Re: (ReacTor) Defining Our Terms: What Do We Mean by "Hard SF"?

On 8/21/24 5:52 PM, Scott Dorsey wrote:

Joy Beeson  <jbeeson@invalid.net.invalid> wrote:

On Tue, 20 Aug 2024 08:09:49 -0700, Paul S Person
<psperson@old.netcom.invalid> wrote:
>

They never even once mentioned that integration and differentiation
are inverses of each other? With various caveats and details, to be
sure.

>
It was asserted, but never explained.  The two courses were entirely
separate.
>
I've read that the proof is childishly simple.

 There are three kinds of calculus class.
 There is a calculus for math majors class, which is all about proofs and
all about how the calculus works inside.  Every procedure that is shown
is proved and students will be expected to explain the proofs.
 There is a calculus for engineering students class, in which you won't
see any proofs at all but where you will be expected to memorize a huge
number of procedures and drilled in order to be able to do differentiation
and integration as quickly as possible.  There is no emphasis on how
anything works, just on how to make it work fast.
 And there is a calculus for poets class, sometimes called an intuitive
calculus class, in which the proofs are handwaved and you get to see some
of the easier mechanisms so that students get a basic understanding of
what integration and differentiation is and how it can be used.
 Some universities teach all three kinds, some only one.  Which one is
appropriate depends on your personal relationship with the calculus.
--scott
 

In broad strokes, I think your three types are pretty accurate.
At my Enormous State University, we have seven flavors of calculus.[1] Possibly less for those who don't think the Calculus for the Biological Sciences and/or Calculus for Business are distinct enough from one of the differently-numbered other courses.[2]
The additional flavors are largely because we have a lot of students who fall into exactly one of these three buckets:
- their HS transcript says they should be ready for calculus, but their placement exam (taken before enrolling) says they shouldn't (hence, Calculus with Review, that does calc a little slower while reviewing necessary pre-calc skills)
- are aiming to teach in middle school[3] (there are some state-imposed requirements)
- are strong enough to accelerate, but don't want to major in math (they end up doing 3 semesters of calc in 2 semesters)
Tony
[1] We used to have 10, which is apparently more upsetting to administrators than 7.
[2] I have taught both the Bio and the Business - they're different, esp the Bio flavor, but it's not worth arguing with people about.
[3] For those students who want to teach math in high school, they are required to get a math degree in addition to whatever educational training they need. Many (all?) of them do a 5 year program where they also end up with a masters (in education).