51–60 of 122 posts
I look at this and profoundly thank the people who make ml libraries for us the rest of us.
From the start of Chapter 2: "In the following four chapters, the basic algebraic structures (groups, rings, fields, vectorspaces) are reviewed, with a major emphasis on vector spaces. Basic notions of linear algebra such as vector spaces, subspaces, linear combinations, linear independence, [...], dual spaces,hyperplanes, transpose of a linear maps, are reviewed." If anyone needs to start even earlier than this, I'v…
I would disagree about the gamedev book reference, unless you are referring to the real basics of linear algebra. The really important concepts for ML are least squares, eigenvalues and vectors, and SVD. Those concepts are not very relevant to game programming. Well, least squares can be solved with projection, which is relevant for converting between coordinate spaces. But game dev isn't going to give you that intui…
So while the book in question might not be the best resource, it probably is a better starting point than the linked doc.
In basic calculus one can burn countless hours memorizing mechanical rules to derive and integrate different function forms, or one can just plug the function into something like wolfram-alpha and get, for a lot of useful cases, a symbolic answer, or at least some approximate answer for a point or interval. The point is, understanding integrals and derivatives doesn't require one to memorize all the mechanical rules.…
You don't need to memorize rules when studying math. Just like you don't need to spend any time to memorize syntax for programming languages. You automatically remember things you use a lot. Once you have spent countless hours doing exercises to the extent that you understand the math, you already remember the rules. If you have not spent countless hours doing exercises, you don't understand anything at this level. Y…
I'm not against memorization though. Memory is very useful when studying math or programming or any other subject. You don't want to have to "reason your way through" every time, shortcuts are very important!. I think of this like brain-memoization. Without it, it would be very inefficient to make progress. A lot has been said about this relationship [1]. Also, I think this is how some breakthroughs happen, "connecting the dots", so to speak.
Maybe when you say: "...spending any time memorizing syntax...", you are thinking flashcards or something like that? Sure, you don't need flashcards, anything you do often enough is gonna be easier to remember.
My comment was more in line with the fact that, with 2000 pages, maybe the author elaborates a lot on things that are very mechanical in nature and maybe require a few pages to describe (and are very inefficient for humans to compute? Just use a computer! :-). Say, Gaussian elimination; couldn't one be told: this is a matrix, this is a determinant, this is the relationship between them, this is what it means to invert the matrix, etc. and skip the full description of Gaussian elimination? (put in an appendix? on a second book? less pages!). I don' think is super helpful to, say, spend a lot of time inverting matrices with pen and paper in order to get proficient in linear algebra.
1: https://www.google.com/search?q=intelligence+memory+relation...
“Math Basics” is quite the misnomer—it gives the impression that one would need to study all of the contents of this book to be an effective practitioner in CS or ML. Memorizing every definition and theorem in this book would be neither necessary nor sufficient for that purpose. Keep in mind it can take an hour, and sometimes way more, to really absorb a single page of a math book like this (do the math). This is mor…
A friend with a math msc aluded at this, that it's kind of a math meme to call material "basic" or "introduction to" for rather advanced stuff. I feel like it's some kind of misguided intellectual humility. Kind of feels vaguely related to how so many Haskell packages are version "0.*".
Earlier quoted context omitted.
Maybe they were referring to Khan Academy? https://www.khanacademy.org/math
I think Khan academy for higher math/physics/chemistry /CS would be invaluable. Maybe it could be crowdsourced in some way?
In basic calculus one can burn countless hours memorizing mechanical rules to derive and integrate different function forms, or one can just plug the function into something like wolfram-alpha and get, for a lot of useful cases, a symbolic answer, or at least some approximate answer for a point or interval. The point is, understanding integrals and derivatives doesn't require one to memorize all the mechanical rules.…
You don't need to memorize rules when studying math. Just like you don't need to spend any time to memorize syntax for programming languages. You automatically remember things you use a lot. Once you have spent countless hours doing exercises to the extent that you understand the math, you already remember the rules. If you have not spent countless hours doing exercises, you don't understand anything at this level. Y…
Strangely, probability theory is completely omitted.
Very first sentence of 2.1 is full of notation, symbols and terms that I, as a prospective student, might not understand. So many teachers seem incapable of stepping outside their sphere of knowledge and seeing what they know and others do not. And so much work went into this.
If you look at any of the later chapters that are trying to teach something new, they are much more gentle and motivate the topic of that chapter: see e.g. “24.1 Affine Spaces” on page 759, or “26.1 Why Projective Spaces?” on page 823, etc.
Other chapters that are meant as a review are similarly terse and quick to the point (like Chapter 2), e.g. Chapter 37 “Topology” on page 1287.
I think it's good when books make conscious choices about what they're teaching versus assuming as a prerequisite (and communicate it to the reader, by using terms like “reviewed” — presumably the yet-to-be-written Introduction chapter will also mention this more explicitly).
Earlier quoted context omitted.
I would disagree about the gamedev book reference, unless you are referring to the real basics of linear algebra. The really important concepts for ML are least squares, eigenvalues and vectors, and SVD. Those concepts are not very relevant to game programming. Well, least squares can be solved with projection, which is relevant for converting between coordinate spaces. But game dev isn't going to give you that intui…
I believe the person you're replying to was attempting to help people like me, who haven't had a math lesson since leaving high school (in my case over 16 years ago) and whose level of math is roughly "You want me to multiply something? Let me get my phone." So while the book in question might not be the best resource, it probably is a better starting point than the linked doc.
Thanks for your comment, it made me feel less alone.