This is basically an unsolicited ad post. It communicates nothing of substance and the entire thing amounts to "click the sign-up button". It doesn't even cover the course contents. How this makes it to the HN front page is mind-boggling. Goatse would at least be more entertaining.
Relearning math as an adult
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Re: Relearning math as an adult
#32I may be biased as I am a trained Mathematician, but I always feel when someone says "Math is Hard", that is because they had bad teachers. Math is easy if you build up from fundamentals, not like physics education where you say "but lets delete everything before because it had an oversimplifying assumption", rather if you build your knowledge entirely sequentially from things you know or assume, you build up a toolb…
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.
If I can compare to another activity, I've always wanted to be an artist as well, and have spend quite a bit of time trying to build up the skills. The problem is that, if I'm honest with myself, is I just don't enjoy the process of creative expression, it doesn't trigger any reward system that means anything for me. I wish it did but there's just nothing there. It was a hard pill to swallow, but I realized I like the idea of being an artist, but I don't enjoy the process. Hence my ultimately crummy artwork!
Sorry, I realized I'm talking about myself more than you, but I hope it's some help. The point I hope it makes is that everyone has a different personality, and from that different reward systems. It sounds to me like yours doesn't align with math, and that's fine. I wouldn't try to force yourself to study something which you don't love, at least if it's optional self study. Find subjects that you love learning, and the results will come naturally.
Re: Relearning math as an adult
#33Can anyone help me with some questions about this program? (I assume the founders will see this thread once they notice the HN hug of death) 1. How exactly is AI being used here? Is there an AI chat-bot that I can ask for help? Do you generate problem-sets with AI? Check answers with AI? Is it GPT-4? 2. Do you utilize Spaced-Repetition in any way? Have you found that to be useful? Thank you
Hi there, my name is Justin Skycak, I'm the Director of Analytics & Algorithms at Math Academy, I developed all of our quantitative software, and I'd be happy to answer your questions.
1. The AI is more like an expert system that emulates the decisions of an expert tutor with regard to what tasks a student should work on at any given point in time (what should the student learn next, what do they need to review). There's a knowledge graph that encodes structural relationships between thousands of math topics (such as prerequisite relationships, but also other types). And then there's an algorithmic reasoning system that looks at a student's answers, overlays them on the knowledge graph, figures out what the student knows (and how well they know it), and decides what learning tasks are going to move the needle most given their personal knowledge profile. The decision-making is inspired by cognitive learning strategies such as mastery learning, spaced repetition, interleaving, minimizing associative interference.
2. Yes, spaced repetition is a core part of the system. Each student has a personalized spaced repetition schedule that adapts to their performance on each topic, and when choosing what topics a student should review or learn next, we're always trying to implicitly "knock out" as many due reviews as possible to maximize learning efficiency. (For instance, if a student is due for a review on one-step ax=b equations, we can implicitly "knock out" that review by having them learn two-step ax+b=c equations instead.)
From a quantitative standpoint, the spaced repetition model was one of the more challenging (but equally fun) parts to build. You normally think of spaced repetition in the context of independent flashcards, but in a hierarchical body of knowledge like mathematics, it gets really complicated because repetitions on advanced topics should "trickle down" to update the repetition schedules of simpler topics that are implicitly practiced (while being discounted appropriately since these repetitions are often too early to count for full credit towards the next repetition).
Our spaced repetition model not only accounts for implicit "trickle-down" repetitions but also minimizes the number of reviews by choosing reviews whose implicit repetitions "knock out" other due reviews (like dominos), and calibrates the speed of the spaced repetition process to each individual student on each individual topic (student ability and topic difficulty are competing factors).
Re: Relearning math as an adult
#34This is basically an unsolicited ad post. It communicates nothing of substance and the entire thing amounts to "click the sign-up button". It doesn't even cover the course contents. How this makes it to the HN front page is mind-boggling. Goatse would at least be more entertaining.
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.
Re: Relearning math as an adult
#35I've been doing similar for about a year. My target is to learn the math needed to make 3d games, so basically algebra, geometry, calculus and linear algebra. I started with brilliant.org, and while I liked the level of polish in the interactive lessons, I found the lesson structure to be out of sequence, often referring to things that haven't been covered yet. They didn't seem to have put as much thought into pedago…
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
Re: Relearning math as an adult
#36When I went back to school for CS, I used this book https://a.co/d/7hlRdnK to relearn math. I couldn’t recommend it more.
It starts with algebra and works through calculus. There is a pretest before every section, so you know what you need to focus on and what you can skip.
Re: Relearning math as an adult
#37It 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…
which other countries? that's certainly not the case in Germany. you might see some proofs in geometry, and maybe some informal derivations of things later on, but "induction" is a university level thing (it's possible that some kids that focus more on maths in school see this kind of stuff earlier, but it's definitely not a universal experience).
Re: Relearning math as an adult
#38Tangential, but: the notes that this post refers to are probably not the best way to learn how transformers work. If you want mathematical precision, those notes are based on this paper from DeepMind:
https://arxiv.org/abs/2207.09238
The paper provides mathematically precise definitions of all the parts of a transformers, though it's showing its age (ha!) in that it doesn't include some formalizations that are common in, for example, Llama.
Re: Relearning math as an adult
#39> 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…
> leading to overcomplication and obscurantism Mathematicians attempt to express ideas in the most readable and clear way possible. It's actually code that must be obfuscated by the constraints of the language and computer. Mathematicians have no constraints preventing them from presenting something in the way that makes the most sense. The part that can be called "Obscurantism" is when they use a high-level abstract…
> Mathematicians attempt to express ideas in the most readable and clear way possible.
I buy this from the mathematicians and scientists that I know and have interacted with.
I also think mathematicians spend more time trying to discover/play with new math than optimizing the communication of what already exists and is communicable.
My speculation is that this naturally leads cruft that needs to be worked through by people entering the field. The cruft can not get too big or people don't enter the field so people are motivated to keep the cruft below a certain level but not the minimum.
The cruft makes it harder to enter the field and once you have over come that hurdle you move on to do things in the field not reduce the cruft.
Other things that make it hard to reduce cruft
1. not everyone is going to agree what is cruft
2. Person X spend time on reducing cruft in sub field Y may find out that Y is no longer hot topic so while there is less cruft there are not many people taking advantage of the reduced cruft in Y.
3. Mathematicians and scientists are reward more for new and interesting things than better pedagogical practice/techniques.
4. Optimizing for communication/pedagogy is mostly a different skill than science/mathematics so you have to split your focus or not dive as deeply into one or both.
5. I am sure there are others.
This seems reasonable to me. It is s system where most everyone is well meaning and want to improve things and where things do improve over time, but where it is still easy to find areas that would benefit from substantial from improvement.
Re: Relearning math as an adult
#40Earlier 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
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.