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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

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 has a trick. If you can see the trick, you can generally figure out how to do the proof. If you can't see the trick, you can't. The same thing is true with all of the very tricky limits they are making her learn to solve. I hold a PhD in aerospace engineering with a minor in applied mathematics. I specialized in control theory. I use calculus every day of my life. 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. I had a heart-to-heart with her about this today. I told her that what she actually needed to understand about calculus was how to use it to solve engineering problems, not how to manipulate polynomial fractions, chain trig identities, and do substitutions of variables. And she was not going to learn that in this class, but that she nevertheless needed to learn the tricky algebra and epsilon-delta proofs simply because this was a hoop she needed to jump through to get to the actual engineering classes. There was a not inconsiderable amount of cursing, but I understood because I hit the same wall, just thirty years prior. Nothing has changed.

just_boost_it 4y ago
I was a civil engineer for a few years and left to do something that interested me more. I was glad I had the broad university treatment rather than a narrow practical one, it meant I had the knowledge to go on and do what I wanted when I figured out what that was.
brianwawok 4y ago
It’s a very complicated IQ test. Most people don’t need weed out level college math. But on the whole, those that pass the bar are more intelligent than those that don’t. Maybe more useful to just take IQ tests to prove credentials than jump through these kind of hoops? Basically none of the “hard” stuff I learned in computer science is part of my career (3rd year physics, linear algebra, etc). But I got to jump those hoops!
- atdrummond 4y ago
  I went to a math oriented boarding school. When one started school, a test was administered to determine one’s initial math course. Students began their studies in a range of classes from Geometry all the way to MVC/Analysis. Having seen the standardized test scores and GPAs of many thousands of students at this school, and knowing many of these individuals personally, there is, at best, only a weak relationship between their terminal math course and their intelligence. We had kids who started in geometry and received perfect GPAs and SATs and were brilliant. We also had kids who started in Calc 2 or MVC and barely graduated.
- zozbot234 4y ago
  Every college class is an IQ test, that's pretty much inherent in any sort of post-K12 education. Calculus is just really badly taught and has a misplaced focus on material (like computing closed forms of tricky integrals) that's less and less relevant in the computer age.
- elcritch 4y ago
  Just because you have a fast computer doesn't mean you don't also need good well tuned software. For computers of the squishy human variety we install this software via learning and practicing. Doing college level maths refines thinking patterns and provides new categories of thinking. Even if you never take a limit or solve a system of equations directly, you know the concepts of them and they can deepen your understanding of many problems.
zozbot234 4y ago
> Every proof has a trick. If you can see the trick, you can generally figure out how to do the proof. Not a good way of teaching a mathematical mindset... How are you supposed to know if your "trick" actually goes through? You'd probably need a full course in real analysis to actually learn the fundamentals.
dgfitz 4y ago
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.
- jimhefferon 4y ago
  Married?
  - rjbwork 4y ago
    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.
    - dgfitz 4y ago
      Aye I did mean literally.
    - lotsofpulp 4y ago
      The confusion arises from “married” not necessarily meaning “married to each other”, in this context, especially since the number of professors is unknown. I did not even think about it as a possibility until I read your comment.
    - Turing_Machine 4y ago
      You would probably be surprised at how little money a textbook author makes per copy. Think $2.00 on a $200 book. It can add up to a significant sum if you're lucky enough to have your textbook adopted by many large universities nationwide, but I'm dubious that anyone is getting rich from a textbook used at only one university, even a large one.
- AngusH 4y ago
  Do you mean that you had to buy the same book 3 times? (or otherwise copy) That's astonishingly bad.
roenxi 4y ago
> 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 run anywhere in a combat situation, and therefore efforts at army fitness training were useless. 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. 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 are people out there who genuinely believe that everything is up for negotiation to a limit that just can't fly in a math course and something needs to screen them out before they get anywhere near anything involving high pressures. People who don't have engineers for parents need to be inducted into the culture from a couple of angles.
- zozbot234 4y ago
