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Ask HN: A math study program?

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Re: Ask HN: A math study program?

#51

Post by wanderingmoose »

equilibrium wrote: post #2

You might want to have a look at The Art of Problem Solving - https://artofproblemsolving.com/

+1 What I find really useful about these books is they allow self-teaching. (in my case a 13 year old kid) The books follow a methodology of presenting problems and having you try to solve them before walking you through the explanations. The chapters build up to "challenge problems" which are carefully crafted to require you to apply what you've learned from the current and earlier chapters. Most of the challenge problems are lifted from math competition problems (with citations), but their use is very well curated.

We are using the printed books, but there are online resources available.

Re: Ask HN: A math study program?

#52

Post by dorchadas »

I'm part of a Discord server that does exactly this. It's run by a math PhD, and he takes you through proof writing and up through the basic fields (algebra, analysis, etc) checking and vetting your proofs. It's great, and I've gone through multiple courses worth of stuff in abstract algebra, linear algebra and analysis. Currently working on some geometric algebra stuff.

You can message him on Reddit if you'd like and see if he'd give you an invite: CheapViolin

Re: Ask HN: A math study program?

#53

Post by Tao3300 »

Penyngton wrote: post #29
Tao3300 wrote: post #26

Earlier quoted context omitted.

> There's no royal road to geometry. Come on. This is totally not what OP was asking for. Pithy adages might seem wise and helpful, but you're dismissing the fact that OP very much asked for the work and the hard road. They want to backtrack and fill gaps in their skill, and just want recommendations on the path to take to get there.

I'm sorry that the phrase riled you. I didn't intend it to be pithy, but simply to demonstrate that it's well known that what OP is asking for doesn't exist. > Is there a course or series of courses I can take that can build my math skill level to solve such problems with ease? It seems to me that this question assumes that there is a "royal road" of courses that will turn him into the mathematician he wants to be, b…

"I'm starting to struggle [how do I get better?]" is a lot different than Ptolemy telling Euclid the Elements is too hard and asking for a shortcut. That much is obvious because OP pretty clearly enjoys the work and wants to do more of it. There are going to be right and wrong ways to go about this.

(Here's where I really go off the rails, but trust that I mean this in the same good humored sense with which I would point out that say, vinegar catches flies better than honey.)

We should also cast doubt on the original quote. One, we only have it according to Proclus, roughly eight centuries after Euclid. Two, Ptolemy I was brilliant in his own right, even among the Diadochi. Three, we don't teach anyone straight from the Elements anymore and have learned a great deal about ways people learn. So while I agree there's no substitute for rigorous practice if you're looking to understand a mathematical concept on an intuitive level, we've certainly found some "highways" since 300 BCE.

Re: Ask HN: A math study program?

#55

Post by lupire »

jayro wrote: post #39
strikelaserclaw wrote: post #21

Earlier quoted context omitted.

jeez, what kind of 11th and 12th grade curriculum teaches topology, real analysis etc...? Is this a syllabus for math whiz kids?

Well, it turns out that when you have mathematically-talented students completing Calculus in 8th-grade, and move on the Linear Algebra and Multivariable Calculus in 9th, you eventually reach Real Analysis and Topology by the end of high-school - although, we haven't gone quite as deep in those particular subjects as the others mentioned. But we do comprehensively cover Differential Equations, Discrete Mathematics, P…

Honestly that looks like superficial rushing for rushing's sake. There is so much advanced and deep elementary math kids could learn.

Re: Ask HN: A math study program?

#56

Post by lupire »

jayro wrote: post #46
yamtaddle wrote: post #44

Earlier quoted context omitted.

Opt-in educational programs of all sorts are usually heavily selection-biased toward students that are well-motivated and generally exceptionally easy to teach—good support from home, probably above-average SES, above-average IQ, et c. Which doesn't mean such programs are useless, just that they're typically far less effective if you try to apply them to a representative slice of the overall student population.

It's true that the students in the school program are high-aptitude, but something like 70% of the students in the middle school where this all started are on the federal free and reduced lunch program (low SES) along with a couple of the top kids in the original cohort, who I taught personally and they were amazing.

> 70 % of the students in the middle school where this all started

but

> a couple of the top kids in the original cohor

Are their parents from a tight-knit immigrant community, highly educated in their previous country, with economic prospects in the US dimmed by language barrier and professional certifications that got dropped at the border?

Re: Ask HN: A math study program?

#57

Post by lupire »

equilibrium wrote: post #2

You might want to have a look at The Art of Problem Solving - https://artofproblemsolving.com/

AoPS leans a little too hard into silly contest math / trivia tricks, not into deep understanding of the underlying mathematics. Also, they have low production values, lacking the nice graphics used in professional school textbooks (before Eureka and the greedy cult of throwaway monochrome textbooks ruined everything) to help students visualize 2D/3D functions and geometry.

The AoPS books jassume that if you are smart enough to learn the tricks and hard problems, you are smart enough to learn deep math later.

Which is a strange premise, because the PhD geniuses who created AoPS, base their credibility on the fact that they aced all these contests when they were kids... But they did it without any of these materials!

They created a "teaching to the test" curriculum, which, while mathematically sound, created a rat race that makes the contests harder every year, requiring more memorization and silly speed training, as more people memorize all the strategize that the original contests expected student to try to creatively discover on their own.

Re: Ask HN: A math study program?

#60

Post by dprophecyguy »

jayro wrote: post #38
AlchemistCamp wrote: post #6

IMO, the clear choice for this is Math Academy. It was started by a very, very early Uber contractor who built the early versions of their dispatcher, their profiler and also the grid system that helped them scale and pretty much saved them during new year's in 2013. Since becoming wealthy from Uber's IPO, he's been pouring money into hiring experts and building the curriculum. The first step was a non-profit program…

Good morning, HN! It's Jason (the founder). My wife (co-founder and co-conspirator) just woke me up to alert me to a sudden spike in demo requests, so I'm a little blurry-eyed at the moment (was up late last night trying my best to get the marketing site functional), but I'd be happy to answer any questions you might have.

Hey Jason, would also like the idea to have a lifetime subscription model for working folks who can use the platform based on time availability.
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