6 ms·

Basic algebra for the substitution model and basic calculus for high order functions and the notion of a transformation in general. Set theory is, probably, th

Basic algebra for the substitution model and basic calculus for high order functions and the notion of a transformation in general. Set theory is, probably, the most fundamental. Everything could be defined as a set or as a function. Lambda calculus, obviously. Some combinators. Basics of linear algebra. No category theory and other bullshit is needed. Sets will do. It is actually very important skill to avoid wasting time in disconnected from reality obscure academic bullshit, be it philosophy, physics or math. Do not follow other people's hallucinations. Have your own.) As a rule of thumb - you need just enough math to understand The Wizards Lectures and SICP. Again, the substitution model, sets (for notion of types and basic collecttions) and high order functions (the "domain and range" mantra) is enough. For algorithms the notion of being bound by some function and orders of growth.

aaachilless 10y ago
What's "The Wizards Lectures"?
- dschiptsov 10y ago
  The set of video lectures from 1986 by Abelson and Sussman. https://groups.csail.mit.edu/mac/classes/6.001/abelson-sussman-lectures/ https://groups.csail.mit.edu/mac/classes/6.001/abelson-sussm... Timeless classic. And nostalgic diving back into 80s. And MIT Scheme on a monochrome monitor with a clicky keyboard.
tetrep 10y ago
Not to start a math war, but why is set theory okay but category theory bullshit? While they're both useful, I think category theory encompasses a bit more than set theory and it's only a little more abstract. I also like the more functional approach that a lot of category theory requires you to take; if you're used to imperative programming it's a pretty different and useful way to think about things and it's great for adding to your critical thinking/general problem solving skills.
- dschiptsov 10y ago
  The difference between the set theory and category theory is the same as between the philosophy of Spinoza and Hegel. The first is grounded in reality, while the second one is an abstract metaphysics bullshit. Developing some abstract vocabulary to describe spherical horses in vacuum contribute nothing to programming, which is a discipline of describing and modeling some aspects and processes of reality. Knowing where to stop in a heuristic-guided search is the most difficult part. In my opinion one should stop after realizing that the subject becomes too abstract and too academic and cease to be a tool of clarification. Let's say that it has something to do with the pragmatism of Ayn Rand, Quality of Robert Pirsig, and to the general scientific method of removing bullshit, dogmas and nonsense in order to let the truth standing.
  - lliamander 10y ago
    Abstract algebra is certainly abstract, but it is far from "metaphysical bullshit". Abstract algebra is just the precise articulation of patterns that we see across different mathematical formalisms. Now, the fact that it is so abstract does mean that your average programmer won't use it on a day to day basis. I'm certainly not going to argue that it is the most important math to understand. However, we are finding that there is uses for it. Not just in a "oh look, I can describe my code using abstract algebra, nifty" sort of way, but in a "knowing this was essential to finding the correct solution" sort of way. For instance, the folks working on .NET's LINQ knew they were implementing monadic comprehensions; they just had the good taste to not use the word "monad". Furthermore, it seems that having an understanding of abstract algebra is essential to making a distributed real-time analytics engine[0] [0]https://www.infoq.com/presentations/abstract-algebra-analytics#mainLogin https://www.infoq.com/presentations/abstract-algebra-analyti...
    - dschiptsov 10y ago
      Oh, monads.. sooner or later they will be mentioned.) Actually it is a canonical example of abstraction for the sake of having an abstraction, which only increases confusion. Monads make no sense in a non-lazy language. http://karma-engineering.com/lab/wiki/Monads2 http://karma-engineering.com/lab/wiki/Monads2
idrios 10y ago
> It is actually very important skill to avoid wasting time in disconnected from reality obscure academic bullshit, be it philosophy, physics or math. Do not follow other people's hallucinations. Have your own. This. So much this. I've lived in a few hacker houses and worked at hacker spaces in the last year. The most impressive programmers I met had picked up just one set of skills (mostly web dev or mobile dev) and while being good at just one thing is less glamorous, these people were actually finishing projects. It was really incredible to watch them create and transform a project into real life in a very short amount of time. The most frustrating people I met were ones trying to learn everything--Machine Learning, IoT, VR/AR, mobile, web full stack--and getting nothing done on a daily basis. The math you need to learn is completely dependent on what programming you want to do. What will be most impressive is your ability to focus on one or two areas and not get distracted into trying to learn all of it, and not feel envy towards those who are experts in domains that you don't know.

