[ANT15] p-adic integers: a primer, and an application (part 1)
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- čas přidán 9. 08. 2022
- The p-adic integers are pretty easy to define, but it's far from obvious what the point of them is, or how we should even think about them. In this video, I describe them as a practical tool: a collection of number systems that are related to the usual integers Z, but where solving equations can be much easier. It would be nice if we could port these results back over from Z_p to Z, but that's a topic for another video...
2.9K views and only 108 likes ??? It's a disgrace. It should be 2.9K likes....people don't know how to appreciate real quality work.
Wait a minute Is 2s complement just a p adic representation?
Yep, it's a (truncated) 2-adic representation!
I also just learnt about this connect recently. Since 2s complement representation is a bit more familiar, I wish p-adic introduction materials start with this and expand to other primes.
@@billy_maths And because of how it is truncated, it only can hold integers.
This whole playlist was most illuminating, thank you
I've been secretly wishing for you to do a video introduction series to p-adics. Very happy to see you actually doing it :)
Keep the good work up 👍
Thank you! More p-adic videos to come soon, I hope :)
Excelente lecture. Many things contribute to a first class lecture: the graphics, the tempo of the presentation, the explanations, the tone of voice and a love of the subject. You have all these qualities.
I just stumbled upin you lecture as I wanted to learn some about p-adic numbers. I'm sure glad I found your site. Please keep up the great work.
When part 2 ? 🙏
I'm really glad that i find your channel. your video quality is very good keep it up!!
This is a rare unique explanation. Thank you!
Amazing! ❤
your videos are fantastic !
thank you
This video is wonderful. Thank you!
thank you so much for this serie of videos , tne content is really really enriching that's the least that I can say. I love how I see things totally differently now , known concepts make much more sense now , if you can do a video about Q_p and the projective line it would be marvelous. Again thanks a lot!!!
Excellent 👌 Can you make a video of the construction of p-adic integers Z_p algebraic way ? For example, we want to solve the equation $x^2=a$ (mod p) and then continue to divide by p and find successive solutions to get the p-adic integers.
Can you make such amazing playlist on algebraic geometry too? I am having a hard time with Hartshorne
Thank you for the very kind comment! I don't think I'll get around to that any time soon, but to my mind, Ravi Vakil has already done a far better job than I ever could: czcams.com/channels/y3u23mZE4TyW88yr6JLx9A.html
I had the completely unfounded notion this was an old one, so there must be a follow-up.
Uploaded 7h ago 😐
Oops! Follow-up very soon, I hope. ;)
Yeah, a buddy of mine told me about them.Tell you what, I'm never visiting Germany or Europe.
3:42
I Just came across this channel and it is fantastic! But I am a little worried that it may have stopped as this video was uploaded a year ago. Are you still going @billy_maths? I really hope that you are.