  > 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. Now computers can do the tricky algebra on their own (and I'm not even mentioning numerical approaches, which are more broadly useful but can be very tricky in their own way), yet the calculus courses have barely changed.
  - roenxi 4y ago
    > 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 engineer. It makes sense to give the will-it-stay-up? job to someone unusually well educated and if they haven't studied those sort of mathematical basics it is pretty suspicious.
david38 4y ago
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.
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pfortuny 4y ago
So you need better teachers. I can show you statistics no human could understand taught to… Business Admin majors.
adrianN 4y ago
Computer science education contains lots of quite tricky algorithms, datastructures, and runtime proofs. So far in my career I haven't had to use anything more complicated than a balanced tree and a hashmap and I certainly didn't have to open my copy of Concrete Mathematics and find bounds for any recurrence equations. On the other hand I do have to be familiar with various idiosyncrasies of operating systems, networks, and an awful amount of tooling, which I managed to almost completely avoid during my time in university. However, I wouldn't want to change the university curriculum. I believe universities should not be seen as preparation for jobs, but as preparations for research. It is quite unfortunate that institutions that just teach the part of the field that is really needed in the job have such low reputations. Two years at a trade school would be more than sufficient to learn everything you _really_ need to know as a programmer in all but the most specialized jobs.
hedora 4y ago
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 lasted less than one rainstorm. When we went back and checked the contracts we signed, they made it clear they assume zero liability for incompetence. Hiring a lawyer is more expensive than renting an excavator, and fixing it ourselves. Anyway, I'm not impressed with the corner of that field I interacted with, and would prefer they tighten the educational standards.
- deleted 4y ago
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- __s 4y ago
  The same argument could be made that what you interacted with was someone designing because their head is lost in the abstract porcelain tower of calculus proofs instead of the practical properties of the materials they were dealing with
- aperson_hello 4y ago
  There's a big difference between applied calculus and theoretical calculus. Colleges teach theoretical and then wonder why students struggle to apply it.
- Schroedingersat 4y ago
  > 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? Yes, but memorizing a bag of tricks for hand solving integrals and ODEs that you will never see in symbolic form without more than a passing exposure to the underlying concepts doesn't help anyone understand anything. Learning mathematical thinking and getting into the groove of that style of problem solving is equally as important (although much less concrete in its applicability for an engineer). But conflating rote memorization of the 'trick' to integrate cos(x)sin(x) with either helps nobody. A first year physics course is a better venue for teaching actual understanding of what derivative means than a purely symbolic presentation of the chain and product rules followed by presentation of a 'quotient rule' as a separate thing to memorize rather than a trivial combination of the other two. As is implementing some simulations of simple dynamical systems. As is intro to epidemiology or ecology. As is playing cookie clicker. Get students to visualise things, and actually experience them rather than memorize symbols. Then formalize themand introduce the language so they can express what they've learnt
tluyben2 4y ago
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.
wumpus 4y ago
> 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.)
a-dub 4y ago
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.
Animats 4y ago
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-calculus_and_Introduction_to_Probability https://archive.org/details/US_Navy_Training_Course_-_Pre-ca...
pstuart 4y ago
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.
lordnacho 4y ago
I both agree and disagree. A university degree is basically a sort of intellectual cave diving exercise. You need to be comfortable exploring in the dark, and sometimes you need to hold your breath under water until you emerge on the other side of the tunnel. There may be no purpose at the end of a given cave. In fact most university courses are like this, you won't use the content later in life. Others can be abbreviated, but on purpose are not, precisely because we want to practice hard things. For instance why do we need to do arithmetic beyond the point where we understand the uses and limitations of a calculator? Similarly for calculus, why do more trig substitutions beyond where you understand how a symbolic calculator works? In the end the purpose isn't to have the knowledge you need, but to be able to find it. For instance, I didn't know anything about option math when I finished, so I read some books on my first job learned it that way. Having said that, I think the attitude of "why on earth do I need this" is unhealthy. It makes it hard to concentrate when you know that you can forget about it the moment the exam ends. Perhaps it's better to develop an appreciation that calculus is at the bottom of a lot of things, and might be a starting point for unknown adventures later on.
