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Grex > Tutoring > #14: Algebra, Geometry, Calculus, Trig, all that good stuff |  |
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| 25 new of 132 responses total. |
remmers
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response 13 of 132:
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Jul 2 16:08 UTC 1997 |
Re #11: Gad, people are still reading Ahlfors' _Complex
Analysis_. That was the textbook when I took complex analysis
in college (the class was taught by Ahlfors as well).
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i
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response 14 of 132:
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Jul 2 17:09 UTC 1997 |
Re: #13
This was Ahlfors *3rd ed.* - (c)1979 - I took it in '86. You probably used
the original - (c)1953. (But the 2nd ed. was (c)1966, so you may have been
a guinea pig for an early draft of it or some such...)
Looking in the Columbia Encyclopedia (5th ed.) under Euler, I found the
formula directly attributed to him with the 5-big-numbers property noted.
But I don't think that's where I originally saw it. <sigh> Perhaps my
memory hails from some untracable & nearly forgotten lecture of math
classes past...
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senna
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response 15 of 132:
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Jul 2 17:41 UTC 1997 |
I think I had a problem similar to that last year. It was a trick question.
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remmers
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response 16 of 132:
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Jul 2 20:02 UTC 1997 |
Re #14: Yes, it was the 1st edition. Glad it's made it to a
third edition. Of course, it's a classic textbook.
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dang
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response 17 of 132:
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Jul 3 00:45 UTC 1997 |
And, too, math doesn't change nearly as much as, say, physics, which requires
a new book (depending on the specific topic) every year. It's a pain to sell
back physics books. I've never been able to sell one back, because they are
always getting a new one.
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rcurl
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response 18 of 132:
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Jul 3 05:51 UTC 1997 |
What level of math/physics are you referring to? Undergraduate physics
hardly changes at all, except for a little decoration with mention of
recent discoveries. Most changes in the selected textbook occur because
of changes in the instructors, who have personal preferences. Perhaps what
you observe is due more to more frequent changes in who teaches physics
than in who teaches math?
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valerie
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response 19 of 132:
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Jul 3 17:12 UTC 1997 |
This response has been erased.
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i
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response 20 of 132:
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Jul 3 18:12 UTC 1997 |
Books change more often because of fads, trends, etc. in how the subject is
taught. America's it's-gotta-be-new-&-improved culture requires that the
education establishment come up with different ways to teach the same old
subject every few years to keep their jobs. The metric system gets shoved
in, then fades. History has to be re-written to prove that all white males
are evil. Every such change requires new textbooks.
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dang
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response 21 of 132:
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Jul 3 23:00 UTC 1997 |
Of my 4 undergrad physics classes so far, only one (Electricity and Magnitism)
had not changed in the previous year. (Granted, I took mechanics in HS, snd
that hasn't changed either)
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rcurl
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response 22 of 132:
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Jul 4 18:41 UTC 1997 |
(I cannot resist obsesrving that neither electricity or magnetism, or
mechanics, has changed since Maxwell....)
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n8nxf
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response 23 of 132:
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Jul 4 19:11 UTC 1997 |
They haven't even changed before Maxwell... Only our understanding of
them has ;-)
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rcurl
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response 24 of 132:
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Jul 5 18:14 UTC 1997 |
touche....
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senna
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response 25 of 132:
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Jul 6 02:43 UTC 1997 |
It *does* strike me as rather interesting that while math laws and physics
never change, and never will, the text books teaching their governance have
to be replaced on a regular basis.
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i
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response 26 of 132:
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Jul 6 16:06 UTC 1997 |
At the high undergraduate & graduate level (at least in math), most of the
educational fashion experts are out of their depth, and its common to see
standard texts run 10-15 years between minor-revision editions. I doubt
that selling more has anything to do with the revisions - I've seen prof.'s
teach classes from an older edition than what the class has, and far more
texts are kept for future reference by students at that level.
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valerie
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response 27 of 132:
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Jul 6 20:49 UTC 1997 |
This response has been erased.
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anderyn
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response 28 of 132:
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Jul 6 21:20 UTC 1997 |
Hhhhm. A *lot* of the books we review are reissues of books published
thirty years ago, and a lot more are revisions of books which are
anywhere from twenty to ten years old. OF course, there are books
which come out every year or tow with new revisions, but that's
uncommon (we usually get every %$!@ book that isn't too basic, so
I see a lot of math textbooks)...
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i
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response 29 of 132:
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Jul 8 01:45 UTC 1997 |
Re: #27
I went through (mainly theoretical) math from about '85 to '89. Sub-senior
level texts certainly turned over faster, even in math. Computer-oriented
math texts seemed to be replaced by a new generation about every 10 weeks
for a while...
