Re: Compression and crypto

"David A. Scott" wrote:
... I lost my book from high school on geometry when I
moved I really hate it thats its impossible to find a decent book
om the subjest anymore. You'd think the copyright date is so old
on some of these books that they could be printed cheaply again

Indeed, the best high-school level science and math texts I've
seen on math were those used by my parents. I guess the reason
we don't see Dover reprints was that none of them ever got
established as a "classic".

At the beginning college level, there are some good classic
texts to choose from. (The main problem is in obtaining good
enough preparation by the time one gets to that level.)

I learned more from Feynman's "Lectures on Physics" and Dirac's
"Principles of Quantum Mechanics" than I did from the official
texts for those classes. These are still in print, I think.

There was an intro text, "Caclulus Made Easy", by Silvanus P.
Thompson, that was far more enlightening than all standard texts
(even mathematically decent ones such as Spivak's). Now that
there is a formal theory of "nonstandard analysis" a lot of its
"artful dodges" are even entirely justifiable. The edition
revised by Martin Gardner is currently in print.

I wonder just how knowledgeble the teachers are. They to
could have been taught with the books there using assuming that
any of them even had geometry.

I have seen several studies of public-school teachers that
found some teachers unable to pass basic knowledge tests that
their students were going to have to pass. Generally there is
some amount of truth in the old adage "Those who can, do; those
who can't, teach." However, many teachers do know their stuff,
both the subject matter and how to effectively guide students.

This thing on books really pisses be off. Its not like
basic euclidian geometry or basic algebra has changed in
the last 100 years. What does it say for the future of this
civilization of good basic books are not longer to be found
on these subjects.

One would think that the Internet should encourage development
of good *and* comprehencive tutorial matter at the K-12 level.
There are some isolated instances of good tutorials on specific
topics, but not (to my knowledge) an entire organized subject
area. (The good, comprehensive sites I know of are aimed at a
higher level of ability. Note that these, and the Wikipedia,
show that it is feasible to produce comprehensive guides.)

Another problem not yet mentioned is that many current K-12
texts (at least in math) redefine standard terms or introduce
new terms for established concepts. An expert in a field
might not be able to work problems out of some texts, simply
because he doesn't know (and can't guess) what the terms mean.
This introduces a communication gap between students and
professionals, quite unnecessarily.

I also read as a kid a set of maybe ten books translated
from the russian it was some sort of survey of mathematics.

Yes, education seems ot have been taken more seriously (or
at least conducted much better) in many other countries.
Translations of Landau & Lifshitz's books in their "Course
on Theoretical Physics" were often used instead of native
English texts when I was studying the subject.

Round the number 25 to the nearest ten? ...

Ford Motor Co. used to issue metal rulers with marks at only
even-numbered millimeters, to enforce a rounding rule "when
both directions are equally close, round to the even digit".
That is supposed to prevent cumulative bias that might accrue
from rounding "ties" always in one direction, such as up.
However, that reasoning is spurious. Any tutorial discussion
of rounding ought to include the matter of, first, the whole
purpose of such quantization and when it might be useful, and
second, the situation when both directions are equally close.
The example of a bank keeping all fractional pennies from
interest computations rather than rounding the result, ought
to be used for memorable "relevance".
.