- howinteresting 4y ago
  I sure hope university isn't like cave diving—it is one of the riskiest things a human can do, and (unlike either caving or diving in isolation) if a person chooses to do it I will question their judgment.
  - forgotpwd16 4y ago
    >unlike either caving or diving in isolation Caving, the activity where people crawl in spaces barely fitting and if take a wrong turn there's a high chance of getting stuck and dying even when it's found they're missing and try to pull them out? Wouldn't really say it's much better. Though cave diving is that plus carrying a big oxygen tank.
    - howinteresting 4y ago
      There's definitely some kinds of caving that are riskier than others.
int0x2e 4y ago
Adding my own personal story as an anecdote - I never completed my bachelor's (double major in physics and CS). I did okay on my physics classes, great on my CS classes (often in the top 2%), yet failed badly on a couple of advanced calculus classes. It got to the point where I was done with most of the requirement and elective classes on the CS and physics side, was already taking graduate courses in CS and lecturing in a course I helped create in CS - yet failed out of my bachelor's. In the end, the industry offers for me to go all into tech got too good, and I managed to advance to middle management with no need for that degree, so I never went back to finish it. I still think academics are important and I am thankful for the stuff I learned there, but I think the fact calculus and "hard maths" are such a strong focal point early on serves no purpose other than serving as an arbitrary filter for most people.
throwaway1851 4y ago
> It is being taught by mathematicians. And as part of teaching it, they are attempting to instill a "mathematical mindset". I think this is a problem not just with calculus, but really with most math instruction. Math is taught by people who are already in love with the special insider world of math. To students who don’t share that love, it’s often unappealing at best - and exclusionary at worst. It weeds out people who don’t need to be weeded. When math is taught in a way that develops practical intuition, it is so much more useful and rewarding.
sfifs 4y ago
This is exactly why I gave up on higher level calculus. It was full of highly illogical "tricks" in a way diametrically opposite to go how physics is rarely illogical. That plus the fact that even with fairly low power computers available then, it was apparent numerical methods would very soon become good enough. Fully agree mathematics for non math majors the should not be taught by mathematics departments in college. Today in a very similar way I find data science is not effective when taught by college professors and their TAs and instead we get our own courses created by people with practical experience.
rramadass 4y ago
You may find the following books useful for your Daughter; 1) Who Is Fourier?: A Mathematical Adventure - A very nice intuitive introduction to Calculus and more. 2) Higher Math for Beginners (Mostly Physicists and Engineers) by Zeldovich et.al. - https://archive.org/details/HigherMathForBeginners https://archive.org/details/HigherMathForBeginners 3) Elements Of Applied Mathematics by Zeldovich et.al. - https://archive.org/details/ZeldovichMyskisElementsOfAppliedMathematics/mode/2up https://archive.org/details/ZeldovichMyskisElementsOfApplied...
keithalewis 4y ago
Something used in only one proof is a trick. If it is used in two proofs it becomes a lemma. Calculus is used as a filter. It is not taught because you will need it in the future, it is used to detect second rate minds. It is debatable whether this is an appropriate use .
retrocryptid 4y ago
Maybe the OP's daughter would be better off as a business major.
- nnoitra 4y ago
  Yeah tbh undergraduate calculus courses are really not that difficult.
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nnoitra 4y ago
I can help her out. ; )
lr1970 4y ago
> I hold a PhD in aerospace engineering with a minor in applied mathematics. ... > And as part of teaching it, they are attempting to instill a "mathematical mindset". ... > I told her that what she actually needed to understand about calculus was how to use it to solve engineering problems, not how to manipulate polynomial fractions, chain trig identities, and do substitutions of variables. I am really surprised that a PhD in aerospace engineering does not see value in "substitution of variables" and also mocking "mathematical mindset". I feel your emotional despair but your criticism seems somewhat misplaced. In USA there is widely held resentment and frustration against STEM in general and mathematics in particular. Math is not an easy subject, it requires concentration and logical thinking. Teaching math is hard. Just few points I learned teaching college level math and also teaching math to my kids: 1. Math thinking should be cultivated in children from early age (starting at 6 or 7 years old) and continue uninterrupted throughout high-school. There is nothing wrong with gently teaching kids basic algebra and geometry concepts. 