Modular Arithmetic is a fundamental component of cryptography. In this video, I explain the basics of modular arithmetic with a few simple examples. Join this channel to get access to perks: / @learnmathtutorials :)
This has got to be the best introduction to modular math I’ve ever seen. Straight to the point and by someone that knows what they’re talking about. I’ve noticed that the people who break it down like this are really good at what they do and the people that try to sound “smart” don’t really understand what they’re trying to teach. Thank you.
Thanks for the tutorial! I attended a lecture about modulo arithmatic and the lecturer managed to make such an easy to undestand topic appear to be rocket science
I've watched many videos and went to many websites to just understand what is mod. Honestly I didn't understand anything till Ive seen ur video. I think it's fair to say you have the best modular arithmetic intro video
Wow! The modular Arithmetic can be a nightmare but this congruence topic was explained in the most simple way that I have seen. Very nice ...thanks for posting this👍
the values in the mod space can be thought of as a circle made up of m-1 terms so 14%12 like a 12hr clock and so you send up on 2 after you move 14 spaces
I just wanna say you 'thank you man! You know I was thinking about it for 3 days that how to solve these types of questions and wonder behind the logic of this.
The wikipedia page on this is a good read. Think of it like a clock, we have 24 hours, but just 12 on an analog clock, so we would say its 5 o'clock, but it could be 05:00 or 17:00, thus 5 and 17 are congruent in mod 12. And thus AM/PM etc etc... You basically create an imaginary limit to infinity where numbers start looping around; like when we say 48 hours or 72 hours, we know how many days that are, because we only have 24 hours in a day, thus 48 hours has to be 2 days. So for example 14 is congruent to 6 in mod 8, because we start counting again at 8.
The best explanation so far. I think it would be better if we could change the symbols and wrote "mod 2" or simply 2 above the congruence symbol. That way things would be much clearer.
I thought modular arithmetic was a rocket 🚀 science until I found your video. Now, modular arithmetic is easy peasy like drinking water 😆. Top man, thanks a lot
The numbers you have specified as mods's (For Example: mod(2)= {0,1}) are actually the remainders of the division done. 5/2's remainder is 1, that is why we place a 1 on top of it.
i was simply curius about cryptography and i saw this. Had no idea what the f was that until now thanks. (it looked simpliest of them all so i clicked it)
In my lecture notes, I was given the following definition: a is congruent to b modulo n if and only if n divides a - b. At first I was dumbstruck, but now everything is starting to click. Thanks, and have an excellent day!
I was mad at first, and I still am. I can barely understand basic math, and now you’re telling me there’s even more math hidden in the math?? It’s almost like this is another mathematical dimension… however I’m glad I understood this.
What we do if we want to find if two numbers are congruent to mod x is we for example 3 and 5 (mod 2) is we multiply 3=2x1 and we get 1 left so +1 and 5=2x2 we also get 1 left and we conclude that the numbers are congruent, so the same logic applies for any other number if we get the same number left we know that they are congruent,if not they arent
You could also think of the modular value (is that correct terminology?) as the remainder. 5 in mod 2 would be 1 because 2 goes evenly into 5 twice, meaning the remainder would be 1. 2 goes evenly into 3 once, also meaning that the remainder is 1.
Modular value sounds legit to me, and yes, it comes from the remainder. I will cover that a little later. For now I just wanted to give everyone a visual representation. I've noticed, that for many students, it's all to easy to get lost in the math, and not see the pattern when jumping straight to the remainder, especially when converting negative numbers to "modular values". Thanks for the comment. :)
