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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

#91

Post by lordnacho »

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 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.

Re: The case for ending calculus requirements for science majors

#92

Post by MikeDelta »

sokoloff wrote: post #90
Chinjut wrote: post #82

Earlier quoted context omitted.

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).

The ' stands for (first-order) derivative. The second would be '' and so on.

sin(0)=0, sin'(0)=1

Re: The case for ending calculus requirements for science majors

#93

Post by nitwit005 »

> Similarly, Thomas Edison said that as a boy he had a “distaste for mathematics.” But this did not stop him from becoming one of the most famous scientific inventors of all time. “I can always hire a mathematician,” said Edison, “but they can’t hire me.”

The perfect solution, assuming you happen to be wealthy enough to hire mathematicians without worry.

Re: The case for ending calculus requirements for science majors

#94

Post by int0x2e »

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…

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.

Re: The case for ending calculus requirements for science majors

#95

Post by Ekaros »

feet wrote: post #22
melagonster wrote: post #9

Earlier quoted context omitted.

apparently, because his GPA, he can't find any job and the only thing can d is waiting for starve and die.

What companies even care about gpa

It is easy legal way filter applicants. And they simply have too many applicants.

Re: The case for ending calculus requirements for science majors

#96

Post by sokoloff »

MikeDelta wrote: post #92
sokoloff wrote: post #90

Earlier quoted context omitted.

> sin'(0) = 1. = 0, not 1, unless I'm misunderstanding your notation (or blowing trig).

The ' stands for (first-order) derivative. The second would be '' and so on. sin(0)=0, sin'(0)=1

Ah, thanks! I was thinking it was inverse (or typo); didn’t get to d sin(x)/x.

Re: The case for ending calculus requirements for science majors

#97

Post by flopriore »

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…

Definitely yes, actually I'm studying computer engineering in Italy (still bachelor degree) and it's mandatory to have the exams of Mathematical Analysis I and II and also the exam of Numerical Analysis, where they teach you floating point numbers, Lagrange interpolation, Gauss method, non-linear equations and quadrature formulas.

Re: The case for ending calculus requirements for science majors

#98

Post by imtringued »

duskwuff wrote: post #35
dunham wrote: post #32

Earlier quoted context omitted.

I remember hearing in college (a couple decades ago) that Chemical Engineering students needed to know a lot about solving differential equations. In the math department, I was told by professors that a lot of other departments were requiring the "pre-calculus" course without requiring calculus as a means of weeding out poorer performing students.

> I remember hearing in college (a couple decades ago) that Chemical Engineering students needed to know a lot about solving differential equations. That stands to reason. Describing the dynamic behavior of a chemical system -- e.g. the amounts of different reactants and products over time, the temperature and pressure of the system, etc -- is exactly the sort of task that differential equations are perfect for.

I only really understood the intuition behind differential equations once I did the control theory course. I didn't need any prior math course.

Re: The case for ending calculus requirements for science majors

#99

Post by elcritch »

brianwawok wrote: post #44
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…

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 thos…

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.

Re: The case for ending calculus requirements for science majors

#100

Post by imtringued »

Tainnor wrote: post #27
elashri wrote: post #24

Earlier quoted context omitted.

You don't need to understand where is calculus come from to tqke real analysis. Hell most academics who use calculus everyday did not study real analysis and they are fine. This extreme angle is not relevant. The difference is that you can't fot example understand physics without calculus but you can understand and study calculus without real analysis.

> 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.

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