2. Stop using useless examples of difficult and boring math (I am looking at you trigonometry). Math exercises should be practical and fun, memorizing math relations is not math. AP Calculus A,B,C are not for everyone and the text-books are awful. 3. Proofs are central to math and should not be avoided. Proofs teach kids logical thinking and this ability is useful in life even if they never touch math again in their life. And, depending on the task, proofs can be very simple. Unfortunately, the way math in taught in America on all levels from school to college is a travesty of education. I have been teaching math to my kids myself (including college level calculus and linear algebra) to spare them the aggravation of main-stream math education. DISCLAIMER: Ph.D in Physics and Applied Mathematics. Was teaching math at two American colleges.
- tomohawk 4y ago
  The top priority in teaching students is to produce future professors for the department, or similar departments at other schools. But that is a vanishingly small percentage of the students being taught. So when the math dept teaches engineering students, there is a mismatch. None of these students have any interest in being a math professor. They are not interested in a mathematical mindset because it will not help them be an engineer. They need an engineering mindset, which is different than a math mindset. A friend of mine went to an engineering school in Sweden, and the math was taught by engineering professors rather than math professors. He ended up with a better understanding of math than I (or any of my classmates) did getting math from math professors. I went to a top tier school in the US.
giardini 4y ago
College math professors may be the original "woke" crowd, trying to slip formal methods into their math classes in a desperate attempt to indoctrinate yet one more mathematician. My college experience: Freshman Fall semester: abstract algebra was the first math course (yes, the full blown groups, rings, lattices, fields, etc.). There was no opt-out (this was a small college) and all science students took the same course. We were mystified - why study this? The three declared math majors were delighted. Freshman Spring semester: we were finally offered calculus. In the classroom physics, chemistry and biology professors were stunned to find students had no knowledge of calculus! When my physics prof first drew an integral on the blackboard, the class unanimously protested: "We haven't been taught that yet!" [To his credit and our undying relief, he taught us calculus for the next 3 classes and did a beautiful job of it. Turns out he had once been a math professor!] Faculty meetings ensued with much shouting. The verdict: an unspoken assumption among faculty was that the first freshman math class would be calculus. But the university had, in the summer hiatus, hired two new mathematics professors, both proponents of a particularly rigorous school of thought. One of them, the new mathematics department chairman, had decided without consultation to change the math curriculum. Ergo abstract algebra as an intro course. The mathematics department chairman was fired and a new chairman installed ASAP. Normality was restored.
morpheos137 4y ago
Are episilon delta proofs even necessary if limits can be reconstitutes as sums of infinite series?
runamok 4y ago
Thank you for this. My failure at calculus in my undergrad really set the tone for my mech eng. degree. I felt exactly what you mentioned: that you needed to memorize the "trick" and then you could solve the equation. I am still embarrassed at my poor performance in undergrad.
pack_stimulus 4y ago
I may be biased, but I cannot see how one can fully comprehend concepts in Dynamics, Solid Mechanics, and other core courses in an undergrad civil/mechanical engineering curriculum without ~six credits in calculus. Yes, you would never face those tricky limits they expect you to solve in high school, but I tend to see those as games that shape the students' frame of mind. Once you pass core engineering courses, you hardly ever have to calculate the forces, torques, and moments by analytical integration either, but having gone through the concepts is what prepares you for their application in practice. The article advocates for teaching statistics in place of calculus. Surely any stat course has to go further than teaching the sample mean and standard deviation. I cannot see how the students would calculate CDF out of PDF without background in calculus.
one1one1 4y ago
Perhaps you don't need to solve any limit because computers can do that for you, but when you try to solve a problem in your mind if you know limits you don't need a computer all the time, you just need to know that some approximations give you an acceptable solution to certain problems and in many cases the approximation is based on a limit. For example in many problems one can foresee the capacity of a process and what kind of error are acceptable is that setting, so you are able to obtain local solutions or assymptotic expansions that save you job.
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just_boost_it 4y ago

