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So you want to study mathematics

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Re: So you want to study mathematics

#91

Post by dwrodri »

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.…

Swinging by to plug my personal favorite resource for refreshing my self on Bayesian stats: https://www.youtube.com/playlist?list=PLwJRxp3blEvZ8AKMXOy0f...

I think statistics is by and large the most proportionally underrated subject proportional to its utility. A good command of stats and probability expands your power to use data to reason about answering questions. The channel author, Ben Lambert, has an alternative playlist where he uses some of the techniques taught in this playlist to solve problems in econometrics. However, a lot of what is taught here builds a great foundation for other domains, on everything from bioethics to data journalism to computer vision.

Another great channel that focuses a bit more on the machine learning side of things is StatQuest with Josh Starmer: https://www.youtube.com/c/joshstarmer

Re: So you want to study mathematics

#92

Post by Buttons840 »

Koshkin wrote: post #68
Buttons840 wrote: post #43

Where's statistics? You mean to tell me I could go through all that and come out not knowing statistics?

Agree, but I have a feeling that statistics is more like (theoretical) physics, in the sense that it is "not math."

Yeah, it's more application oriented and philosophical than the pure calculation of pure math. I think it's under-taught in schools though. I think it's more useful than calculus for most people and should be taught before it.

Re: So you want to study mathematics

#93

Post by mathgenius »

Modern calculus (analysis) was invented because people shot themselves in the foot working with topology and wondering exactly what is a "curve" ? I am a big fan of this approach to learning mathematics, just forge ahead and when (if) things fall apart then go back and fix up the foundations. To this end I recommend a couple of books. "The Knot Book" by Adams is a very interesting exploration in topology (without requiring all the years of study at university before you are allowed to learn exactly what a topology is). And in another direction, group theory was invented because the study of symmetry gets very tricky! But if you want to dive in anyway then have a look at Conway's "The symmetries of things". It is a lot of fun. Most modern group theory (or algebra) books don't actually have any pictures of symmetric things, just endless formulas and lemmas. If you want to be a pro, then you gotta learn that stuff, but there's definitely pathways into higher mathematics that don't require you to learn that.

Re: So you want to study mathematics

#94

Post by [deleted] »

hintymad wrote: post #46

I find it hard to believe that the author started to appreciate physics by reading The Feynman Lectures on Physics before any exposure to physics or even algebra, and in less than three years went from barely knowing high school math to enjoying advanced mathematical physics and graduate-level quantum physics. It looks this is one-in-a-million level brilliance as learning the sheer amount of requirement knowledge in…

[deleted]

Re: So you want to study mathematics

#95

Post by Melatonic »

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.…

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 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.

Re: So you want to study mathematics

#96

Post by pphysch »

dang wrote: post #72
pphysch wrote: post #33

Earlier quoted context omitted.

I'm not sure what your point is. Are you implying that you are not contributing to the mystification and idealization of mathematics? In other words, I do not see how you are dealing with the "baggage" of learning mathematics beyond name-dropping it. In my opinion, the mysticism is the baggage. And then the rest of the blogpost reads like a conventional curriculum within the conventional academic regime with which we…

Please don't post in the cross-examining style. We want curious conversation here. This is in the site guidelines: https://news.ycombinator.com/newsguidelines.html .

I don't follow. The author dismissively ctrl-V'd a paragraph with no further explanation, and my response asking for elaboration gets shadow-buried by a mod. What?

Re: So you want to study mathematics

#97

Post by PartiallyTyped »

mathgenius wrote: post #93

Modern calculus (analysis) was invented because people shot themselves in the foot working with topology and wondering exactly what is a "curve" ? I am a big fan of this approach to learning mathematics, just forge ahead and when (if) things fall apart then go back and fix up the foundations. To this end I recommend a couple of books. "The Knot Book" by Adams is a very interesting exploration in topology (without req…

Speaking of group theory, I can recommend "A book of abstract algebra". I think that it's a very approachable introduction to the topic. As a person with a CS degree doing ML, it changed my perspective on so many different topics, I can't recommend it enough.

https://www.goodreads.com/book/show/8295305-a-book-of-abstra...

Re: So you want to study mathematics

#98

Post by staindk »

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.…

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.

Re: So you want to study mathematics

#99

Post by eftychis »

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.…

Well you can think of it like going to the gym. You don't exactly see people doing squats during their daily life, but you can see the results of people having a good physical core.

This needs to be explained further during education and motivated appropriately. We have a short-term utilitarian perspective, and we need to take a step back at times and recall that it takes time and lots of sculpting to transform a wood log to a art piece.

As you can jog everyday for fun and/or for the challenge you can also jog to improve your physical health. And not doing proofs is like declaring a guy can weight-lift by just watching videos on youtube and never lifting a weight. Or a guy can "code" without writing a line of code.

Re: So you want to study mathematics

#100

Post by zinclozenge »

potbelly83 wrote: post #85

As a math PhD I have to say the only way you're going to learn mathematics is if you actually have a pressing need to do so. i.e. You have a project at work that needs some math, you have a hobby that needs some math. In this case you just learn what you need. Just learning math for its own sake outside of a University STEM track is just too hard (I wouldn't be able to do it and I've tried).

This is true. When I started my first job, I tried casually learning more from where I stopped after I finished school. My motivation slowly waned as I realized I vastly preferred playing video games than watching lectures and trying to do some problem sets.
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