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Relearning math as an adult

gmays.com

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Re: Relearning math as an adult

#91

Post by whatshisface »

tayo42 wrote: post #90
jorgesborges wrote: post #28

I’m a thirty-something with an arts degree who decided to learn math. Basically I was tired of reading popular science and being fed metaphors to understand concepts. I wanted to “see” it for myself. I spent time online at Khan Academy and friends for a year or so on and off. It was fine but meandering? So I enrolled in community college! It’s great. I have a clearer path, immediate feedback, teachers, and an obligat…

> working toward a bachelor of science in physics. Thats cool, I kind of want to do that. But also Im stuck with wondering, I put all this work into that, what do I do at the end?

You could get a PhD in physics, and if you time it right, you will die right after graduation, the moment when all of your classmates realize they're staring down 40 years of software engineering. The tombstone could read, "I figured it out."

Re: Relearning math as an adult

#92

Post by dcw303 »

MrVitaliy wrote: post #80
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

I think it's a weird way to learn math, and I learned it this way in school. Most of these courses just teach information memorization and recall. sin(x)^2 + cos(x)^2 = 1, etc. I would start with something like Elementary Analysis: The Theory of Calculus, and work from there. You'll eventually arrive at the same place -- Calculus but from a much stronger mathematical foundation.

I have not found that to be the case, the books I have read have gone into deep foundational detail to build up knowledge. Perhaps you're referring to Vol 1 & 2 of "The Art Of Problem Solving"? I haven't read them but from what I know they are a distillation of core concepts for students looking to do competitive maths.

It's confusing because that title is also the name of the publisher / website of the series of the books I'm reading.

Re: Relearning math as an adult

#93

Post by galaxyLogic »

ginbazinga wrote: post #79

If OP still wants to learn the mathematical foundation of transformers, I built a free alternative learning tool: https://afaik.io/nebula?mode=nebula&category=blueprint&id=ed... It's also based on an underlying knowledge graph, connecting concepts across various subjects like maths, machine learning, physics, etc. You can check the graph for transformer here: https://afaik.io/nebula?category=brickset&id=VLlOnZLl&mode…

I find the concept of "underlying knowledge graph" interesting. What does it mean?

I assume it means such a graph connects the topics together as "pre-requisites". To understand A you need to already understand B and C, and to understand B you need to understand D and ... etc.

But the thing about such a graph is that really it must be a tree, not just a directed graph. Why? Because there cannot be cycles in it. If to understand A you need to understand B, and to understand B you would need to understand A, you could never understand either of them. Right?

Re: Relearning math as an adult

#95

Post by paulpauper »

There is so much interest in self-learning math or physics. We're in something of an autodidacticism boom. The amount of work to even have any hope of being proficient at this is substantial. For some reason it's always self-learning math or physics, which are among the two most difficult subjects. You got your work cut out. Even if you understand the basic concepts, understanding papers is another level above that.

Re: Relearning math as an adult

#96

Post by paulpauper »

jorgesborges wrote: post #28

I’m a thirty-something with an arts degree who decided to learn math. Basically I was tired of reading popular science and being fed metaphors to understand concepts. I wanted to “see” it for myself. I spent time online at Khan Academy and friends for a year or so on and off. It was fine but meandering? So I enrolled in community college! It’s great. I have a clearer path, immediate feedback, teachers, and an obligat…

Videos are good to get some barebone knowledge, but are too superficial or unstructured to replace classroom settings, with graded exams and homework.

Re: Relearning math as an adult

#97

Post by galaxyLogic »

ChainOfFools wrote: post #66
hintymad wrote: post #6

Earlier quoted context omitted.

> Math is easy if you build up from fundamentals To a certain point, I guess. Most people hit a wall of abstraction at some point, either because the abstraction is too hard or because the abstraction stops being relevant so the person loses drive to learn. For me, the wall is model theory and the second course of abstract algebra. They are both too hard and too abstract for me to push through.

> abstraction stops being relevant I found this to be the points where abstractions being learned today are only precursors for abstractions that will be learned tomorrow. Another way to put it is at the stage where you're learning to make tools that are themselves only used to make other tools, not used to get results outside of the domain of tool making. These stages have no apparent relevance outside of math, and…

I remember memorizing multiplication tables in school.

