/sci/ - Science & Math

https://youtu.be/az2WOnxsLhc

>>11194119
>bresenham's line algorithm
going down your route I found
https://en.wikipedia.org/wiki/Midpoint_circle_algorithm

>>10981629
Forgot. Probably it was some standard-ish springer book. I turned it into a gif, tho.

>>10981635
I'm fine with categories, it's just that the topology stuff is always about proving things I'm not sure I care for.

>>10947040
Looking a bit deeper into the Polyomino, I think it might be that as a research topic one may find into under the name "polycube", see e.g. the references therein,
https://en.wikipedia.org/wiki/Polycube
e.g.
https://arxiv.org/pdf/1311.4836v1.pdf

Pure mathematics is the only thing that truly matters.

https://www.amazon.com/Algebra-Classic-Classics-Advanced-Mathematics-dp-0134689607/dp/0134689607/ref=mt_paperback?_encoding=UTF8&me=&qid=

I have the first edition from 1990 in front of me. I don't think I held this book in my hand before.

Artin cites Birkhoff, MacLane and van der Waerden as his influences.

Looks very slow going, at least in the beginning, and he writes one should go to chapter 5 quickly, where it gets interesting - that chapter is called Symmetry.
He writes in the introduction he wants to focus on matrix groups instead of permutation groups in this text. As well as on lattices.
He highlights in that it contains talk about the Todd-Coexter-algorithm as well as PSL_2.
https://en.wikipedia.org/wiki/Todd%E2%80%93Coxeter_algorithm
https://en.wikipedia.org/wiki/Projective_linear_group
He writes he doesn't cover dual spaces, which I find a bit shocking. On the other hand, it deals with SU(2) in more detai (as seen on the cover).
Ring theory and number theoretical topics are found in the second half of the book.

One of my motivations is to maybe implement some of the algorithms - I tend to use Python (but also C++, Mathematica or Haskell/Idris). I'd actually like more about (semi-)rings, but that's only late in this book.

Chapter 1. is about matrices.
Multiplicative structure, row reduction, determinants, permutations, Cramers rule.
https://en.wikipedia.org/wiki/Cramer%27s_rule
There's about 50 exercises at the end of the chapter, but some are really just understanding-checks without work.

Chapter 2., at page 40 in my edition, is then about the definition of groups.

>>10918765
I have a week of vacation, so I figured it's a good way. The book wasn't my idea but it looks for a soft enough while nontrivial enough angle to get some traction. Best someone (I may do some) post the exercises and people may respond with a capital letter spoiler tag or something.

>>10918748
I'm a physishit from Vienna

I might be misinterpreting you, but you seem to take a hyper-Platonic position on math. Pure math as taught in the mathematics department can (and arguably should) be entirely dissociated from "the world".

That said, the topics that were initially most studied are often tied to more physical and economical questions, simply because that's where outsiders come to mathematicans and ask for help, or where mathematicans with broader interest or capital interest will naturally get into.

But again, if you seek to tie math to logos in the world, then I think you're doing yourself a disfavour as far as the full scope (and thus the essence of) mathematics is concerned.

I might be misinterpreting you, but you seem to take a hyperplatonic position on may. Pure math as taught in the mathematics department can (and arguably should) be entirely dissociated from "the world".
That said, the topics that were initially most studied are often tied to more physical and economical questions, simply because that's where outsiders come to mathematicans and ask for help, or where mathematicans with broader interest or capital interest will naturally get into.
But again, if you seek to tie math to logos in the work, then I think you're doing yourself a disfavour as far as the full scope (and thus the essence of) mathematics is concerned.

I make gifs when bored

otherwise ... math gif general I guess

here some more visualizations I did

Say you have 100 anons in two threads, one is a general with 80 and another is a smaller one with 20 people.
Now if suddenly 50 of the 100 people decide to switch thread (where the 50 are randomly choosen, independent of their current room), then how many anons are expected to be in the general afterwards?

Surely if both threads had 50 people at the start, then a random switch would lead to the expectation of again 50 in both. But if it's 80 to 20, then after the switch the general will have less people. It's a kind of entropy growth. How to approach that formally, tho?