolynomial[target, x]
>>>>
>>>>>> 1 + (1 + (1/
>>>>>> 3 + (-(1/
>>>>>> 12) + (7/
>>>>>> 120 + (-(1/
>>>>>> 60) + (1/144 - (41 (-8 + x))/20160=
>>> ) (-7 + x)) (-6 +
>>>>>> x)) (-5 + x)) (-4 + x)) (-3 + x) (-=
>>> 2 + x)) (-1 + x)
>>>>
>>>>>> and now the next term:
>>>>
>>>>>> Array[f, 1 + Length@target]
>>>>
>>>>>> {1, 2, 3, 6, 11, 23, 47, 106, 235, 322}
>>>>
>>>>>> But, unsurprisingly, the next term in A000055 is 551, not 322.
>>>>
>>>>>> A000055 actually starts with another three 1s, but that doesn't
>>>> change
>>>>>> things much:
>>>>
>>>>>> target = {1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, 235};
>>>>
>>>>>> FindLinearRecurrence@target
>>>>
>>>>>> FindLinearRecurrence[{1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, 235}]
>>>>
>>>>>> (fail)
>>>>
>>>>>> FindSequenceFunction@target
>>>>
>>>>>> FindSequenceFunction[{1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, 235}]
>>>>
>>>>>> (fail)
>>>>
>>>>>> f[x_] = InterpolatingPolynomial[target, x]
>>>>
>>>>>> 1 + (1/24 + (-(1/
>>>>>> 40) + (1/
>>>>>> 90 + (-(1/
>>>>>> 280) + (1/
>>>>>> 1008 + (-(43/
>>>>>> 181440) + (191/3628800 - (4=
>>> 37 (-11 + x))/
>>>>>> 39916800) (-10 + x)) (-9 + =
>>> x)) (-8 + x)) (-7 +
>>>>>> x)) (-6 + x)) (-5 + x)) (-4 + x) (-3 + x) =
>>> (-2 + x) (-1 +
>>>>>> x)
>>>>
>>>>>> Array[f, 1 + Length@target]
>>>>
>>>>>> {1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, 235, -502}
>>>>
>>>>>> So I ask you, from the data alone: what's the next term?
>>>>
>>>>> It's the sort of question where one might expect a specialist to
>>>>> recognize a familiar sequence. It's all context.
>>>>
>>>>> Consider that in a narrow mathematical sense, spectroscopy is an
>>>>> utterly ambiguous, "ill conditioned" problem. But show me a gigagauss
>>>>> cyclotron spectrum, and I'll recognize it as such (see the
>>>>> acknowledgment at the end of arxiv.org/pdf/astro-ph/0306189: the
>>>>> authors were struggling to contrive an interpretation from atomic
>>>>> physics before one of them showed the spectrum to me). But I expect
>>>>> very few could do this, since few have the background.
>>>>
>>>>>> If one had the Encyclopedia of Integer Sequences handy, those SAT
>>>>>> questions could be interesting. But they'd still be nonsense.
>>>>
>>>>> No they are not. Remember that the SAT isn't about the ability of a
>>>>> student to function in some ideal abstract world of infinite
>>>>> possibility. In the real world of academia, every single question
>>>>> they
>>>>> will encounter will be ambiguous in some sense. The issue here is
>>>>> whether the student has enough common culture with the test writer to
>>>>> find the same answer. And that's *always* an issue.
>>>>
>>>>>> Bobby
>>>>
>>>>>> On Fri, 01 Jan 2010 04:32:58 -0600, Noqsi <j... at noqsi.com> wrote:
>>>>>>> On Dec 31, 1:16 am, DrMajorBob <btre... at austin.rr.com> wrote:
>>>>
>>>>>>>> This is a little like those idiotic SAT and GRE questions that ask
>>>>>>>> "What's
>>>>>>>> the next number in the following series?"... where any number
>>>> will =
>>>
>>>>>> do.
>>>>>>>> Test writers don't seem to know there's an interpolating
>>>> polynomial=
>>>
>>>>>> (for
>>>>>>>> instance) to fit the given series with ANY next element.
>>>>
>>>>>>> Explanations in terms of epicycles may be mathematically adequate
>>>> in=
>>> a
>>>>>>> narrow sense, but an explanation in terms of a single principle
>>>>>>> applied repeatedly is to be preferred in science. The ability to
>>>>>>> recognize such a principle is important.
>>>>
>>>>>>> And my mathematical logician son (who's looking over my shoulder)
>>>>>>> directed me tohttp://www.research.att.com/~njas/sequences/for
>>>>>>> research on this topic. When he encounters such a sequence in his
>>>>>>> research, he finds that knowledge of a simple genesis for the
>>>> sequen=
>>> ce
>>>>>>> can lead to further insight.
>>>>
>>>>>> --
>>>>>> DrMajor... at yahoo.com
>>>>
>>>> --
>>>> DrMajor... at yahoo.com
>>>
>>>
>>
>>
>> --
>> DrMajorBob at yahoo.com
>>
>
--
DrMajorBob at yahoo.com
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