I was a civil engineer for a few years and left to do something that interested me more. I was glad I had the broad university treatment rather than a narrow practical one, it meant I had the knowledge to go on and do what I wanted when I figured out what that was.

brianwawok 4y ago

It’s a very complicated IQ test. Most people don’t need weed out level college math. But on the whole, those that pass the bar are more intelligent than those that don’t. Maybe more useful to just take IQ tests to prove credentials than jump through these kind of hoops? Basically none of the “hard” stuff I learned in computer science is part of my career (3rd year physics, linear algebra, etc). But I got to jump those hoops!

atdrummond 4y ago
I went to a math oriented boarding school. When one started school, a test was administered to determine one’s initial math course. Students began their studies in a range of classes from Geometry all the way to MVC/Analysis. Having seen the standardized test scores and GPAs of many thousands of students at this school, and knowing many of these individuals personally, there is, at best, only a weak relationship between their terminal math course and their intelligence. We had kids who started in geometry and received perfect GPAs and SATs and were brilliant. We also had kids who started in Calc 2 or MVC and barely graduated.
zozbot234 4y ago
Every college class is an IQ test, that's pretty much inherent in any sort of post-K12 education. Calculus is just really badly taught and has a misplaced focus on material (like computing closed forms of tricky integrals) that's less and less relevant in the computer age.
elcritch 4y ago
Just because you have a fast computer doesn't mean you don't also need good well tuned software. For computers of the squishy human variety we install this software via learning and practicing. Doing college level maths refines thinking patterns and provides new categories of thinking. Even if you never take a limit or solve a system of equations directly, you know the concepts of them and they can deepen your understanding of many problems.

zozbot234 4y ago

> Every proof has a trick. If you can see the trick, you can generally figure out how to do the proof. Not a good way of teaching a mathematical mindset... How are you supposed to know if your "trick" actually goes through? You'd probably need a full course in real analysis to actually learn the fundamentals.

dgfitz 4y ago

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.

jimhefferon 4y ago
Married?
- rjbwork 4y ago
  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.
  - dgfitz 4y ago
    Aye I did mean literally.
  - lotsofpulp 4y ago
    The confusion arises from “married” not necessarily meaning “married to each other”, in this context, especially since the number of professors is unknown. I did not even think about it as a possibility until I read your comment.
  - Turing_Machine 4y ago
    You would probably be surprised at how little money a textbook author makes per copy. Think $2.00 on a $200 book. It can add up to a significant sum if you're lucky enough to have your textbook adopted by many large universities nationwide, but I'm dubious that anyone is getting rich from a textbook used at only one university, even a large one.
AngusH 4y ago
Do you mean that you had to buy the same book 3 times? (or otherwise copy) That's astonishingly bad.

roenxi 4y ago

> 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 run anywhere in a combat situation, and therefore efforts at army fitness training were useless. 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. 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 are people out there who genuinely believe that everything is up for negotiation to a limit that just can't fly in a math course and something needs to screen them out before they get anywhere near anything involving high pressures. People who don't have engineers for parents need to be inducted into the culture from a couple of angles.

zozbot234 4y ago
> 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. Now computers can do the tricky algebra on their own (and I'm not even mentioning numerical approaches, which are more broadly useful but can be very tricky in their own way), yet the calculus courses have barely changed.
- roenxi 4y ago
  > 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 engineer. It makes sense to give the will-it-stay-up? job to someone unusually well educated and if they haven't studied those sort of mathematical basics it is pretty suspicious.

david38 4y ago

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.

