Permutations, Latin squares, number systems | Group theory episode 3

#abstractalgebra #grouptheory #numbersystem #permutations #sudoku Groups are closely related to permutations, Latin squares, and sudoku puzzles. We explain where these permutations come from. We also look at the complex numbers and other number systems again, this time from the perspective of group theory. But first we spend a few moments looking at modular arithmetic. I need to clarify something at 6:00. On the left, you see a general-purpose equation that works for any group. When talking abstractly about all possible groups, mathematicians use the word "multiplication", and they write it as a dot. So the word "multiplication" can stand for many things such as "concatenation", "composition", or, yes, even "addition". On the right, we have a specific group: addition modulo 4. So even though the group operation is addition*, I also refer to it as *multiplication at the same time. This may be confusing. But it pays to get used to this, because you will encounter it all the time when studying group theory. Thanks to one of our patrons for pointing this out. You too can support our channel on Patreon to get early access to new videos: https://www.patreon.com/user?u=86649007 Here are some interesting links: [3B1B]    • Euler's formula with introductory group th...   A good, short introduction to group theory, and a connection to complex numbers. This is a good example of looking at the complex numbers through the lens of group theory. [SIGMA]    • Modular Inverses, Generators, and Order: L...   A nice introduction to modular arithmetic, using a clock. Also talks about generators. [CTC]    • The Network   Here you can play the sudoku I showed you in the video. No cheating now: don't look at the solution before you try it yourself ;-) 0:00 Introduction 0:32 Modular addition 2:51 The addition table 4:51 Latin squares 7:26 Permutations 10:22 Number systems 12:34 Rational numbers 15:06 Complex numbers 16:15 The complex roots of unity This video is published under a CC Attribution license ( https://creativecommons.org/licenses/... )