On 12/27/2021 2:34 PM, rbowman wrote:
> The high school I went to had an 'enriched curriculum' program. In the
> summer between my junior and senior years I took a linear equations
> course in preparation for calculus during my senior year. The course was
> in the afternoon after the normal school schedule and was taught by a
> professor from RPI. The high school was almost adjacent to the RPI
> campus so it was common to have interactions like that. The text was
> Thomas, which was what was used at RPI.
Brrrrrre.... RPI. Why not change the world? LOL
I went to school in a warmer clime that didn't care to change the world! :)
However I like that you also enjoy reading older texts such as Thomas is.
My high school taught the following, which was typical in the day I think.
Freshman = Algebra 1 (required for graduation - dumbshits took it later)
Sophomore = Geometry first half (required for college prep)
Sophomore = Trig the second half (required for college prep)
Junior = Algebra 2 (required for college prep)
Senior = Calculus (recommended for college prep in the science field)
So I took all of that, but I honestly can't say I remember much of it.
I had to take Calculus again in college but only one year of it as I was in
the biological sciences so we didn't need that (we took statistics though).
What I remember is the front and back of the textbook had a long list in a
table of integrals, which, if memorized, was extremely important for passing
the test. But, of course they were easily best forgotten soon thereafter.
About the only real takeaway was that an integral is the area under the
curve and a derivative is the slope of that curve at any given point.
> Calculus definitely was not part of the normal high school curriculum.
> The standard senior level math course was spherical trig. In retrospect,
> since I do a lot of GIS work, spherical trig would have been more
> useful. This was 1964.
I've been studying the true source of gravity, which according to Minkowski
and others (Marcel Grossman, Einstein, Christoffel, Ricci and more) is due
to the geodesics inherent in spherical trig as I understand it anyway.
You might be able to help me as I'm trying to learn how to create geospatial
PDFs for my grandchildren who are planning a week long hike into the
wilderness which spans multiple USGS quadrangles.
Unlike us, they shun paper maps so I'm trying to create a specific map for
them with the gpx track on the map and the map being an amalgam of
geospacial PDFs so that their smartphones can show them where they are on
that custom geospacial PDF.
I can tell you more about what I need if you're interested but it's kind of
off topic for this newsgroup where it's more for the freeware groups since
each kid is expected to download and use the maps and the map software on
their Android or Apple phones.
> After graduation, I entered RPI and had a second dose of the aptly named
> math professor, Dis Maly. His wife had taught the linear equations
> course and was great; his droning could put a hyperactive 6 year old to
> sleep.
You may have a fantastic background in better understanding the true source
of gravity, which, it seems to be, is due to the curvature in 4 dimensions
of what looks like straight lines to us in three dimensions, and where we're
moving along those four dimensions at only one speed - the speed of light.
>> Well, I took calculus in college. I never needed it. Did you?
>> (Of course I'm not a mechanical engineer or a rocket scientist but neither
>> are most people. Did you ever really NEED calculus in your entire life?)
>
> Not really. The concepts are valuable but as far as sitting down with
> pencil and paper and solving anything no. You can know what a FFT is and
> even how to program the solution without delving into the notation.
The only thing I learned from college about fourier transforms was that if
you took any periodic signal, it would devolve down to a discrete set of
sine waves. That was interesting (I remember the "Gibb's Effect" though,
which threw a kink in the math - but only until final exams as I promptly
forgot about that until this very moment - too many decades to care later).
I've never needed an FFT nor integrals or even derivatives other than to
know the first deriviative is speed, the second is acceleration, etc.
When I need to calculate a volume, I break it down into sections of that
volume. It's rare you really have the equation anyway (aka the function f(x)
to do the proper math). I'm told Desmos and Geogebra will help though.
> When
> I roll up my extension cord I realize that if I crank the spool at a
> constant rpm the speed at which the cat will need to chase the loose end
> increases as a function of the circumference of the wire on the spool
> but neither I nor the cat ever sat down and worked it out.
:)
Likewise, the air resistance goes up with the square of the speed, I think,
which tells me the faster I go, the worse my incremental gas mileage will
be.
On a note about the extension cord, what they should teach in high school is
how to wrap up a hundred or two hundred footer without kinks. Yes, I know
they loop it in a special way. But you have to practice it.
Seems to me we can start a thread on what _should_ be taught to kids that we
old farts learned (or wish we had learned) when we were younguns.
>> At least physics is taught as problem sets.
>
> Physics at RPI was a two year course.
Mine was for the bio sci majors so it was only a year of baby physics.
We never got past the classical physics for example.
> We used Resnick & Halliday since
> Robert Resnick was a professor there. I consider that the most valuable
> college course I took. While I eventually migrated to software from
> hardware I can't say FORTRAN IV proved to be all that useful although
> there still is a lot of Fortran lurking around.
I took Fortran before IV existed. :)
Cobol too.
Yuck.
Error 45.
That's all you get.
IBM JCL.
Yuck.
Punched cards though. That was fancy stuff.
Winchester drives too. Maybe 16KB of memory was allotted to us?
Don't remember.
Heady stuff that was in the days of the raised refrigerated floors and
punched cards and long feed folded printer paper printouts in the bins with
your login on the first page all alphabetically sorted by the "operators."
> Fortunately it has
> progressed past Hollerith cards. Being a lousy typist I do much better
> with a decent programming editor.
Ah. You missed my typing class with IBM selectrics in college.
Fancy stuff they were.
Heavy as a boat anchor.
Spinning ball and all that.
All girls.
Except me.
Whooo hoo.
I haven't had it that good (male to female ratio anyway) since then.
Sigh.
Anyway, maybe we should start a thread on what kids _should_ be taught.
Also if you can help me on my map problem for the grandkids, I'd love that.