A teenager question

x-no-archive:yes
toto wrote:
On Thu, 14 Aug 2003 12:45:14 GMT, Rosalie B.
wrote:
toto wrote:
On Thu, 14 Aug 2003 02:04:33 GMT, Rosalie B.
wrote:

That may be, but when I was in school calculus was not required - not
even of a science major in college

I don't imagine it was required of liberal arts majors, but anyone in
science, math or engineering had to take it when I was in college and
that was in the early 60s. Physics in particular cannot be done on
the college level without calculus.

Well as I said - I've never had physics, or astronomy which was the
science course of choice for liberal arts people.

WHen I entered college (Oberlin) in 1955, if I had 4 years of hs math
I didn't have any required math courses in college. I was a zoology
major (I had a boyfriend who was a math person and he didn't consider
the biological sciences as 'real' science so maybe that's it.) In any
case - biology is still considered science AFAIK.

I had 4 years of hs math - alg 1, alg 2, geometry, and the fourth year
was trig and solid geometry. We didn't have calculus available in my
hs.

I did well at geometry, but I had a lot of trouble with algebra -
nearly flunking it, and I've had to work hard at doing it - I can do
it but it is hard work for me. Logic OTOH is fun.

I cannot imagine a science major not taking calculus.

You don't have to imagine it. Just accept it. It happened. I was
there.

But calculus isn't necessary for a lot of people, though an
understanding of limits and inductive proof is something that
students shoud have, imo. These are precalculus concepts
though not calculus ones.

And there are many areas of mathematics that don't
really require much in the way of calculus for understanding
them.

But I wasn't involved in areas of math that don't require calculus,
unless you include statistics and logarithmic scales as not requiring
much calculus.

You were in college earlier than I was. I do wonder about the

Yes that's absolutely true - I graduated in 1959

mathematical rigor in your high school classes.

For example, was your high school geometry more memorizing
proofs or did you have to construct your own? I know that mine
seemed geared to memorization and my children's were much
less so as they had to actually create more proofs of their own
and with more rigor.

I had a very good geometry teacher and as I recall, he would give us
something to prove and we had to apply the proofs we knew in order to
get the answer to the question. He wouldn't tell us how to do it -
that was the test. Is that constructing a proof?

It is a LONG time ago - as I had geometry in 1953-1954. My 8th grade
algebra teacher (the only good algebra teacher I had) made us derive
formulas for things like lift and drag, and inclined planes etc. I
guess I might have had a bit of physics in there too.

Logarithms don't require calculus to understand them.
Statistics today uses quite a bit of calculus in terms of formulas,
but it's more plug-in plug-out than a theoretical basis. Often
engineers have more of that then theoretical math also.

Yes, my mathematical boyfriend was pretty disparaging of physics as
being just 'applied math'. [ I dated dh before I met this particular
boyfriend, but dh moved to another school district before I met him.
Broke up with him in college and started to date dh again.]

My dd#3 was a math major, and dd#1 was not only a math major but has
her masters in math, and works in a math/computer field. dd#2 is an
engineer - like her daddy - EE. One of my granddaughters (dd of
dd#1) is currently an intern in civil engineering. Two BILs are
engineers, and one niece and one nephew are engineers so I'd be
surrounded - except that one niece is also an MD, one is a teacher,
two are writers, and one and dd#3 are professional horse trainers.

I must say I don't understand logarithms - I have to memorize the
formulas without really understanding them. So I have no way of
knowing whether this is a deficiency of mine or because I haven't had
calculus.

grandma Rosalie

wrote:

Yes, my mathematical boyfriend was pretty disparaging of physics as
being just 'applied math'.

Let's see if I can remember the old saw (which I don't actually believe, but
which always cracks me up):

Biology is applied chemistry
Chemistry is applied physics
Physics is applied math
Math is applied logic
Logic is applied philosophy
Philosophy is applied religion
Religion is applied bull**** ...

--Helen

"H Schinske" wrote:

Yes, my mathematical boyfriend was pretty disparaging of physics as
being just 'applied math'.

Let's see if I can remember the old saw (which I don't actually believe,
but
which always cracks me up):

Biology is applied chemistry
Chemistry is applied physics
Physics is applied math
Math is applied logic
Logic is applied philosophy
Philosophy is applied religion
Religion is applied bull**** ...

I like this - I must keep it. My saying is:

If it moves it's biology.
If it reacts it's chemistry.
Everything else is physics.

Jean

--
"And he said:
Your children are not your children. They are the sons and daughters of
Life's longing for itself. They come through you but not from you, and
though they are with you, yet they belong not to you." Khalil Gibran

Return address is unread. Replies to firstnamelastname @eircom.net.

In article ,
toto wrote:

You were in college earlier than I was. I do wonder about the
mathematical rigor in your high school classes.
snip discussion

Rigor can be introduced much earlier (in Algebra I).

For example when the quadratic formula is introduced, were you simply
given the formula to use or did you derive it? And how was that
derivation done? Rigor involves using correct mathematical notation
and deriving and proving things instead of just accepting them and
plugging in numbers.

Remember, we don't have "Algebra I" here; we are taught a course called
Mathematics (with various levels) with IIRC 6-week units on geometry, trig,
stats, calculus etc, varied so we didn't get bored, but still saw and used the
connections between the different areas of maths. To my mind, for example,
calculus is just a specialist part of algebra.

