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Relearning math as an adult

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Re: Relearning math as an adult

#251

Post by larodi »

imetatroll wrote: post #169
larodi wrote: post #144

I feel like the author, and did like the author for like year now. And I know lots of people feel this way, and we're telling each other to like "learn math, man, coding is something LLMs be doin in 10 years". Indeed, these ML/AI papers are indeed full of cryptic writing, but in essence they are not so difficult compared to like... understanding what a FSM is and how to produce a minimal automata it from regex (hey M…

Do "current gen" llms use Markov Chains? I have been wanting to look into trying to understand this stuff but I honestly don't know where to begin. I guess I should clarify that I prefer being able to purchase textbooks or use free online sources.

There are many attempts at using attention-less approaches to the architecture, and Markov Chains being one of them. Nothing to compete with transformers yet though, AFAIK. Some people experiment with graph-based rules systems, like very smartly compressed grammars (otherwise the task is NP-Hard i think).

Re: Relearning math as an adult

#252

Post by programjames »

jurgenaut23 wrote: post #143
programjames wrote: post #125

Earlier quoted context omitted.

Normalizing flows and neural ODEs are becoming a bigger thing, and they do involve some more heavy maths.

Yes, and if you look at neural operators, then you're in for something that even math majors need to put a bit of effort into.

Oh, I read that paper about a year ago. I feel like it could have been explained better, but the concepts aren't that hard if you've taken numerical methods.

Re: Relearning math as an adult

#253

Post by juunpp »

eps wrote: post #126
juunpp wrote: post #27

Earlier quoted context omitted.

That's basically what it is. There is nothing to learn from this post other than "smash that beta sign-up button". Has anyone tried that course? Is it any good?

Yes, it's very good. Math Academy is much more dense and on-point that Khan's. You don't have to sit through 15 minutes of video when 2 minutes worth of text explanation does it. It uses spaced repetition for topics that you aren't good at, and for recently learned subjects. The topic dependency tree and automatic progressing to "unlocked" topics is obvious in retrospect, but here it's done very cleanly and unobtrusi…

> Math Academy is much more dense and on-point that Khan's. You don't have to sit through 15 minutes of video when 2 minutes worth of text explanation does it.

This is precisely what bothers me about KA. I guess they're trying to ease into the topic, but I find that kind of repetition annoying and distracting.

Re: Relearning math as an adult

#254

Post by juunpp »

dcw303 wrote: post #8

I'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'm in that camp and can suggest a few recommendations in order of:

https://d3dcoder.net/ -- The DX12 book is the latest edition. The books have several chapters at the beginning covering 3d transformations.

https://foundationsofgameenginedev.com/ -- The first installation, Mathematics. This will cover a lot more ground and derive things from first principles while not being overly formal.

https://www.mathfor3dgameprogramming.com/ -- A lot more formal than most game/graphics math books, and goes into more depth, particularly on the linear algebra.

Re: Relearning math as an adult

#255

Post by juunpp »

juunpp wrote: post #27
UncleOxidant wrote: post #22

So... basically an ad for Math Academy? How about some free resources like Khan Academy?

That's basically what it is. There is nothing to learn from this post other than "smash that beta sign-up button". Has anyone tried that course? Is it any good?

Replying to myself since I can't edit: thanks for the feedback. I am compelled to look into the course after reading all the replies here.

Re: Relearning math as an adult

#256

Post by clbrmbr »

I was literally doing random exercises out of Apostol’s Calculus the other night. But I’d love to do good exercises from something more recent and advanced… gotta find my copy of Chris Bishop’s pattern recognition.

Re: Relearning math as an adult

#257

Post by tayo42 »

mr_mitm wrote: post #236
tayo42 wrote: post #90

Earlier quoted context omitted.

> 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?

Then you will have gained insight into how the world works on a fundamental level. Isn't that something in its own right? I can only speak for myself, and did go on to get a PhD, but even on a bachelor level, studying physics changed how I see the world and how I think.

