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The case for ending calculus requirements for science majors

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Re: The case for ending calculus requirements for science majors

#131

Earlier quoted context omitted.

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 abbrev…

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.

>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.

Re: The case for ending calculus requirements for science majors

#132

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…

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.

Re: The case for ending calculus requirements for science majors

#133

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…

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

Re: The case for ending calculus requirements for science majors

#134

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…

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.

Re: The case for ending calculus requirements for science majors

#135
post #27

Earlier quoted context omitted.

> Hell most academics who use calculus everyday did not study real analysis and they are fine. That's an American perspective, I believe. In many European countries, many STEM students routinely learn real analysis. In fact, the term "calculus" doesn't even exist in e.g. German, it's all called "Analysis". Sure, a course tailored for physicists, chemists or computer scientists may (or may not, depending on the instit…

I'my always confused by Americans and their calculus because I really don't understand the essence of what difference there is between real analysis and calculus. The internet answer of "calculus is real analysis for engineers" doesn't help because you can have real analysis tailored for computer scientists and it is still real analysis.

As far as I understand, calculus = analysis without proofs - or at least without rigorous proofs. You might do some hand-waving and elementary transformations, but you're probably not gonna invoke the Least Upper Bound axiom of the real numbers.

Re: The case for ending calculus requirements for science majors

#136

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 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.

Re: The case for ending calculus requirements for science majors

#137

Earlier quoted context omitted.

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.

>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.

There's definitely some kinds of caving that are riskier than others.

Re: The case for ending calculus requirements for science majors

#138

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…

>not only my generation of kids had been forewarned of calculus' 'terrors' I think the real terror as a youngster is that you could fail a timed exam and have to repeat the whole course.

That, I agree, is very true.

I recall the horrible stress and anxiety I experienced early on in high school when I ran out of time in a mathematics exam and thus couldn't complete all of it. Panic started to set in because I faced the dilemma of having to decide which of the questions I could best answer (and that was far from being clear). The alternative option was to sketch out parts of more of the questions and leave each partially unanswered (on grounds of obtaining some marks fór at least having some knowledge of the material).

I cannot remember exactly what I did but I think it was a mixture of those two approaches. What I vividly do recall however was that I wrote a somewhat sarcastic comment on top of my examination paper with words to the effect that the examination was too long to do within the allotted time.

Under the circumstance, that wasn't the wisest of moves, it didn't win me any Brownie points with the teacher. Also, I was ridiculed and humiliated by my classmates as they laughed and crackled at me when the teacher stopped to read my comment out during his handing out of the marked papers.

I can't remember what marks I received except that it was borderline fail (and I can't even remember what side of the line the marks were on). I do recall the only consolation I had was that some kids received lower marks in the examination than I did.

There are two reasons for why that exam remains particularly memorable, the first is that it was first [but not the last] time I'd done badly in what I considered an important and key subject (unlike languages which back then I considered of little importance—much to my later chagrin and regret); and second, I knew that I could have done much better if I had had more time to compete it. Still that's hardly a reasonable excuse for being poorly prepared (which was a fact).

Here, I'd also make a distinction between examinations where one simply doesn't know answers to questions and those where one cannot provide satisfactory or adequate answers in the time available (for whatever the reasons), as marks won't necessarily provide an accurate assessment of a student's actual knowledge of a subject.

Again, that's unlikely to be a problem if one is sufficiently prepared. Nevertheless, there are some students who are particularly adept at doing well in exams and I'm quite envious of them or their ability. Especially, so those who've less interest in a subject than me and or who have demonstrated by other means that they've less knowledge of it than I have.

So be it, the world's not fair, and neither are examinations the ideal way to determine one's knowledge—but likely they're still the best method we have for said purpose.

Re: The case for ending calculus requirements for science majors

#139
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…

You don't need tricks to solve the limit of (x^2)sin(2x)/sqrt(x) as x->0, only to know equivalent infinitesimals, so that sin(2x) can be replaced by 2x in this limit and 2x^3/sqrt(x) can be simplified to 2x^(3-1/2) so the limit is zero. Moreover, you should know that x^2 and sin(2x) are really smaller compared to sqrt(x) so that the limit is zero. Knowing how to compare two infinitesimals can help you to replace a difficult process for an easier one, just like in differential equations sin(x) is replaced by x for small vibrations. That kind of knowledge allows you obtain an approximate solution in many real processes. So I don't consider that knowledge a bag of tricks. Furthermore, replacing sin(2x) for 2x is just the process of taking the linear approximation (the tangent line near x=0 for y=sin(2x)), so this is just an example of the power of calculus to replace a difficult question with an easier one. Also you learn to explore the world near a point (like a miscroscope) by the process of taking the linear approximation or taylor expansion of a function near a point, then you iterate this procedure to nearby points just like what happens when you solve a differential equation by Euler method. So I should say that there is a framework to solve problems via approximate solutions and computing limits is just a good first step to enter the realm of Calculus.

Re: The case for ending calculus requirements for science majors

#140

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…

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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