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tsty
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response 30 of 132:
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Jul 8 09:02 UTC 1997 |
hells bells, newtonian mechanics hasn't changed in 300 years! amazing,
it's still 'new' to students.
i did get a teacher to try teaching math as a language, translatable
to/from english. about a year later, she said she was ahving much
better success with er students as a result. i smiled.
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aruba
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response 31 of 132:
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Jul 8 17:16 UTC 1997 |
Re #30: That's a great idea, teaching people to translate between math and
English. I saw a low of college freshmen who had no clue how to do that.
Doesn't anyone have a problem? I suppose I could dig some out, but most of
my good ones have been used up in previous math items.
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aruba
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response 32 of 132:
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Jul 10 02:13 UTC 1997 |
Ok, all I have at present are logic problems, but here goes. I'll go through
a chapter in Raymond Smullyan's book "The Lady or the Tiger?", which has a lot
of good stuff in it.
-------------------
Many of you are familiar with Frank Stockton's story "The Lady or the Tiger?",
in which the prisoner must choose between two rooms, one of which contains a
lady and the other a tiger. If he chooses the former, he marries the lady; if
he chooses the latter, he (probably) gets eaten by the tiger.
The king of a certain land had also read the story, and it gave him an idea.
"Just the perfect way to try my prisoners!" he said one day to his minister.
"Only, I won't leave it to chance; I'll have signs on the doors of the rooms,
and in each case I'll tell the prisoner certain facts about the signs. If the
prisoner is clever and can reason logically, he'll save his life - and win a
nice bride to boot!"
"Excellent idea!" said the minister.
THE TRIALS OF THE FIRST DAY
On the first day, there were three trials. In all three, the king explained
to the prisoner that each of the two rooms contained either a lady or a tiger,
but it could be that there were tigers in both rooms, or ladies in both rooms,
or then again, maybe one room contained a lady and the other room a tiger.
The First Trial
"Suppose both rooms contain tigers," asked the prisoner. "What do I do
then?"
"That's your hard luck!" replied the king.
"Suppose both rooms contain ladies?" asked the prisoner.
"Then, obviously, that's your good luck," replied the king. "Surely you
could have guessed the answer to that!"
"Well, suppose one room contains a lady and the other a tiger, what happens
then?" asked the prisoner.
"In that case, it makes quite a difference which room you choose, doesn't
it?"
"How do I know which room to choose?" asked the prisoner.
The king pointed to the signs on the doors of the rooms:
I II
IN THIS ROOM THERE IN ONE OF THESE ROOMS
IS A LADY, AND IN THERE IS A LADY, AND
THE OTHER ROOM IN ONE OF THESE ROOMS
THERE IS A TIGER THERE IS A TIGER
"Is it true, what the signs say?" asked the prisoner.
"One of them is true," replied the king, "but the other one is false."
If you were the prisoner, which door would you open (assuming, of course,
that you preferred the lady to the tiger)?
----------------------
(Of course I expect a full explanation of your answer!)
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remmers
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response 33 of 132:
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Jul 10 02:18 UTC 1997 |
Well, I => II, so if I were true, so would II. Hence if one of
them is true and the other false, I must be the false one. So
II must have the lady, and I'd go with that.
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mcnally
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response 34 of 132:
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Jul 10 05:55 UTC 1997 |
John's logic is hard to argue with.. Can we proceed to the second day's
test?
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aruba
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response 35 of 132:
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Jul 10 07:23 UTC 1997 |
Very nice, John.
The Second Trial
And so, the first prisoner saved his life and made off with the lady. The
signs on the doors were then changed, and new occupants of the rooms were
selected accordingly. This time the signs read as follows:
I II
AT LEAST ONE OF THESE A TIGER IS IN
ROOMS CONTAINS A LADY THE OTHER ROOM
"Are the statements on the signs true?" asked the second prisoner.
"They are either both true or both false", replied the king.
Which room should the prisoner pick?
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toking
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response 36 of 132:
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Jul 10 15:06 UTC 1997 |
II cause if I is true then their is a lady in one room and if I is
true the II is also true
if I is false then both rooms must contain a tiger and if I is false
then II is also false, meaning that I doesn't have a tiger in it, which
would be impossible, because I being false says so.
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aruba
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response 37 of 132:
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Jul 10 15:31 UTC 1997 |
Right:
Both false => (I) both rooms contain tigers and (II) room I does not
contain a tiger, two statements which are clearly in conflict. So they can't
both be false, which means (according to the king) they must both be true.
Both true => (I) either there is a lady in room I or there is a lady in
room II, and (II) there is not a lady in room I. So there must be a lady in
room II.
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