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pfortuny 4y ago

So you need better teachers. I can show you statistics no human could understand taught to… Business Admin majors.

adrianN 4y ago

Computer science education contains lots of quite tricky algorithms, datastructures, and runtime proofs. So far in my career I haven't had to use anything more complicated than a balanced tree and a hashmap and I certainly didn't have to open my copy of Concrete Mathematics and find bounds for any recurrence equations. On the other hand I do have to be familiar with various idiosyncrasies of operating systems, networks, and an awful amount of tooling, which I managed to almost completely avoid during my time in university. However, I wouldn't want to change the university curriculum. I believe universities should not be seen as preparation for jobs, but as preparations for research. It is quite unfortunate that institutions that just teach the part of the field that is really needed in the job have such low reputations. Two years at a trade school would be more than sufficient to learn everything you _really_ need to know as a programmer in all but the most specialized jobs.

hedora 4y ago

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 lasted less than one rainstorm. When we went back and checked the contracts we signed, they made it clear they assume zero liability for incompetence. Hiring a lawyer is more expensive than renting an excavator, and fixing it ourselves. Anyway, I'm not impressed with the corner of that field I interacted with, and would prefer they tighten the educational standards.

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__s 4y ago
The same argument could be made that what you interacted with was someone designing because their head is lost in the abstract porcelain tower of calculus proofs instead of the practical properties of the materials they were dealing with
aperson_hello 4y ago
There's a big difference between applied calculus and theoretical calculus. Colleges teach theoretical and then wonder why students struggle to apply it.
Schroedingersat 4y ago
> 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? Yes, but memorizing a bag of tricks for hand solving integrals and ODEs that you will never see in symbolic form without more than a passing exposure to the underlying concepts doesn't help anyone understand anything. Learning mathematical thinking and getting into the groove of that style of problem solving is equally as important (although much less concrete in its applicability for an engineer). But conflating rote memorization of the 'trick' to integrate cos(x)sin(x) with either helps nobody. A first year physics course is a better venue for teaching actual understanding of what derivative means than a purely symbolic presentation of the chain and product rules followed by presentation of a 'quotient rule' as a separate thing to memorize rather than a trivial combination of the other two. As is implementing some simulations of simple dynamical systems. As is intro to epidemiology or ecology. As is playing cookie clicker. Get students to visualise things, and actually experience them rather than memorize symbols. Then formalize themand introduce the language so they can express what they've learnt

tluyben2 4y ago

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.

wumpus 4y ago

> 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.)

a-dub 4y ago

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.

Animats 4y ago

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-calculus_and_Introduction_to_Probability https://archive.org/details/US_Navy_Training_Course_-_Pre-ca...

pstuart 4y ago

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.

lordnacho 4y ago

I both agree and disagree. A university degree is basically a sort of intellectual cave diving exercise. You need to be comfortable exploring in the dark, and sometimes you need to hold your breath under water until you emerge on the other side of the tunnel. There may be no purpose at the end of a given cave. In fact most university courses are like this, you won't use the content later in life. Others can be abbreviated, but on purpose are not, precisely because we want to practice hard things. For instance why do we need to do arithmetic beyond the point where we understand the uses and limitations of a calculator? Similarly for calculus, why do more trig substitutions beyond where you understand how a symbolic calculator works? In the end the purpose isn't to have the knowledge you need, but to be able to find it. For instance, I didn't know anything about option math when I finished, so I read some books on my first job learned it that way. Having said that, I think the attitude of "why on earth do I need this" is unhealthy. It makes it hard to concentrate when you know that you can forget about it the moment the exam ends. Perhaps it's better to develop an appreciation that calculus is at the bottom of a lot of things, and might be a starting point for unknown adventures later on.

