We don't need calculous, software does most calculations. One has to wonder though, based on what principles does the software do those calculations. Black magic I presume?
The case for ending calculus requirements for science majors
81–90 of 142 posts
Re: The case for ending calculus requirements for science majors
#82Earlier quoted context omitted.
> In twenty years of engineering practice I have never once had to take a difficult limit, and can probably count on one hand the number of times I've had to take a limit of any kind. In principle, I agree that calculus doesn't need to be mandatory. However this apparently respectable counterargument is misframing the situation. A bit like me saying that a given soldier never placed top 3 in a race, or indeed had to…
"Everyone knows that nearly no engineers use calculus in their day job. Therefore, the purpose and measure of success isn't whether an engineer uses calculus in their day job. It is a great signal of technical problem solving ability, it is really powerful having a large pool of people who are trained in working with rates, areas and margins." I'm not saying that calculus is useless in an engineer's education - far f…
I wouldn't describe it as a useless trick to know that sin(2x) ≈ 2x for small x. I'd describe this as a basic part of understanding what it means to say sin'(0) = 1.
Re: The case for ending calculus requirements for science majors
#83Very much yes. I am currently trying to tutor my daughter through college-level calculus. She wants to be a civil engineer. Civil engineers, obviously, need to know calculus. But calculus is not being taught to her by engineers. It is being taught by mathematicians. And as part of teaching it, they are attempting to instill a "mathematical mindset". Which means, in practice, that it is an entry to proofs. Every proof…
I think a rigid foundation is a good thing for reasons that might not be obvious. I have never had to use much calculus for any job I had over the past 30 years and the rigorous Dijkstra formal methods that were punched into me at university are not often practical, however, they do help me to understand things on a deeper level and allow me to document things in a clearer fashion. I recently needed proofs to show why one of our solutions was more secure than any existing solution in payments and the auditors were delighted it was written on 1 A4 pdf in terse formulas instead of the gibberish they usually get (they said they often get 80 page presentations (yes, actual powerpoint) they have to distill into something that even makes logical sense let alone passes, but that is what they get paid for). It is good for the mind imho.
Re: The case for ending calculus requirements for science majors
#84Very much yes. I am currently trying to tutor my daughter through college-level calculus. She wants to be a civil engineer. Civil engineers, obviously, need to know calculus. But calculus is not being taught to her by engineers. It is being taught by mathematicians. And as part of teaching it, they are attempting to instill a "mathematical mindset". Which means, in practice, that it is an entry to proofs. Every proof…
> But calculus is not being taught to her by engineers.
30+ years ago, when I started undergrad, calc for engineers, pre-meds, and scientists were 3 different classes. Seems like your daughter should choose a more enlightened school.
(Math majors all avoid calc thanks to AP.)
Re: The case for ending calculus requirements for science majors
#85Very much yes. I am currently trying to tutor my daughter through college-level calculus. She wants to be a civil engineer. Civil engineers, obviously, need to know calculus. But calculus is not being taught to her by engineers. It is being taught by mathematicians. And as part of teaching it, they are attempting to instill a "mathematical mindset". Which means, in practice, that it is an entry to proofs. Every proof…
succeeding in college calculus is highly dependent on a good precalculus foundation. (it's the actually hard part). consider picking up a good precalculus textbook. (if the author or publisher of the calculus text has one, definitely get that one.)
avoid test prep or quick refresher books. you want the longform text that has examples of all the tricks needed.
Re: The case for ending calculus requirements for science majors
#86Very much yes. I am currently trying to tutor my daughter through college-level calculus. She wants to be a civil engineer. Civil engineers, obviously, need to know calculus. But calculus is not being taught to her by engineers. It is being taught by mathematicians. And as part of teaching it, they are attempting to instill a "mathematical mindset". Which means, in practice, that it is an entry to proofs. Every proof…
You can't hope to understand first year physics without calculus. To be a reasonable civil engineer, don't you need to understand structural engineering, including dynamics, which requires differential equations? On the other hand, what do I know? The civil engineering plans for our place had glaring errors that the construction workers caught after doing half the earthmoving. Even after it was fixed, the results las…
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Re: The case for ending calculus requirements for science majors
#87Earlier quoted context omitted.
My college used calc 1/2 as “weed out” classes. The best part was the professors were married, the same calc book was used for calc 1/2/3, and they revved the book every semester, basically rearranging the problem sets so you had to buy a ~200 book for 3 semesters, or make friends with someone who would let you photocopy the problem sets. My entire faith in academia was broken as a result.
Married?
I think they meant it literally, to further reinforce the fact that they were colluding to extract profit out of their students via yearly textbook revisions.
Re: The case for ending calculus requirements for science majors
#88Very much yes. I am currently trying to tutor my daughter through college-level calculus. She wants to be a civil engineer. Civil engineers, obviously, need to know calculus. But calculus is not being taught to her by engineers. It is being taught by mathematicians. And as part of teaching it, they are attempting to instill a "mathematical mindset". Which means, in practice, that it is an entry to proofs. Every proof…
What's needed for that is the U.S. Navy calculus book from WWII. The Navy needed people to understand calculus because navigation and fire control systems are devices that do integration, analytic geometry, and trigonometry. Since they still do that, with more software and fewer gears, there's a current version of the book.[1]
From the book: "The proofs of theorems shown in this section will be omitted in the interest of brevity."
You need calculus for anything that involves calculating the physics of the real world. But not as a proof system.
The same is true of geometry as taught in schools. There's an emphasis on proofs because those were a big deal when geometry was being invented. But if you need to solve geometry problems, you seldom if ever do proofs.
I've worked on proof of correctness systems, and there are times when you need heavy formalism. But it's a means to an end, not an end in itself. The end is programs that don't fail, not more proofs. I used to argue this with mathematicians when I was working on that sort of thing. There's still a tendency in software proof of correctness to fall in love with the formalism as an end in itself.
[1] https://archive.org/details/US_Navy_Training_Course_-_Pre-ca...
Re: The case for ending calculus requirements for science majors
#89Very much yes. I am currently trying to tutor my daughter through college-level calculus. She wants to be a civil engineer. Civil engineers, obviously, need to know calculus. But calculus is not being taught to her by engineers. It is being taught by mathematicians. And as part of teaching it, they are attempting to instill a "mathematical mindset". Which means, in practice, that it is an entry to proofs. Every proof…
This is spot on, but should be extended down the stack. For those with less direct need of math should get "math literacy" with principles and real world application of same.
Re: The case for ending calculus requirements for science majors
#90Earlier quoted context omitted.
"Everyone knows that nearly no engineers use calculus in their day job. Therefore, the purpose and measure of success isn't whether an engineer uses calculus in their day job. It is a great signal of technical problem solving ability, it is really powerful having a large pool of people who are trained in working with rates, areas and margins." I'm not saying that calculus is useless in an engineer's education - far f…
I wouldn't describe it as a useless trick to know that sin(2x) ≈ 2x for small x. I'd describe this as a basic part of understanding what it means to say sin'(0) = 1.
> sin'(0) = 1.
= 0, not 1, unless I'm misunderstanding your notation (or blowing trig).