So you want to study mathematics • Hacker News Board

Re: So you want to study mathematics

#161

Post by ghaff » Mon, Mar 07, 2022, 10:46 PM UTC

jll29 wrote: post #62

joatmon-snoo wrote: post #49

Earlier quoted context omitted.

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

Calculus and linear algebra seem to _totally_ dominate the curriculum in most (all?) countrie. What about meta-mathematics? Topology? Logics? History of mathematics? Philosophy of mathematics? Combinatorics? Number theory? Discrete mathematics? Graph theory? In the post, the fieds under "electives" are by far the most interesting ones, IMHO. And I fully agree, in-depth knowledge of probability theory as well as descr…

Interestingly the ascent of linear algebra is a relatively recent thing. I have an engineering degree but while I was certainly exposed to basic matrix stuff, never took a linear algebra class. When I was an undergrad, you took differential equations in addition to basic calculus for engineering. (You needed for system dynamics among other things but it was very cookbook.)

Linear algebra became a lot more interesting once you had cheap computers and Matlab.

Re: So you want to study mathematics

#162

Post by macrolime » Mon, Mar 07, 2022, 10:48 PM UTC

narrator wrote: post #128

brimble wrote: post #31

Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…

If you just want to learn math for purely practical reasons, Khan Academy ( http://www.khanacademy.org ) is great. It might have added more lessons, but when I went through it, it went up through 1st year college calculus. The thing that makes it VASTLY better than most self study math programs or books is that there are hundreds of exercises that you can do, and see if you got the right answer. If you didn't, it wil…

Where are there exercises?

I just tried clicking on some linear algebra topic, but it seems there are just videos

https://www.khanacademy.org/math/linear-algebra/alternate-ba...

Re: So you want to study mathematics

#163

Post by ghaff » Mon, Mar 07, 2022, 10:50 PM UTC

staindk wrote: post #98

joatmon-snoo wrote: post #49

Earlier quoted context omitted.

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

Super agree. I took calc 1 and stats 1 & 2. Much preferred the stats and it set me up for understanding all kinds of science lingo in articles and papers. I also indirectly use stats fairly often at work.

There are different types of stats. I took a stats course in my grad engineering program. Not being the best person at math I think I probably struggled with the math sufficiently to get distracted from the concepts. When I breezed through a stats course when getting an MBA I understood the concepts much better--though the professor was almost certainly better as well.

Re: So you want to study mathematics

#164

Post by jpz » Mon, Mar 07, 2022, 10:50 PM UTC

joatmon-snoo wrote: post #49

brimble wrote: post #31

Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

You can’t understand much about statistical inference without calculus.

It’s all integrals over pdf’s. A lot of integration by parts and other things in the core curriculum.

Re: So you want to study mathematics

#165

Post by pmyteh » Mon, Mar 07, 2022, 10:53 PM UTC

Bostonian wrote: post #78

joatmon-snoo wrote: post #49

Earlier quoted context omitted.

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

I wonder how much statistics someone can understand without calculus. For example, how do you explain what a continuous probability density function (such as the Gaussian) is without calculus?

I teach introductory quantitative research methods to communication undergrads, most of whom have no calculus. (Which is essentially optional in the UK as it's taught at A Level after most students have specialised away from maths).

They don't seem to have a problem intuiting what a plotted PDF is showing. I think that's because in some sense it can be read analogously to a histogram. Of course, they don't have the tools to generate or manipulate one. But that's honestly not something that applied social science researchers have to do often when using traditional methods.

Re: So you want to study mathematics

#166

Post by ghaff » Mon, Mar 07, 2022, 10:54 PM UTC

dhosek wrote: post #64

joatmon-snoo wrote: post #49

Earlier quoted context omitted.

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

Or the math covered in finite math classes which is a mix of combinatorics, stats, probability and linear algebra. I remember doing my time in the math tutorial room during my grad school days and helping the kids from the business calc classes who were learning math they weren't going to use from books written by people who didn't understand the domain that they were trying to teach math for. Seriously, what busines…

When I tutored in business school--mostly related to math-related things (which itself says something about the level of math knowledge among those who weren't engineering undergrads)--pretty much the only calculus that came into play was finding maxima and minima of curves in economics which was both simple differentials and mostly pretty academic anyway. A little later I did some more complex optimization problems but that was done by software (LINDO at the time) anyway.

Re: So you want to study mathematics

#167

Post by mmmpop » Mon, Mar 07, 2022, 10:55 PM UTC

ghaff wrote: post #156

JadeNB wrote: post #125

Earlier quoted context omitted.

> If anything should be dropped from a highschool level its all of the insane memorization you have to do for some of the lower level math classes - I found that totally useless. You then learn some basic calculus and realize "I just wasted so much of my life" and never need to memorize those things again. What sort of memorizations do you have in mind that you no longer need to memorize once you know calculus?

Pretty much all the classic Newtonian formulae you memorize in high school physics classes can be derived (relatively) easily once you bring calculus in. A general problem with high school classes in particular--still somewhat true in certain university classes but much fewer--is that there are dependencies across classes. So you end up with a lot of "Memorize this thing because you don't have an advanced enough back…

In my high school experience, this was avoided if you had the desire and aptitude to just take Honors Physics instead.

To work around the fact that many of us were still in precalc, our teacher just taught us the power rule, the relationship between slopes of tangent lines, etc., without diving into the "why" of why those things worked.

That said, yeah maybe for the most basic of university of physics the whole "derive it on the fly" strategy works, I guess? But when you get to more advanced courses like mechanics of materials, you'll do yourself the favor and take to memorizing at least a few of the commonly used equations.

Re: So you want to study mathematics

#168

Post by bitexploder » Mon, Mar 07, 2022, 10:56 PM UTC

susanrigetti wrote: post #21

Py-o7 wrote: post #17

This felt like it was written by a physicist or engineer. Too much emphasis on differential equations and not enough on things like topology, functional analysis and/or non-introductory parts of algebra like say representation theory.

guilty as charged! :)

As someone with a keen interest in learning Engineering part time, I found your write ups really helpful though! I enjoy learning math but like to have an angle towards a practical and useful application. It keeps me a little more motivated than pure math learning. With ADHD the concept of being able to build cooler things always keeps me going. But somewhere along the way of learning purely theoretical things for too long my brain just loses interest (not enough reward), even though I enjoy it in the moment it is hard to get to the starting line and take the first step after a while :)

Re: So you want to study mathematics

#169

Post by wbsss4412 » Mon, Mar 07, 2022, 10:58 PM UTC

zozbot234 wrote: post #150

Melatonic wrote: post #95

Earlier quoted context omitted.

Not sure I agree with that - you also have to take into account that calculus is a requirement for many other sciences. I suppose you could just of course make it a pre-req for things like that but I found that in highschool rarely did they go that deep. Physics becomes a hell of a lot easier with basic calculus for example. If anything should be dropped from a highschool level its all of the insane memorization you…

Calculus is also a requirement for statistics and probability. You simply cannot meaningfully talk about the latter without referencing the former.

You can certainly make significant headway with some basic combinatorics and basic tables for things like the normal distribution, no calculus needed. This is in fact how most people currently learn statistics.

Re: So you want to study mathematics

#170

Post by pjbeam » Mon, Mar 07, 2022, 10:59 PM UTC

joatmon-snoo wrote: post #49

brimble wrote: post #31

Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

My prob and stats courses required the calc sequence (US based math undergraduate).