I do not know the term "the quadratic formula" as if there was only one -- do
you mean ax^2+bx+c=0? Or its general solution for x? We derived pretty much
everything from first principles. I must say that if my Dad (who went through
the Soviet education system at a good time and later became an electronics
engineer) thought my mathematical education was good, then it probably was. I
didn't do the top strand; I did the next one down. The top strand got into
matrices and imaginary numbers.

I do remember that at the time I was learning calculus, so was everyone else
-- even in the simplest course, Maths in Society (known as Maths In Space or
Vegie Maths. A few years later they introduced an even more basic maths
course, which was immediately nicknamed Choko Maths -- Vegie Maths without the
flavour! I would guess Choko Maths doesn't cover calculus at all).

I wouldn't describe integration as a fancy way of adding; it's how
you obtain the area (and therefore volume) under a curve.

That's the application. You are however, adding the smaller and
smaller sections when you do the actual integration.

Ah, now I see what you're getting at. But the "fancy adding" isn't the
salient feature to me; it's what you use it for: volumes of solids in
rotation. Not that I can think of any practical use for this any more!

But I'm vey rusty -- haven't used calculus since school, whereas I
used trig just recently to work out how wide an awning would need
to be to keep the sun out of a room at my latitude.

Using the formulas is fine, but what I think most college math
professors are after is not the use and calculation (that's an
engineering province and most of the calculations are now done
by computers once the formulas are programmed), but the actual
ability to figure out why the formulas work and to derive the ones
you might need or develop new formulas that work.

Darned if i can remember *why* the formulas work -- I was just glad that I had
remembered corectly that sin(theta) was the ratio of opposite to hypotenuse,
so I could then solve for the adjacent using cos(theta)! Turns out that at my
latitude and whatever the room height was, I need an awning 6' wide -- a nice
width for an outdoor table.

--
Chookie -- Sydney, Australia
(Replace "foulspambegone" with "optushome" to reply)

"...children should continue to be breastfed... for up to two years of age
or beyond." -- Innocenti Declaration, Florence, 1 August 1990

On Sat, 16 Aug 2003 22:55:51 +1000, Chookie
wrote:

In article ,
toto wrote:

You were in college earlier than I was. I do wonder about the
mathematical rigor in your high school classes.
snip discussion

Rigor can be introduced much earlier (in Algebra I).

For example when the quadratic formula is introduced, were you simply
given the formula to use or did you derive it? And how was that
derivation done? Rigor involves using correct mathematical notation
and deriving and proving things instead of just accepting them and
plugging in numbers.

Remember, we don't have "Algebra I" here; we are taught a course called
Mathematics (with various levels) with IIRC 6-week units on geometry, trig,
stats, calculus etc, varied so we didn't get bored, but still saw and used the
connections between the different areas of maths. To my mind, for example,
calculus is just a specialist part of algebra.

I do not know the term "the quadratic formula" as if there was only one -- do
you mean ax^2+bx+c=0? Or its general solution for x? We derived pretty much
everything from first principles. I must say that if my Dad (who went through
the Soviet education system at a good time and later became an electronics
engineer) thought my mathematical education was good, then it probably was. I
didn't do the top strand; I did the next one down. The top strand got into
matrices and imaginary numbers.

I do mean the general solution for x here.

And if you derived things then your mathematical education was
probably pretty decent.

Did you do proofs? Euclidean Geometry as a strand in one or more
of your courses? US schools make that a separate class, but more
schools are now teaching integrated courses that don't separate
algebra and geometry from each other.

Did you do any co-ordinate geometry? That integrates algebraic
formulas for distance between two points and area and volume
with graphing.

I do remember that at the time I was learning calculus, so was everyone else
-- even in the simplest course, Maths in Society (known as Maths In Space or
Vegie Maths. A few years later they introduced an even more basic maths
course, which was immediately nicknamed Choko Maths -- Vegie Maths without the
flavour! I would guess Choko Maths doesn't cover calculus at all).

I wouldn't describe integration as a fancy way of adding; it's how
you obtain the area (and therefore volume) under a curve.

That's the application. You are however, adding the smaller and
smaller sections when you do the actual integration.

Ah, now I see what you're getting at. But the "fancy adding" isn't the
salient feature to me; it's what you use it for: volumes of solids in
rotation. Not that I can think of any practical use for this any more!

I agree that for most people it's the applications that are important,
but the *ideas* allow you to apply the concept to unfamiliar problems.

Fancy adding is the *how,* the specific manipulations used can
change some.

But I'm vey rusty -- haven't used calculus since school, whereas I
used trig just recently to work out how wide an awning would need
to be to keep the sun out of a room at my latitude.

Using the formulas is fine, but what I think most college math
professors are after is not the use and calculation (that's an
engineering province and most of the calculations are now done
by computers once the formulas are programmed), but the actual
ability to figure out why the formulas work and to derive the ones
you might need or develop new formulas that work.

Darned if i can remember *why* the formulas work -- I was just glad that I had
remembered corectly that sin(theta) was the ratio of opposite to hypotenuse,
so I could then solve for the adjacent using cos(theta)! Turns out that at my
latitude and whatever the room height was, I need an awning 6' wide -- a nice
width for an outdoor table.

Glad you figured out what you needed. That is what mathematics is
useful for in real life.. It's just not the whole story and schools
need to teach more than the formulas. It sounds to me like your
school did do that.




--
Dorothy

There is no sound, no cry in all the world
that can be heard unless someone listens ..
Outer Limits