The case for ending calculus requirements for science majors

Yeah tbh undergraduate calculus courses are really not that difficult.

> 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.

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.

Another comment on this thread talked about the difference between a mathematical mindset and an engineering mindset, and I think that's exactly right.

As a researcher and controls engineer, I certainly appreciate the necessity of rigorously proving the behavior of new algorithms. On occasion I develop those proofs myself. I'm not very good at it, and I appreciate those who are.

But.

Compared to the amount of time I spent in grad school honing my ability to generate proofs (courses in both real and numerical analysis, on top of the very applied math-flavored controls courses), the amount of time I spend either reading or producing stability proofs is minuscule. On the other hand, I spend an enormous amount of time solving constrained optimization problems. Both require calculus. But guess which topic I never got formally taught in grad school?

The point being that while I appreciate proofs and mathematical rigor and clever algebraic manipulations, including changes of variables, in practice not only do I virtually never use those things, but the mindset I need when approaching an engineering problem is really quite distinct from the mindset I had to adopt when working my way through real analysis.

I'll go one more step and say that in a lot of cases the two mindsets can actually be mutually exclusive. My advisor was brought up in a nonlinear controls lab where rigor was everything. Today, controls is being consumed by deep reinforcement learning, which is driven primarily by experiment. We get an idea for a new approach that might work, we try it out and see whether it works. We then go back and try to understand mathematically why it works. My advisor is unable to work that way; he must have things proven first, and only then will he even look at experimental results.

He's been completely left behind by the field. He's unable to brainstorm about new things to try, because he can't accept that experimentalists can move faster than theoreticians. We've had vigorous arguments about this. I think that if enough experimentalists can show repeatable results, that's a good indication that mathematically there's something there worth investigating. He just thinks the experimentalists are all building a house on sand.

It was specifically the civil engineer that screwed up, and the errors involved trigonometry and integrals.