An undergrad (non-measure theoretic) probability book with basic linear algebra and calculus is the best preparation. If you solidly understand the basic tools of probability, you can learn statistics quite easily in my experience. Without that understanding, statistics will likely seem like a bunch of recipes. However, if you are comfortable with probability, you can write down the actual problem you have and find the statistical tool you’re after with a little googling.
Thank you for the guide! It's very helpful. This comment [1] describes my background with math.
Something related: I often feel like I'm doing math when I work with information, especially when drawing out concepts and their relationships. Like 3D Tetris, but with recursion. There are also patterns in categorization. One of my purposes in learning math is to be able to quantify relationships between concepts, and create models, etc. What would I need to know about in this case?
I’m not sure what the best advice is for someone with a brain injury, however I feel for you. I didn’t realize I had an attention disorder until I was 25 and it explained why I would screw up signs and struggle to understand formulas.
However I will say that, as you learn more math, the intuition and big picture thinking is way more important than details. I normally forget the specifics of how something works, but I know what I’m trying to do and what thing I need to look up to do it. There is very little need to memorize things besides having enough “RAM” for the moment. You always have pen and paper to write stuff down!
Regarding modeling, the sky is kind of the limit. The more math you know, the more abstractions you learn and start to see in the world. Dynamical systems is a good field to look at but I’m biased because it’s my main topic. Despite its usual applications in physical modeling, an algorithm is basically a time-discrete dynamical system: you recursively apply a function to a state and that gives you a new state. I have certainly seen algorithms analyzed from that perspective before.
Another area you might find interesting is Algebra. This isn’t like the algebra you took in school but more about looking at a space of objects that interact via some operation and characterizing what you know about the space given that operation. A classic example is that rotation operations form an algebraic structure known as a “group” due to the fact that any two rotations gives you a third, rotations are invertible (you can cancel a rotation by rotating in the opposite manner), and they follow the associative property. There’s a book I’ve been meaning to read about how to use this kind of algebra to design safer and more intuitive APIs by considering the data structures of the APIs as objects and functions / methods as operators on those objects.
Any advice is good, I just have to start at the beginning in a way that most people don't. Beyond that, normal advice is fine. I can adjust that advice to the quirks of my systems.
Dynamical systems is a great new keyword! Algorithms are a perfect example. I am exploring system dynamics from a metacybernetic point of view (via the viable system model). My focus is the dynamics of humans in complex systems, how systems change human behavior and vice versa.
Does big picture thinking in math involve understanding/intuition of the implications of formulas, and how they interact with other formulas (or other mathematical entities, I don't know if formula is a general enough term for "group of math actions")?
Graph dynamical systems looks promising, because I draw similar pictures when showing relationships over time. Fractals are always good, drawing fractals taught me to think recursively.
I am also interested in the way models create understanding, and how technical models can be visually altered to aid in understanding. I have a background in visual psychology, and see many mistakes that cloud the meaning of what is being communicated.
This book seems to start where you need it to start.
You don't need much beyond basic calculus. Most suffer from some mental block they got installed at a young age akin those that say "I'm bad at math" because their teacher sucked. Dive in and you won't regret it.
I have been a math teacher and although I can't guarantee that I didn't suck, I can say that most of kids don't develop this attitude because of teachers, but because of their parents. "My mum says that she sucked at math/music/whatever as well, so do I!" is far too common. As a teacher I just didn't have resources to influence this attitude either.
Yes, parents can be horrible too.
Unfortunately it's somehow socially acceptable and even worthy of pride in some circles, to be "bad at math". It's seems very rare for someone to openly say "I'm bad at [my native language]" or "writing".
I feel stats is has a somewhat similar effect even among those with math education. Several friends who have a degree in math recoil at the first mention of stats concepts.
> It's seems very rare for someone to openly say "I'm bad at [my native language]" or "writing".
It is actually even fashionable in non-english countries. Declaring "I'm bad at [my native language], I only use english anyway" makes you a better person somehow. And it's not rare in other areas either – in post-truth world it's trendy not to know things.
I didn't mean that in all of them and everyone in any of them. But it has been always the case everywhere in the world. It's the mechanism how languages die - gravitation to the bigger languages. Hundreds of languages die in Russia not only because of limited education in regional languages, but because it's more fashionable to be russian than representative of smaller nation. In world level this gravitation is towards english mainly.
In my country it's especially fashionable not to know a native language for a people in tech. "It's impossible to talk about tech anyway in native languages, so we all should use english anyway in future" is very common. I tried to fight with it localizing/translating software for many years, but I've given up for now.
Not OP, but I recently had a manager in Germany (I'm in the US) say something like that.
Not that he was bad at German, necessarily, but that it was overly complex vs English, so he and his significant other even used English at home when they both didn't have to.
This is just one example, of course.
I was actually surprised to hear him say that (though it may have been to thwart my attempts at speaking some German when we had a meeting. I don't know any German,lol).
My mental block is a brain injury that went undiagnosed until I was 30. I can't really hold more than two numbers in my head at a time. I struggled through math in school because it was lecture based, and the books were written to accompany a lecture.
I can learn math fairly well if I have the right written material and the right direction. However, I do not retain math skills: without active practice, I revert back to "how do fractions work?"
For example, I did extremely well in a college algebra course that was partially online (combined with Khan Academy to catch up). I could do my tests perfectly in pen, much to the amusement of the assistants. I could make connections and see the implications and applications of the math. Roughly three to six months later, I was back to forgetting fractions.
I can't learn these things over time, but I can learn them all at once. I'm collecting resources for my next math adventure.
Yes. What would you like to know? I am better at answering specific questions.
The injury was diagnosed via SPECT scan. Two of them: one after mental activity, one after physical relaxation. This also revealed that my brain relaxes with mental activity, and "lights up" with physical relaxation.
No, I don't know how. The clinic also took a medical history and said, based on my symptoms, it probably happened in early childhood as a baby.
I always knew there was "something" wrong with me, so I jumped at the opportunity to get a brain scan. The clinic was a little suspect in that they claimed to be able to diagnose mental health issues via the scan, but they combined the scan with more traditional evaluations.
Of which many that don't make it because they've had some early bad experience rather than actually being unable to. And there is a parallel for those with some basic mastery of algebra and calculus and have some mental block towards stats.
