Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Tony Nance 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 Organization: A noiseless patient Spider Lines: 64 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Thu, 22 Aug 2024 00:31:37 +0200 (CEST) Injection-Info: dont-email.me; posting-host="02e57e1cd88a95a553e9dbf3cee5ccaf"; logging-data="33816"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19WZwSKH37rmsuQmzUQioJCvzMbsZugjFI=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:Z9aVaT7pDNrYBB5BK1Qgp3QDNdo= Content-Language: en-US In-Reply-To: Bytes: 4216 On 8/21/24 5:52 PM, Scott Dorsey wrote: > Joy Beeson wrote: >> On Tue, 20 Aug 2024 08:09:49 -0700, Paul S Person >> 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).