Thanks a lot, I do my best! Let me know if you have any questions, and if you're looking for more on partitions and Bell numbers - I have a few more related videos... Recurrence Relation for Bell Numbers: th-cam.com/video/sPGudyLalmE/w-d-xo.html Recurrence proof: th-cam.com/video/abfCpVASfLM/w-d-xo.html
I was introduced to this bell triangle as a way to count the number of possible equivalence relations on a set of n elements.... Back then I didn't know that every possible way to partition a set can be associated with an equivalence relation.
Glad it helped, thanks for watching! Being wrong is one of the most interesting parts of math, always satisfying to realize what you're missing when you can't quite crack a problem!
I have a question about these Bell numbers. I was messing around with the infinite factorial sum for e. 1/n! Then , I decided to see what would happen if I replaced 1 with n, so I wrote n/n!, and the answer was e. Then, I squared the top n, and the answer I got was 2e. Then, I cubed the n, and the answer I got was 5e. I kept going with this, and I only got multiples of e: 2, 5, 15, 52, 203, 877, 4140... Even with the first two sums I did, 1 is just n^0, and n is n^1, so I get the first two 1's of the sequence. Why do these Bell numbers show up with e?
Thank you, so glad it helped! I don't know if you saw my other two lessons on this topic, here they are if not! Bell Numbers and their Recurrence Relation: th-cam.com/video/abfCpVASfLM/w-d-xo.html Proof of the Recurrence: th-cam.com/video/sPGudyLalmE/w-d-xo.html
Thanks for watching! I made a couple other videos on this topic if you're interested. th-cam.com/video/sPGudyLalmE/w-d-xo.html th-cam.com/video/abfCpVASfLM/w-d-xo.html
Please provide a geometric and animated proof of WHY adding Stirling numbers of the second kind add up to Bell numbers. Also: please provide a non-recursive, closed formula for the Bell number and make a video that explains the formula in an intuitive way.
10:14 I get confused on this part for the last 2 elements why not add {3},{4} but he then immediately jumps to 3 elements which is 1,2,3? Edit: Okay nvm, he added it later on
Thank you, I do my best! If you're looking for more on partitions and bell numbers, check out my two related videos... th-cam.com/video/sPGudyLalmE/w-d-xo.html th-cam.com/video/abfCpVASfLM/w-d-xo.html
Thanks for watching, glad it was helpful! Check out the other two lessons I did on this topic if you're interested! th-cam.com/video/sPGudyLalmE/w-d-xo.html th-cam.com/video/abfCpVASfLM/w-d-xo.html
Hi man, I am really struggling with problems of the binomial theorem and pigeon hole principle from this book "A walk through combinatorics, Bona", if possible can you suggest a few good books to start these topics off with? Thank you!
I haven't read much straight combinatorics, so I can't say much about that (I have been wanting that particular book though). Proofs by Jay Cummings is a wonderful modern intro to proofs book that devotes some time to the Pigeonhole Principle. But you may not find it any more thorough or useful than what's in Bona's. I am a big fan of Book of Proof, which is a free proofs book you can find online, but I honestly can't recall whether or not it has pigeonhole principle in it. I'd think it would, but I can't actually remember seeing it. I always sing the praises of A First Course in Graph Theory by Chartrand and Zhang, but that's all for Graph Theory, which comes later in the Bona text. I of course have over a hundred videos on graph theory.
you just showed that the recurrence relation works and all the possibilities of parting a set. i expected an explanation on why is it the way it is. so overall, it's a stupid video.
![Combinatorics of Set Partitions [Discrete Mathematics]](/img/n.gif)
props to ur enthusiasm. If all teachers were as enthusiastic as you know knows maybe we would actually attend the lectures. Thx so much
Great explanation thank you! I can also see the passion you have for the subject which is amazing, keep the great work.
Thanks a lot, I do my best! Let me know if you have any questions, and if you're looking for more on partitions and Bell numbers - I have a few more related videos...
Recurrence Relation for Bell Numbers: th-cam.com/video/sPGudyLalmE/w-d-xo.html
Recurrence proof: th-cam.com/video/abfCpVASfLM/w-d-xo.html
المُنقذ شكرًا جزيلًا.. I said in Arabic that you are Savior, so Thank you very much.
Explanation is crystal clear
I was introduced to this bell triangle as a way to count the number of possible equivalence relations on a set of n elements.... Back then I didn't know that every possible way to partition a set can be associated with an equivalence relation.
Thanx it help me alot in public service exam for teaching.
❤️Love from INDIA 🇮🇳
So glad to hear it, thanks for watching and much love back from the east coast of the USA!
ooho 🤩 the outro is fire 🔥🔥🔥
Thank you it helped a lot i really like your way of teaching please keep it up i appreciate your work 😊
Understood in just one go, thank you sir 😁
Glad to hear it! Thanks a lot for watching and let me know if you ever have any video requests!
It was an amazing explanation, thank you so much!
You're very welcome!
Just osssm ❤️❤️❤️❤️loved it ..
Great explaination ..
Guys watch this , without any time waste...
Thanks so much, I am glad it helped!
Great explanation
Thank you!