It is, which is why I was interested in the first place. But physics the way it is taught is pretty rigorous and study is intense for someone with a passing curiosity. And idk if there is a way around the math for some of the stuff.

Re: Relearning math as an adult

#258

Post by hyperthesis »

gmadsen wrote: post #220
hyperthesis wrote: post #202

Earlier quoted context omitted.

Could you elaborate on this please: "the exercises guide you to "invent" the important parts of the theory." BTW: I think time not doing exercises is just as important; it's when your mind tries to piece together the data. Coincidentally(?) time resting, after physically exercising, is when your muscles strengthen.

Sure, texts like "linear algebra done right" or "Understanding Analysis" do a unusually good job of integrating large multi part examples where the reader works through them and proves the theorems themselves before they are explained in the book. The nominal case for most math texts is definition, lemmas, theorems, and sometimes they provide examples, and other times, readers are expected to make their own examples.…

Thanks! I think I now recognize this from Spivak (Calculus), where much of the teaching is literally in the exercises. You are guided along, deriving/proving many things along the way, some incidental, some cumulative. (There's also important exposition in the exercises.)

A downside is you lose the thread if you skip exercises (e.g. do alternate ones) - the exercises are an integrated whole. But it's a lot to do all of them.

I hadn't gotten the impression that these helped show why exactly the axioms were choosen - though could well be there and I just didn't see it.

Re: Relearning math as an adult

#259

Post by tuukkah »

apwell23 wrote: post #248
tuukkah wrote: post #244

Earlier quoted context omitted.

I hear these problem types are not as common as they used to be, but here's some recent examples in this direction. Fall 2023: "Prove that 2^12345678910 - 1 is divisible by 1023." Spring 2022: "Using induction, show that the sum of the numbers on the line n of Pascal's triangle equals 2^n." Here's the full exam from fall 2023: https://yle.fi/plus/abitreenit/2023/syksy/matematiikka_pitka...

I cannot seem to access that link outside finland. That is indeed a tough proof to solve sight unseen. Any reason you say that students are seeing that question for the first time in the test. Seems like a famous questions, even chatgpt got the proof correctly .

I think the pressing question here is what the Anki cards contained w.r.t. these problems :-)

The high school curriculum and the text books are not focused on proofs or famous questions. Further, the goal of the exam is to find out your position in the normal distribution of your peers' math skills. You are not supposed to be able to beat everyone else by rote learning (so if you can do it, it's quite a hack!).

I don't think ChatGPT is a good comparison, because it has obviously memorized much more than a human could, and a test to poke its strengths and weaknesses would look different.

Re: Relearning math as an adult

#260

Post by blagie »

ammasant wrote: post #81
MrVitaliy wrote: post #80

Earlier quoted context omitted.

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.

You learned using the AOPS books? Don't be fooled by the titles, these books exclusively use a proof-based approach to construct a pretty wide foundation around these topics.

AoPS are among my favorite math books, but they're definitely not proof-based or particularly rigorous in terms of formalism.

They do focus on complex problem solving, which is equally important. The key value-add of AoPS are interesting, often beautiful examples and problems.

However, they don't do proofs or formalism much. They don't do applications or show what math is useful for. And they completely, totally, and universally screw up units (you'll have problems trying to equate a length with an area and similar; that's true of their classes as well, and RSM is similar).

I don't think there's a one-stop-shop for math, though, which does everything right. AoPS is at the peak of their particular game (which is right in the name: problem-solving).

That's best complemented by:

- Something which does data, applications, visualizations, and storytelling well.

- Something which does early exposure / surface learning well

- Something which is more formal and rigorous in terms of proofs and derivations

- Something which touches on a broad set of interesting topics (graph theory, oddball parts of geometry, etc.)

- In 2024, I would add something which does computational mathematics well

Nothing I know of does all those well in a one-stop-shop.

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