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From: Tony Nance <tnusenet17@gmail.com>
Newsgroups: rec.arts.sf.written
Subject: Re: (ReacTor) Defining Our Terms: What Do We Mean by "Hard SF"?
Date: Wed, 21 Aug 2024 18:31:36 -0400
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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).