Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

The case for ending calculus requirements for science majors

quillette.com

Post reply on HN
Print view View original

61–70 of 142 posts

Re: The case for ending calculus requirements for science majors

#61

Post by GlenTheMachine »

roenxi wrote: post #55
GlenTheMachine wrote: post #40

Very 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…

> 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 from it.

I'm arguing that knowing the algebraic tricks required to take the limit of (x^2)sin(2x)/sqrt(x) as x->0 is useless. It's just a display of the mastery of very intricate algebra, exactly the same as all the other displays of mastery of intricate algebra she has had to master and will continue to be required to master.

What she actually needs is a solid understanding of the physical meaning of derivatives and integrals, how we arrive at them via numerical approximations, the fact that the velocity of a rigid body can be described as the integral over the forces that body is experiencing, etc.

That connection is literally never made in calculus.

The connection is of course made in the parallel calculus-based physics class she is taking. Which has its own problems, but is far superior as an introduction to calculus than the actual calculus class is.

Re: The case for ending calculus requirements for science majors

#62

Post by spookie »

zozbot234 wrote: post #59
spookie wrote: post #56

Earlier quoted context omitted.

I've a bachelor's in CS, and I've learned real analysis. As someone pointed out, maybe being in an European university led to it. And it's probably, the most useful course I've taken. If you're going to perform a bunch of floating point ops, I hope you've taken real analysis. They're enough of a Russian roulette to begin with, let's make sure you aren't making my day worse hunting down for some weird ass rounding err…

If you're going to perform a bunch of floating point ops and are not using interval arithmetic to precisely bound the result (and perhaps constructive real arithmetic, if you want guarantees of tight-enough bounds), you'll need a numerical analysis class as well. Real analysis will teach you about the theory of how real numbers are defined, but computation and the need for approximate results throughout bring challen…

Very much true. Have taken it as well. My train of thought was more along continuity and such, since I'm mostly working on CG right now. But I guess Numerical Analysis has even greater value in the context I provided above.

Re: The case for ending calculus requirements for science majors

#63

Post by zozbot234 »

roenxi wrote: post #60
zozbot234 wrote: post #57

Earlier quoted context omitted.

> Plus, don't underestimate the impact of forcing people to acknowledge that there is exactly one right answer and that it can be proven. There's plenty of classes in a civil engineering degree to instill that particular lesson. Why does it have to be calculus? It's just legacy - it used to be that limits and integrals could only be computed by hand, so any aspiring engineer would have to practice that skill a lot. N…

> Why does it have to be calculus? It doesn't, but it has to be something . So the proposal isn't 'get rid of calculus' as much as 'replace it with X which will be better at achieving the outcomes we think are important'. Like the original article did with statistics, which is a decent proposal. That being said if my civil engineer hadn't ever studied calculus I, personally, would prefer to find a different civil eng…

The mathematical foundations of "will it stay up" questions are a lot more challenging than what you'll find in any calculus course. I'm all for teaching less calculus, and more theory of structural engineering. (Setting statistics aside, which does require calculus but not of the pointless-algebra-tricks kind.)

Re: The case for ending calculus requirements for science majors

#64

Post by Jap2-0 »

> The real question is: Why should passing calculus be required to major in biology any more than passing biology should be required to major in math?

Interesting question, why should I be required to pass biology?

There are a lot of good points addressed thoroughly in other threads here, but (while calculus may fill a bit of a different role) education to a little bit of depth in a variety of areas does seem to be part of the role of a college (at least at present). I think requiring statistics to be taken more broadly would be great for our society, but calc (especially when taught well) definitely touches on areas of thinking that other subjects don't cover.

(Obviously slightly biased perspective from a math major.)

Re: The case for ending calculus requirements for science majors

#65

Post by david38 »

GlenTheMachine wrote: post #40

Very 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 studied computer science. It came with some math - four semesters of calc, diff eq, linear, discrete, etc. FOUR semesters of calc!

It’s only use has been to tutor my daughters.

Re: The case for ending calculus requirements for science majors

#66

Post by hilbert42 »

jqgatsby wrote: post #33
hilbert42 wrote: post #21

I like calculus and I've always liked it more than other branches of mathematics. That's not to say that I consider myself a true expert in the subject as I'm not (I still find some aspects of the subject difficult). I like calculus because it allows us to put a measure on how things in our world change, it greatly simplifies our calculations of the rate at which these changes occur than we would otherwise be without…

that's funny, I ended up buying the book based on exactly the same HN comment and received it today. The idea that calculus could be learned based on the dual numbers is really intriguing to me, especially because I've been studying them in conjunction with their cousins the double (or split-complex) numbers, and trying to understand the whole Cayley-Klein geometry framework, for some years now. It's sort of a never-…

Yeah right. I'm not a mathematician by profession so much of my time has been spent just plugging values into equations. The trouble with that is twofold, first one can forget those less frequently used esoteric tricks one was taught, and second, one can overlook whole swathes of the subject - those parts outside one's normal orbit.

I never seem to have enough time to sit down and do nothing but mathematics for its own sake.

Re: The case for ending calculus requirements for science majors

#67

Post by RhysU »

GlenTheMachine wrote: post #61
roenxi wrote: post #55

Earlier 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…

> The connection is of course made in the parallel calculus-based physics class she is taking...

The physicists as always (a) are pragmatically out-front but (b) don't worry about whether their tools are internally sound so long as they make useful predictions.

Sounds about right. It is important for the aforementioned daughter to know this cultural difference between physicists and mathematicians if she is to be a good engineer. I believe this can only be learned firsthand if it is to be appreciated.

Re: The case for ending calculus requirements for science majors

#68

Post by ivansavz »

GlenTheMachine wrote: post #61
roenxi wrote: post #55

Earlier 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…

It sounds like your daughter might enjoy reading my MATH+PHYS book. It covers mechanics and calculus in an integrated manner. I don't do all the proofs, so might not be a good fit for a proofs-based, course, but lots of illustrations and intuition.

Preview here: https://minireference.com/static/excerpts/noBSmathphys_v5_pr...

Concept map here: https://minireference.com/static/conceptmaps/math_and_physic...

Also be sure to check out the SymPy, in case you don't know already: https://minireference.com/static/tutorials/sympy_tutorial.pd... very good for checking answers...

Re: The case for ending calculus requirements for science majors

#69

Post by aoki »

zozbot234 wrote: post #63
roenxi wrote: post #60

Earlier quoted context omitted.

> Why does it have to be calculus? It doesn't, but it has to be something . So the proposal isn't 'get rid of calculus' as much as 'replace it with X which will be better at achieving the outcomes we think are important'. Like the original article did with statistics, which is a decent proposal. That being said if my civil engineer hadn't ever studied calculus I, personally, would prefer to find a different civil eng…

The mathematical foundations of "will it stay up" questions are a lot more challenging than what you'll find in any calculus course. I'm all for teaching less calculus, and more theory of structural engineering. (Setting statistics aside, which does require calculus but not of the pointless-algebra-tricks kind.)

> statistics aside, which does require calculus but not of the pointless-algebra-tricks kind

https://en.wikipedia.org/wiki/Gaussian_integral

Re: The case for ending calculus requirements for science majors

#70

Post by Overtonwindow »

I tried to get a degree in electrical engineering, but calculus halted that. I’m just not good at calculus. I would’ve really liked to of been an engineer. The professors were not good, they were all mathematicians, and it was all very rote and bland.
Post reply on HN