Ask HN: Would anybody be interested in a series of primers on HS maths topics?

[wadd1e]

So with my exams coming to an end and a rather long summer beginning, I wanted to put my time to good use and work on something that people find useful.

I've come across various HN posts where folks said they were trying to relearn maths from school that they missed out on due to poor teachers/resources etc.

I love pure maths and over time I've learnt gained a strong intuition for high-school level calculus and analysis so I figured I should put my knowledge to good use and create a series of blog-style posts(which will be free because I'd like to make this available to everyone I can) which will teach ideas in a rigorous and complete way while still being accessible.

So I guess I have two questions:

A) would you be interested in such a thing? B) if so, what are the sorts of topics you would like to see?

[ColinWright]

This comes up again and again, and I think absolutely there is space in the world for a site that takes people through some of the basics,and then iteratively deepens. I'd be happy to provide supplementary/complementary material where appropriate.

Part of the problem is that people don't know what they want. Another part of the problem is that people ask about really advanced things that they are not ready for, and where they don't have time to dedicate to learning the basics.

So you have a challenge with what to include, how to arrange it, how to get people hooked,and how to get them to put in the sustained effort needed to gain a genuine understanding, rather than a superficial "I know what's going on."

For your own interest ... what would you start with?

People seem to like the idea of studying (or more accurately, to have studied) Linear Algebra, and perhaps Graph Theory.

I wonder what else ...

[wadd1e]

>Part of the problem is that people don't know what they want. Another part of the problem is that people ask about really advanced things that they are not ready for, and where they don't have time to dedicate to learning the basics.

Yeah I do totally see that, and my idea is to make a resource that gives you the value that you extract out of it, although it's a fine line between making yet another boring textbook and a resource that is engaging but also informative.

>For your own interest ... what would you start with?

This is where I am a bit torn, because on one hand, I'd love to jump in to cool stuff that people learnt _how_ to do but were never taught the ideas behind them. For example, integral substitution seem to be taught in this rather boring way where you're told to mechanically execute a bunch of steps that people just need to memorise to pass their exam.

I'd love to jump right in and derive the idea of a substitution from the Reimann integral definition, and go into some detail about the intuition behind it. And then perhaps I can explore more calculus like the idea of limits(which are typically another terribly explained) and then move on to Taylor series expansions etc.

But at the same time I don't want the barrier of entry to be really high, so mabye starting with the idea of derivatives, and then approaching higher level topics might be a better structure?

[EA-3167]

As far as sites like that go, I wonder if modeling it on a previous success like Physics Forums might not be a good idea? A combination of solid moderation, experts who want to volunteer their time, a hefty and accessible knowledge-base, and fellow learners in the mix seems to be key.

The fact that we're talking about HS level helps I think, since the number of applicable experts is pretty high.

[mindcrime]

A) yes, absolutely

B) whatever you feel like talking about

On related note, you might consider participating in the Summer of Math Exposition competition[1].

[1]: https://3blue1brown.substack.com/p/some3-begins

[wadd1e]

Oh thanks for reminding me of SOME, I might try participating for sure. The reason I asked B) is because I need a starting point since there's so much I could talk about, so e.g. "limits always confused me", "integrals never truly clicked", "the idea of derivatives and really the whole of calculus went by too quickly", or "polynomials and their properties are still a mystery" would be the sorts of starting points I'm looking for.

[latexr]

I remember a teacher in ninth grade warning students who up to that point found maths to be easy without studying: that would no longer be the case. From anecdotal memory, I think what happened was a shift from real problems to abstract concepts. Up until then maths problems had been rooted in the real world and could be solved with logic, but suddenly there were graphs and asymptotes and cosines and a bunch of other stuff without a clear connection to their usefulness to the world.

High school teachers didn’t fare better. One of them, when we were learning statistics, said there was no way we’d be able to complete the given homework on our own without a tutor. On the contrary, it was the most enjoyable and approachable maths had been for years. Finally something which connected to the real world again.

In retrospect, I think I had a string of mediocre teachers which sapped my excitement. As an adult I watched two second gif loops which clicked in my head ideas which weren’t made clear by previous explanations.

To answer your question, I’d be interested in analytic geometry and any concepts which would related to computer graphics.

Where would you post? Is there a feed we could subscribe to?

[wadd1e]

>From anecdotal memory, I think what happened was a shift from real problems to abstract concepts

Funnily enough, I am the exact opposite; I struggle with statistics and mechanics since they are very linked to the real world and I seem to thrive in understanding abstract ideas. The more abstract, the better :)

I like to think of abstract mathematics as a bunch of code in a library, the code on it's own is vast and has no real purpose when it is standalone, but it becomes immediately useful when a program with a purpose uses it in tangible ways. I would definitely love to make abstract mathematics make sense as a part of the project.

>To answer your question, I’d be interested in analytic geometry and similar concepts which would related to computer graphics.

Those are good suggestions that I didn't think about at first; function transformations and polar coordinates are definitely worth exploring, and a lot of computer graphics involves calculus and linear algebra that I do plan on covering already.

>Where would you post? Is there a feed we could subscribe to?

Still figuring details out, but probably on my .github.io domain(and if the project receives enough attention, I might move it onto it's own domain) and I'll likely use an email based system or an RSS feed after I tackle the "make good learning resources" problem.

[throwawayadvsec]

A) Hell yeah

B) Prerequisites to Machine Learning math(so prerequisites to Linear algebra, multivariate calculus and "advanced" probabilities/statistics)

B.2) it would be best if it's only the prerequisites to ML math and nothing else

[sn9]

Just write it and share it and see if anyone finds it useful.

The people who need it most probably won't know what to ask for.

[the__alchemist]

I would review Khan first, and compare what value you'd like to add compared to it.