I was trying to find this by myself. But now I know I was wrong. Thank you very much for the video 😍
Glad it helped, thanks for watching! Being wrong is one of the most interesting parts of math, always satisfying to realize what you're missing when you can't quite crack a problem!
Great explanation sir❤😇
Thank you!
I have a question about these Bell numbers.
I was messing around with the infinite factorial sum for e. 1/n!
Then , I decided to see what would happen if I replaced 1 with n, so I wrote n/n!, and the answer was e.
Then, I squared the top n, and the answer I got was 2e.
Then, I cubed the n, and the answer I got was 5e.
I kept going with this, and I only got multiples of e: 2, 5, 15, 52, 203, 877, 4140...
Even with the first two sums I did, 1 is just n^0, and n is n^1, so I get the first two 1's of the sequence.
Why do these Bell numbers show up with e?
its mathemagic 🤩
Killer Explanation.
Awesome video thanks !
Thanks for watching!
Great Explanation! Thank you so much
Thank you, so glad it helped! I don't know if you saw my other two lessons on this topic, here they are if not!
Bell Numbers and their Recurrence Relation: th-cam.com/video/abfCpVASfLM/w-d-xo.html
Proof of the Recurrence: th-cam.com/video/sPGudyLalmE/w-d-xo.html
This is gold... Holy Molly...
Thanks for watching! I made a couple other videos on this topic if you're interested.
th-cam.com/video/sPGudyLalmE/w-d-xo.html
th-cam.com/video/abfCpVASfLM/w-d-xo.html
Great
Explanatio level is on fire🔥🔥
Thank you! If you want some real fire, check out my math songs! th-cam.com/play/PLztBpqftvzxW7a66b0dJPgknWsfbFQP-c.html
Amazing trick and teaching is very good attractive
Thanks a lot, glad you liked it!
Very Very useful
Glad to hear it, thanks for watching!
Please provide a geometric and animated proof of WHY adding Stirling numbers of the second kind add up to Bell numbers. Also: please provide a non-recursive, closed formula for the Bell number and make a video that explains the formula in an intuitive way.
10:14 I get confused on this part
for the last 2 elements why not add {3},{4} but he then immediately jumps to 3 elements which is 1,2,3?
Edit: Okay nvm, he added it later on
Please make full vedios and more for all combinatorics topics,thankyou!!😊
You're very welcome and thank you for watching! More combinatorics videos are on the way!
Awesome sir u teach awesome 👌 👏 👍 😎 😀
Thank you, I do my best! If you're looking for more on partitions and bell numbers, check out my two related videos...
th-cam.com/video/sPGudyLalmE/w-d-xo.html
th-cam.com/video/abfCpVASfLM/w-d-xo.html
Amazing Explanation! ...Thank you ❤️
Glad it helped! Thanks for watching!
I liked your video...it's very help for us sir...👌👌
Thanks for watching, glad it was helpful! Check out the other two lessons I did on this topic if you're interested!
th-cam.com/video/sPGudyLalmE/w-d-xo.html
th-cam.com/video/abfCpVASfLM/w-d-xo.html
😍😍😍😍sir amazing explanation
Thank you! I am glad it was clear and let me know if you ever have any questions!
What does n choose k mean?
Thank you!
No problem - thanks for watching!
thanks- well done!
My pleasure, thanks for watching!
Thank you ❤️
You’re welcome 😊
Where is your combinatorics playlist?
Awesome
thanks
No problem, thanks for watching!
Well-earned sub from me! Great video
Thanks Griffin!
Awesome video :)
Thank you!
broooooooooo thank uuuuuuuuuuuu
Glad to help!
Hi man, I am really struggling with problems of the binomial theorem and pigeon hole principle from this book "A walk through combinatorics, Bona", if possible can you suggest a few good books to start these topics off with? Thank you!
I haven't read much straight combinatorics, so I can't say much about that (I have been wanting that particular book though). Proofs by Jay Cummings is a wonderful modern intro to proofs book that devotes some time to the Pigeonhole Principle. But you may not find it any more thorough or useful than what's in Bona's. I am a big fan of Book of Proof, which is a free proofs book you can find online, but I honestly can't recall whether or not it has pigeonhole principle in it. I'd think it would, but I can't actually remember seeing it. I always sing the praises of A First Course in Graph Theory by Chartrand and Zhang, but that's all for Graph Theory, which comes later in the Bona text. I of course have over a hundred videos on graph theory.
@@WrathofMath yes yes your graph theory proofs help a lot bro. Are you in linkedIn btw? We can connect maybe if you're interested.
@@WrathofMath Also, you can make a Video on Ferrers shapes if possible they 're pretty interesting thoo
Niccceeee!! 👑👑👑
Thanks for watching!
Отлично. Лайк.
Hi to my new crush 🥰.please notice me💙 i just love how you simplify things..
Thank you for watching! 😊 Let me know if you ever have any video requests! Elegant simplicity and beauty, math is filled with it!
You didn't explain the recurrence relation.
th-cam.com/video/sPGudyLalmE/w-d-xo.html
you just showed that the recurrence relation works and all the possibilities of parting a set. i expected an explanation on why is it the way it is. so overall, it's a stupid video.