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Relearning math as an adult

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Re: Relearning math as an adult

#51

Post by JustinSkycak »

maroonblazer wrote: post #25

>> The ‘Foundation Series‘ is what I’m starting with. It’s for adults to help streamline learning (it skips the stuff that kids need, but adults don’t) and work back up through college-level math relatively quickly (emphasis on relatively ). I'm curious to know what 'stuff' he's referring to. And what about it makes it such that kids need it but adults don't. And if that's true, are we SURE kids need it? I had horrib…

Hi there, my name is Justin Skycak, I'm the Director of Analytics & Algorithms at Math Academy. I can speak a bit as to the stuff that's skipped in the Foundation Series.

After developing a curriculum that covers all the standards for 4th grade through AP Calculus BC, as well as plenty of advanced university courses (many of which are still under construction, but the structure is mapped out pretty comprehensively), we found that roughly a third of 4th grade through AP Calculus BC topics were not actually prerequisites for university math. So, we created a streamlined Mathematical Foundations course sequence that cuts out those topics. Those topics are necessary to check the box on grade-level / common core standards, but they're not really necessary for adult learners who want to pursue advanced university courses as soon as possible but lack the necessary foundational knowledge.

I'll also send your question to my colleague Alex Smith, our Director of Content, who designed the Mathematical Foundations courses himself and can elaborate more on the specifics.

Re: Relearning math as an adult

#52

Post by raincole »

fiforpg wrote: post #15

> but I needed a good reason that would justify the time investment It should be understood though that there are cases when math(-like) language is abused, leading to overcomplication and obscurantism [1]. In mathematics, there is always the temptation of formalizing for formalization's sake. Indeed, 99% of pure math is non-constructive ("there exists a group such that", "the algorithm converges in O(N) steps"), as…

Man, this article is an ad for Math Academy. I'm 100% sure that at the level of what Math Academy teaches, you don't need to worry about "non-constructive" or "pure math".

Re: Relearning math as an adult

#53

Post by AlchemistCamp »

dcw303 wrote: post #35
AlchemistCamp wrote: post #20

Earlier quoted context omitted.

I totally agree with you on the value in using Chat GTP when stuck. What's the scope of The Art of Problem Solving? How far does the series go?

AOPS audience is gifted high school kids, so it doesn't get up to the college level. The core texts are: - Prealgebra - Intro to Algebra - Intro to Counting & Probability - Intro to Geometry - Intro to Number Theory - Intermediate Algebra - Intermediate Counting & Probability - Precalculus - Calculus

Ah, okay. I actually took calculus in 8th grade. I studied another two years past that, dropped out, and then later did a complete 180 and graduated with a literature degree.

I'm now over 40 and interested in relearning the math I learned long ago and pushing a bit further than I had before.

Re: Relearning math as an adult

#54

Post by davorak »

dcw303 wrote: post #32
cloogshicer wrote: post #4

Earlier quoted context omitted.

This assumes that climbing the ladder comes easy. To me at least, it doesn't. It requires tedious labor, and lots of repetition for every single step. That's the main difference I keep noticing between me and people who say they like math or find it easy. They just look at each step of the ladder once, and immediately "get" it, sometimes even skipping steps. In contrast, I need to repeatedly step up and down the ladd…

My theory is that people who like math have a reward system that responds well to gaining an understanding on empirical concepts. I have that, and it does drive me to keep studying math. Not that I find it easy though, I don't think I'm able to skip steps, and I often have to repeat things I've already done before they sink in. The difference is that I find this process enjoyable, so I don't mind spending the time. I…

> The difference is that I find this process enjoyable, so I don't mind spending the time.

This is definitely the difference for at least some of the people out there, however...

Imagine however that you do enjoy it at the start so you move on from topic Y to topic Y+1, then to to Y+2. However you find that you no longer understand Y and you need Y when you are doing trying to learn Y+3 so you study Y+3 and Y, now your progress in Y+3 has been slowed down.

