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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#71

Post by polishdude20 »

wwarner wrote: post #31

I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy. To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus. Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple thin…

Putting on a play is a very human interactive activity. Until math lets you interact with many humans in a rich experience, it won't be put on a pedestal like drama.

Re: Proof you can do hard things

#72

Post by sanderjd »

batman-farts wrote: post #60

It's a bit sad that calculus remains the stereotypical example of difficulty in most curriculums. Throughout childhood, I remember it seeming like some sort of complex, inscrutable, untouchable phantom hanging in the distance at the far end of the high school math course progression. If somebody had told me that calculus is how you transition between dimensions, or that techniques of integration would enable me to ge…

Motivating topics for students is so important and underrated. It's also super hard I think. For one thing, everyone responds to different motivation. Some people are motivated to learn basic algebra more by the possibility of extending it into applied math so they can get a good job as an engineer. Others don't have any interest in that, but rather would be motivated by the beauty of pure math. And students themselves have no idea what they like.

But yeah, I can think of so many examples of things that I would have been way more into in school if I understood how they mapped onto the adult world. Statistics is probably at the top of that list though.

Re: Proof you can do hard things

#73

Post by gmadsen »

jskherman wrote: post #62
lcnPylGDnU4H9OF wrote: post #43

Earlier quoted context omitted.

What did they do with Excel and R?

As a chemical engineering student, it's a whole lot of formulas cobbled together to spit out calculations that would otherwise be done on hand (especially empirical methods that compute estimates where a clean answer is not possible like $\int{\frac{\sin{x}}{x}}$). The formulas usually come from what you study in school (e.g. the Redlich-Kwong equation in Physical Chemistry to estimate the properties of real/non-idea…

all those formulas were derived using calculus...

Re: Proof you can do hard things

#74

Post by User23 »

jskherman wrote: post #62
lcnPylGDnU4H9OF wrote: post #43

Earlier quoted context omitted.

What did they do with Excel and R?

As a chemical engineering student, it's a whole lot of formulas cobbled together to spit out calculations that would otherwise be done on hand (especially empirical methods that compute estimates where a clean answer is not possible like $\int{\frac{\sin{x}}{x}}$). The formulas usually come from what you study in school (e.g. the Redlich-Kwong equation in Physical Chemistry to estimate the properties of real/non-idea…

Engineers didn’t do those calculations by hand. They were done by “computers” who were mostly youngish women with slide rules.

Re: Proof you can do hard things

#75

Post by bee_rider »

cameldrv wrote: post #57
bee_rider wrote: post #53

Earlier quoted context omitted.

Calculus is needed to understand, like, basic sophomore and junior year engineering stuff. You can maybe pass the tests without understanding where the models came from if your professors are just really lazy and only give you canned problems, but that isn’t a goal we should strive for. And engineers should usually be using battle-tested models rather than coming up with their own derivations, so to some extent using…

I wonder if there’s a way to teach Calculus in a more practical way. I use the principles of Calculus constantly in many aspects of my job, but I don’t think I’ve ever done say, integration by parts professionally. Understanding deeply what an integral and a derivative are is a very useful skill though.

As an undergrad I tutored folks in a sort of “calculus for non-STEM students” class that focused more on practical stuff and applications… and TBH I think trying to shield them from the complexity didn’t really do them any favors. I often found that they had some practical algorithm memorized step-by-step and some graphical or conceptual intuition, but when the steps and intuition betrayed them we’d end up spending a while backtracking to find where they lost track of the concrete rules, and then we could work our way forward to catch up to their intuition. Practical results are good guideposts but don’t replace full understanding I think.

That’s just my perspective, though, I have a pretty simplistic, algebraic way of looking at math. I could never be a mathematician or see true beauty in math, it is just a bunch of little rules to me.

IMO calculus class is fundamentally just relatively abstract compared to the stuff before it. But once you’ve finished it, your engineering and science classes should be full of practical, reinforcing applications, right?

Re: Proof you can do hard things

#76

Post by m463 »

wwarner wrote: post #31

I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy. To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus. Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple thin…

I've found that some disciplines need calculus, others don't. I've found deeply understanding logic and binary/hex MUCH more important than calculus in my career.

Re: Proof you can do hard things

#77

Post by chasing »

> You know they will never use it in adulthood, outside of certain career choices.

Just going to register my dislike of this particular trope. Mostly because "certain career choices" is doing a huge amount of work. "Certain career choices" can give you access to a very high income. They can give you access to a deeper understanding of some pretty interesting stuff and put you in a position to accomplish all sorts of amazing things.

People use calculus in the sciences, of course, but also in business, the arts, music, politics, and beyond.

We learn calculus when we're young as a part of expanding ourselves, casting the widest possible net to find that intersection of what we're good and and what we're excited by. And to fill our quiver with as many arrows as possible for when we hit the adult world. And, of course, to build our self-esteem by showing ourselves we can accomplish hard things.

But I would highly recommend against taking the attitude that "you'll probably never use it." That's counter-productive. And the people who "don't use things" are boring...

Re: Proof you can do hard things

#78

Post by thfuran »

gmadsen wrote: post #67
roflyear wrote: post #49

Earlier quoted context omitted.

You don't use calc much when you use R, unless you're working on a problem that involves calculus, which isn't many problems, usually? R is usually used to do data stuffs in my experience. Like, "take in this data from this CSV, and do these manipulations" which may involve math but not often calculus.

using those "data stuffs" are usually based on calculus. Statistics and probability are both defined in terms of calculus. calculus is the most basic of mathematical machinery, that it is essentially a requirement to do anything else.

You're kind of arguing that you can't walk without studying kinematics.

Re: Proof you can do hard things

#79

Post by m463 »

gmadsen wrote: post #67
roflyear wrote: post #49

Earlier quoted context omitted.

You don't use calc much when you use R, unless you're working on a problem that involves calculus, which isn't many problems, usually? R is usually used to do data stuffs in my experience. Like, "take in this data from this CSV, and do these manipulations" which may involve math but not often calculus.

using those "data stuffs" are usually based on calculus. Statistics and probability are both defined in terms of calculus. calculus is the most basic of mathematical machinery, that it is essentially a requirement to do anything else.

Are probability and statistics really practically based on calculus? Most math curriculums do not have a calculus requirement to take statistics.

Re: Proof you can do hard things

#80

Post by tjmc »

WesleyJohnson wrote: post #46

I lost interest in school around the 10th or 11th grade. I never took any math classes beyond what was required to graduate way back in '96 in Florida. I also didn't go to college. I've been a professional web developer since 2005 and a development manager (who still codes) since 2017. I don't understand the first thing about Calculus or even logarithms. I'm sure if I did, I'd probably be a better developer. I've had…

I liked Khan Academy. Got me all the way through Mechanical Engineering and I didn't start until I was 38
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