howinteresting 4y ago
I sure hope university isn't like cave diving—it is one of the riskiest things a human can do, and (unlike either caving or diving in isolation) if a person chooses to do it I will question their judgment.
- forgotpwd16 4y ago
  >unlike either caving or diving in isolation Caving, the activity where people crawl in spaces barely fitting and if take a wrong turn there's a high chance of getting stuck and dying even when it's found they're missing and try to pull them out? Wouldn't really say it's much better. Though cave diving is that plus carrying a big oxygen tank.
  - howinteresting 4y ago
    There's definitely some kinds of caving that are riskier than others.

int0x2e 4y ago

Adding my own personal story as an anecdote - I never completed my bachelor's (double major in physics and CS). I did okay on my physics classes, great on my CS classes (often in the top 2%), yet failed badly on a couple of advanced calculus classes. It got to the point where I was done with most of the requirement and elective classes on the CS and physics side, was already taking graduate courses in CS and lecturing in a course I helped create in CS - yet failed out of my bachelor's. In the end, the industry offers for me to go all into tech got too good, and I managed to advance to middle management with no need for that degree, so I never went back to finish it. I still think academics are important and I am thankful for the stuff I learned there, but I think the fact calculus and "hard maths" are such a strong focal point early on serves no purpose other than serving as an arbitrary filter for most people.

throwaway1851 4y ago

> It is being taught by mathematicians. And as part of teaching it, they are attempting to instill a "mathematical mindset". I think this is a problem not just with calculus, but really with most math instruction. Math is taught by people who are already in love with the special insider world of math. To students who don’t share that love, it’s often unappealing at best - and exclusionary at worst. It weeds out people who don’t need to be weeded. When math is taught in a way that develops practical intuition, it is so much more useful and rewarding.

sfifs 4y ago

This is exactly why I gave up on higher level calculus. It was full of highly illogical "tricks" in a way diametrically opposite to go how physics is rarely illogical. That plus the fact that even with fairly low power computers available then, it was apparent numerical methods would very soon become good enough. Fully agree mathematics for non math majors the should not be taught by mathematics departments in college. Today in a very similar way I find data science is not effective when taught by college professors and their TAs and instead we get our own courses created by people with practical experience.

rramadass 4y ago

You may find the following books useful for your Daughter; 1) Who Is Fourier?: A Mathematical Adventure - A very nice intuitive introduction to Calculus and more. 2) Higher Math for Beginners (Mostly Physicists and Engineers) by Zeldovich et.al. - https://archive.org/details/HigherMathForBeginners https://archive.org/details/HigherMathForBeginners 3) Elements Of Applied Mathematics by Zeldovich et.al. - https://archive.org/details/ZeldovichMyskisElementsOfAppliedMathematics/mode/2up https://archive.org/details/ZeldovichMyskisElementsOfApplied...

keithalewis 4y ago

Something used in only one proof is a trick. If it is used in two proofs it becomes a lemma. Calculus is used as a filter. It is not taught because you will need it in the future, it is used to detect second rate minds. It is debatable whether this is an appropriate use .

retrocryptid 4y ago

Maybe the OP's daughter would be better off as a business major.

nnoitra 4y ago
Yeah tbh undergraduate calculus courses are really not that difficult.

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nnoitra 4y ago

I can help her out. ; )

lr1970 4y ago

> I hold a PhD in aerospace engineering with a minor in applied mathematics. ... > And as part of teaching it, they are attempting to instill a "mathematical mindset". ... > I told her that what she actually needed to understand about calculus was how to use it to solve engineering problems, not how to manipulate polynomial fractions, chain trig identities, and do substitutions of variables. I am really surprised that a PhD in aerospace engineering does not see value in "substitution of variables" and also mocking "mathematical mindset". I feel your emotional despair but your criticism seems somewhat misplaced. In USA there is widely held resentment and frustration against STEM in general and mathematics in particular. Math is not an easy subject, it requires concentration and logical thinking. Teaching math is hard. Just few points I learned teaching college level math and also teaching math to my kids: 1. Math thinking should be cultivated in children from early age (starting at 6 or 7 years old) and continue uninterrupted throughout high-school. There is nothing wrong with gently teaching kids basic algebra and geometry concepts. 2. Stop using useless examples of difficult and boring math (I am looking at you trigonometry). Math exercises should be practical and fun, memorizing math relations is not math. AP Calculus A,B,C are not for everyone and the text-books are awful. 3. Proofs are central to math and should not be avoided. Proofs teach kids logical thinking and this ability is useful in life even if they never touch math again in their life. And, depending on the task, proofs can be very simple. Unfortunately, the way math in taught in America on all levels from school to college is a travesty of education. I have been teaching math to my kids myself (including college level calculus and linear algebra) to spare them the aggravation of main-stream math education. DISCLAIMER: Ph.D in Physics and Applied Mathematics. Was teaching math at two American colleges.