I learned that 3 x 9 = 27. You just had to memorize that, right? Well then I realized that if 3 x 10 = 30, then 3 x 9 must be one fewer '3' added together by the multiplication, which means take out one '3' from the set of 3s you are adding together by multiplication when doing 3 x 10, which comes to 30 - 3 = 27.

That means I didn't really need to memorize 3 x 9, I needed the above simple rule in addition to the fact that n x 10 is always what you get when you take the digit 'n' and add a 0 after it.

So learning multiplication tables was hard, until I learned the rule of looking for an easier-to-remember result and then adding or subtracting something to it. Of course I also had to understand that multiplication is really just repeated addition.

My teacher never taught me this trick, just told us to recite the multiplication tables in out heads again and again. But after doing that for some time I figured out the above trick myself.

Learning math beyond multiplication is hard if you cannot multiply numbers in your head, because lots of math presentations assume that of course you know that 3 x 9 = 27. Or something similar. It is not just about understanding the concepts, it's about being able to perform calculations, in your head. Else you cannot understand the explanations of new concepts. Even though we have pocket-calculators, we still need to be able to do calculations in our heads to understand new topics. in math.

So, learning what is 3 x 9 is not hard AFTER you have learned n * 10, and this trick. I assume something like that happens in the minds of mathematicians. They know a lot of math already which makes it easier to understand new results when they already know a lot. To learn what is n * 10, you had to learn 1 x 10, 2 x 10, 3 x 10 etc. and then understand the pattern in there.

Learning something is easy if you already know lots of related stuff. So it's not about learning more and more difficult things, it is about just learning more and more, related things. It is about having more and more (learned) data in your head.

I assume that is also why LLMs work so well: They have lots of data.

In summary: Learning math is not "difficult", it is tedious.

Re: Relearning math as an adult

#98

Post by jacquesm »

gmays wrote: post #75
jacquesm wrote: post #49

Earlier quoted context omitted.

Why am I not surprised that a marketeer shows up in an 'organic' posting about a company.

FYI this is the guy that wrote the comment you replied to: https://www.justinmath.com He's true math nerd, and definitely not a marketer. In fact, I don't think a single marketer works at the company. It's a bootstrapped labor of love and I've been following their journey for almost a decade. I get the skepticism, but some things are legit.

I'm sure there are math nerds that work in marketing.

Your whole blog post comes across as an advert, that may not have been your intention but that's what it looks like to me, legit or not.

Re: Relearning math as an adult

#99

Post by pvg »

dcw303 wrote: post #68
pvg wrote: post #47

Earlier quoted context omitted.

Are you using any of the stuff you're learning for whatever practical 3d game-making things you're working on? Just curious how it's working out, you've picked a pretty broad foundation as a starting point.

I took a brief detour late last year to study "Linear Algebra: Theory, Intuition, Code", and to my surprise it stuck pretty well. The author said the pre-reqs were just "basic high school math", but I'm glad I had recently done lots of algebra and geometry, as the difference between that and some vague memories of stuff I did 30 years ago in school is pretty wide. I haven't started any 3d game projects yet. For that,…

Yeah, it sounds like you're not far from the point where you can start jumping ahead and working backwards to fill in the bits that you're missing - that's what many people naturally and instinctively try and it can work but can also be frustrating if one misjudges one's degree of proficiency. You don't often see 'I'm just going to give myself a full secondary school maths refresher' which is more demanding on time and self-discipline but at least we know it's pretty reliable given those things.

Re: Relearning math as an adult

#100

Post by gsdgsdfg »

People here mention KhanAcademy and AOPS series for self learning. I've used both when relearning Math as an adult. But there is one more resource which is absolutely terrific: Henry Sinclair Hall's books. Not only they are good (way better than the aforementioned ones), but being published in the 19th century, they are in public domain now and can be downloaded from the Internet Archive free of charge: https://archive.org/search?query=creator%3A%22Hall%2C+H.+S.+... And, also, How to Prove it by Velleman is a must read.
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