Really your goal was to get o Y+7 though that is where you can start breaking new ground and contributing but as you try Y+4 and Y+5 the gains stop and maybe even reverse. You are now on a learning treadmill(perhaps sometimes falling off and having to restart too) redoing Y-1,2,3,4,5 not moving forward. Often it is possible to find a trick/skill/simplification/etc to continue moving forward to get to Y+6,7.

How long would you find the process fun on that treadmill though? I think it is common to not find covering the same ground over and over fun or never being able to make it to the point where you are part of peer group where you can contribute. An understandable result is when those people invest elsewhere, where they see better returns.

Re: Relearning math as an adult

#55

Post by lebean »

kirubakaran wrote: post #42
xupybd wrote: post #34

Earlier quoted context omitted.

Thank you for bringing that visual memory back. Why do I struggle to remember my anniversary date but have that image burned into my brain.

You need an AI art of your anniversary date in the form of a goatse

Adding this to my arsenal of memorization tricks.

Re: Relearning math as an adult

#57

Post by aoki »

elteto wrote: post #40
dcw303 wrote: post #35

Earlier quoted context omitted.

AOPS audience is gifted high school kids, so it doesn't get up to the college level. The core texts are: - Prealgebra - Intro to Algebra - Intro to Counting & Probability - Intro to Geometry - Intro to Number Theory - Intermediate Algebra - Intermediate Counting & Probability - Precalculus - Calculus

Are you doing the online classes or only the books? I wanted to register for the online classes but they seem to be heavily oriented towards interactive learning.

The ones that have “instructors” and class times have chat-based sessions that you can skip if you prefer. Part of the homework is based on an adaptive problem system (Alcumus, which you can actually use for free) and part is weekly problem sets mostly based on the textbook. Writing (proof) problems are graded by a human so it is a useful way to get feedback on your proof-writing skills (if you know you are worse at it than a college math major).

Re: Relearning math as an adult

#58

Post by aoki »

AlchemistCamp wrote: post #53
dcw303 wrote: post #35

Earlier quoted context omitted.

AOPS audience is gifted high school kids, so it doesn't get up to the college level. The core texts are: - Prealgebra - Intro to Algebra - Intro to Counting & Probability - Intro to Geometry - Intro to Number Theory - Intermediate Algebra - Intermediate Counting & Probability - Precalculus - Calculus

Ah, okay. I actually took calculus in 8th grade. I studied another two years past that, dropped out, and then later did a complete 180 and graduated with a literature degree. I'm now over 40 and interested in relearning the math I learned long ago and pushing a bit further than I had before.

There’s also an intermediate number theory class that’s basically at the level of a college elementary NT course (one that does not assume abstract algebra), an Olympiad geometry class, and a group theory class. The first two do not have a text, the third has a text but you can’t get it without enrolling.

Re: Relearning math as an adult

#59

Post by AlchemistCamp »

hintymad wrote: post #14
redcobra762 wrote: post #12

Earlier quoted context omitted.

We did proofs in 7th grade as part of geometry, in a semi-rural United States middle school.

Good to know. I guess education in the US has local standards? I have this impression of the US not teaching proof because in a number of introductory math classes in my college, the profs dedicated chapters to teach basics of induction, how to write proofs, and etc.

> I guess education in the US has local standards?

Very much so! The US didn’t have a Department of Education until the 90s.

Re: Relearning math as an adult

#60

Post by aoki »

redcobra762 wrote: post #12
hintymad wrote: post #10

It looks how do do proofs is at university level in the US. I wonder why other countries start to teach kids how to do proofs from grade 7. They start with rigorous proofs in Euclidean geometry, the move to solid geometry, then to proofs in elementary functions, sets, number theories, and etc, then to polynomials and simple discrete maths and analytic geometry. By the time a kid graduates high school. using things li…

We did proofs in 7th grade as part of geometry, in a semi-rural United States middle school.

The “standard” place for geometry is 10th grade (after algebra 1 in 9th grade). A few geometric ideas have been moved from geometry to algebra 1 so that slope can be explained using similar triangles but this is just about memorizing explanations instead of doing proofs.

Today, if you aren’t in an honors geometry section, you likely learn a handwavy version of two-column proofs and do some pretty linear proofs that way. No symbolic logic, no mathematical writing.

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