tomohawk 4y ago
The top priority in teaching students is to produce future professors for the department, or similar departments at other schools. But that is a vanishingly small percentage of the students being taught. So when the math dept teaches engineering students, there is a mismatch. None of these students have any interest in being a math professor. They are not interested in a mathematical mindset because it will not help them be an engineer. They need an engineering mindset, which is different than a math mindset. A friend of mine went to an engineering school in Sweden, and the math was taught by engineering professors rather than math professors. He ended up with a better understanding of math than I (or any of my classmates) did getting math from math professors. I went to a top tier school in the US.

giardini 4y ago

College math professors may be the original "woke" crowd, trying to slip formal methods into their math classes in a desperate attempt to indoctrinate yet one more mathematician. My college experience: Freshman Fall semester: abstract algebra was the first math course (yes, the full blown groups, rings, lattices, fields, etc.). There was no opt-out (this was a small college) and all science students took the same course. We were mystified - why study this? The three declared math majors were delighted. Freshman Spring semester: we were finally offered calculus. In the classroom physics, chemistry and biology professors were stunned to find students had no knowledge of calculus! When my physics prof first drew an integral on the blackboard, the class unanimously protested: "We haven't been taught that yet!" [To his credit and our undying relief, he taught us calculus for the next 3 classes and did a beautiful job of it. Turns out he had once been a math professor!] Faculty meetings ensued with much shouting. The verdict: an unspoken assumption among faculty was that the first freshman math class would be calculus. But the university had, in the summer hiatus, hired two new mathematics professors, both proponents of a particularly rigorous school of thought. One of them, the new mathematics department chairman, had decided without consultation to change the math curriculum. Ergo abstract algebra as an intro course. The mathematics department chairman was fired and a new chairman installed ASAP. Normality was restored.

morpheos137 4y ago

Are episilon delta proofs even necessary if limits can be reconstitutes as sums of infinite series?

runamok 4y ago

Thank you for this. My failure at calculus in my undergrad really set the tone for my mech eng. degree. I felt exactly what you mentioned: that you needed to memorize the "trick" and then you could solve the equation. I am still embarrassed at my poor performance in undergrad.

pack_stimulus 4y ago

I may be biased, but I cannot see how one can fully comprehend concepts in Dynamics, Solid Mechanics, and other core courses in an undergrad civil/mechanical engineering curriculum without ~six credits in calculus. Yes, you would never face those tricky limits they expect you to solve in high school, but I tend to see those as games that shape the students' frame of mind. Once you pass core engineering courses, you hardly ever have to calculate the forces, torques, and moments by analytical integration either, but having gone through the concepts is what prepares you for their application in practice. The article advocates for teaching statistics in place of calculus. Surely any stat course has to go further than teaching the sample mean and standard deviation. I cannot see how the students would calculate CDF out of PDF without background in calculus.

one1one1 4y ago

Perhaps you don't need to solve any limit because computers can do that for you, but when you try to solve a problem in your mind if you know limits you don't need a computer all the time, you just need to know that some approximations give you an acceptable solution to certain problems and in many cases the approximation is based on a limit. For example in many problems one can foresee the capacity of a process and what kind of error are acceptable is that setting, so you are able to obtain local solutions or assymptotic expansions that save you job.

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