aaachilless 10y ago

What's "The Wizards Lectures"?

dschiptsov 10y ago
The set of video lectures from 1986 by Abelson and Sussman. https://groups.csail.mit.edu/mac/classes/6.001/abelson-sussman-lectures/ https://groups.csail.mit.edu/mac/classes/6.001/abelson-sussm... Timeless classic. And nostalgic diving back into 80s. And MIT Scheme on a monochrome monitor with a clicky keyboard.

tetrep 10y ago

Not to start a math war, but why is set theory okay but category theory bullshit? While they're both useful, I think category theory encompasses a bit more than set theory and it's only a little more abstract. I also like the more functional approach that a lot of category theory requires you to take; if you're used to imperative programming it's a pretty different and useful way to think about things and it's great for adding to your critical thinking/general problem solving skills.

dschiptsov 10y ago
The difference between the set theory and category theory is the same as between the philosophy of Spinoza and Hegel. The first is grounded in reality, while the second one is an abstract metaphysics bullshit. Developing some abstract vocabulary to describe spherical horses in vacuum contribute nothing to programming, which is a discipline of describing and modeling some aspects and processes of reality. Knowing where to stop in a heuristic-guided search is the most difficult part. In my opinion one should stop after realizing that the subject becomes too abstract and too academic and cease to be a tool of clarification. Let's say that it has something to do with the pragmatism of Ayn Rand, Quality of Robert Pirsig, and to the general scientific method of removing bullshit, dogmas and nonsense in order to let the truth standing.
- lliamander 10y ago
  Abstract algebra is certainly abstract, but it is far from "metaphysical bullshit". Abstract algebra is just the precise articulation of patterns that we see across different mathematical formalisms. Now, the fact that it is so abstract does mean that your average programmer won't use it on a day to day basis. I'm certainly not going to argue that it is the most important math to understand. However, we are finding that there is uses for it. Not just in a "oh look, I can describe my code using abstract algebra, nifty" sort of way, but in a "knowing this was essential to finding the correct solution" sort of way. For instance, the folks working on .NET's LINQ knew they were implementing monadic comprehensions; they just had the good taste to not use the word "monad". Furthermore, it seems that having an understanding of abstract algebra is essential to making a distributed real-time analytics engine[0] [0]https://www.infoq.com/presentations/abstract-algebra-analytics#mainLogin https://www.infoq.com/presentations/abstract-algebra-analyti...
  - dschiptsov 10y ago
    Oh, monads.. sooner or later they will be mentioned.) Actually it is a canonical example of abstraction for the sake of having an abstraction, which only increases confusion. Monads make no sense in a non-lazy language. http://karma-engineering.com/lab/wiki/Monads2 http://karma-engineering.com/lab/wiki/Monads2

idrios 10y ago

> It is actually very important skill to avoid wasting time in disconnected from reality obscure academic bullshit, be it philosophy, physics or math. Do not follow other people's hallucinations. Have your own. This. So much this. I've lived in a few hacker houses and worked at hacker spaces in the last year. The most impressive programmers I met had picked up just one set of skills (mostly web dev or mobile dev) and while being good at just one thing is less glamorous, these people were actually finishing projects. It was really incredible to watch them create and transform a project into real life in a very short amount of time. The most frustrating people I met were ones trying to learn everything--Machine Learning, IoT, VR/AR, mobile, web full stack--and getting nothing done on a daily basis. The math you need to learn is completely dependent on what programming you want to do. What will be most impressive is your ability to focus on one or two areas and not get distracted into trying to learn all of it, and not feel envy towards those who are experts in domains that you don't know.