this is literally the best youtube video I've watched all year. I have been smiling for the past 5 minutes due to how fascinating this is. mindblowing and perfect explanation. thank you so much for making my day
You can check out the second video talking about generating function and the Poisson distribution: ruclips.net/video/UQ0oquYk0vc/видео.html Also check out this video on Fibonacci numbers: ruclips.net/video/Hl61mJxILA4/видео.html
Congratulations. You have taught me an intuitive understanding of something my lecturer did no manage to communicate across for the duration of the module.
I have been trying to understand the concept of generating functions for quite a while. But couldn't find any good videos. Finally found it. Thanks you to you 👍👍👍
Your tutorial is really very beautiful... I have never seen such vivid explanation about discrete mathematics. You told in your tutorial that generating function is like a machine with various push buttons. But I don’t understand (x x/dx ) button . Could you please give me an example about the application of that button,Sir.
In the final example, why is there a 1 in the red and green probability functions? I don’t think I quite understand where that is coming from. Other than that, very simple video to understand thanks!
So a generating function is simply solving dif eq with power series. Is there a methodology when a power series solution is impossible i.e. a non analytical differential equation. Would this then warrant fractional derivatives to smooth out planes of discontinuity?
For the last example, given the restrictions, wouldn't it be impossible to chose 6, 8 or 10 red candies? So why would they be incorporated in calculating the probability?
@@Anonymous-kj6cu There's this book: www2.math.upenn.edu/~wilf/DownldGF.html I'm much more familiar with network science applications which are nicely covered in www.amazon.com/Networks-Mark-Newman/dp/0198805098
Hi, thank you! Could you give a few examples where it can be used in practice? Maybe it finds some applications in computer science or physics or robotics perhaps.
It's useful for many combinatorial problems in general. The area that I'm most familiar with is network science. It's one of the most basic tools to study the properties of a network. For instance, you can study how a disease may spread through a social network.
YES! The most intuitive explanation I've seen yet, beating that of my prof's. Thank you very much!
this is literally the best youtube video I've watched all year. I have been smiling for the past 5 minutes due to how fascinating this is. mindblowing and perfect explanation. thank you so much for making my day
Thank you very much your kind words! Very much appreciated!
wow ,that's really impressive , you have a unique skill at simplify concepts
It's a good introduction to get an intuitive idea on what generative functions can do before you deep dive into a textbook. Great video!
Why would anyone dislike these videos? Amazing work sir!!
You can check out the second video talking about generating function and the Poisson distribution: ruclips.net/video/UQ0oquYk0vc/видео.html Also check out this video on Fibonacci numbers: ruclips.net/video/Hl61mJxILA4/видео.html
Very early reply
@@EngineeringSolution321 😆
Congratulations. You have taught me an intuitive understanding of something my lecturer did no manage to communicate across for the duration of the module.
This was such a useful, intuitive, helpful and concise video! Thank you so much!
thank you, I was looking again and again through videos who were barely explaining what the generating function is
Thanks for precise introduction to generating functions. Would appreciate if you upload more stat-related contents on youtube.
here from reddit. amazing explaination. keeping simple things simple. no overcomplexing. retained everything. nice work dude.
I have been trying to understand the concept of generating functions for quite a while. But couldn't find any good videos. Finally found it. Thanks you to you 👍👍👍
Great introduction to generating functions! Very easy to understand! Thank you!
What a beautiful video! Thank you for posting this on reddit. And please continue to do so.
Explained so well , otherwise it was just a theory topic for me now I got practical insight. Thanks😊
Understanding the functionality of Generating function really helps for learning combinatorics, thanks!
Very nice video! Intuitive, clear, and concise. Great examples to demonstrate the power of generating functions. Keep it up!
Very high quality video. Thanks so much.
you made it very easy to grasp idea of generating function, thanks
Should the polynomial for even number of red candies be: 1 + x^2 + x^4 + x^6 + x^8 + x^10 instead? It looks like the x^8 term is missing.
Indeed! 😬
It helped me a lot to understand better of moment generating function.
Ah, I just made the connection! So the moment generating functions I learned in statistics are a special example of generating functions.
What a great explanation! Thank you so much.
bless up brother. you saved my grade
This 7mins video is much better than my professor's teaching
Very lucid explanation! Thank you so much.
This is such a cool way to explain maths
Easy to understand! You are good teacher!
Best video I’ve seen on generating functions.
This video is SOSOSO useful for my 2nd year stats class
This is how maths should be taught! keep up the good work :)
This is what should be in the freaking book!
Great explanation, Should consider making more videos.
Your tutorial is really very beautiful... I have never seen such vivid explanation about discrete mathematics. You told in your tutorial that generating function is like a machine with various push buttons. But I don’t understand (x x/dx ) button . Could you please give me an example about the application of that button,Sir.
It is just an example of a mathematical operation that you can use. It's about taking a derivative and then multiply x.
Thanks a lot! Now I understand that it will be (x d/dx) instead of (x x/dx) ....Waiting for your new video on discrete math & combinatorics....
Great intuitive explanation! Thanks!
Beautiful Video 😉 It helped me a lot.
Thank you, very concise & informative!
Watching at the time of the pandemic, Amazing
Amazing explanation!
so clear about the proof in the first three minutes thanks !
amazing explanation! just wondering what you said that the new generating function represents? 5:17 - 5:24. especially the last word.
The new generating function represents the probability of the "sum of values from the original generating functions" that are multiplied together.
Very informative video. Thanks for posting this!
Brilliant video
omg this is soo coool!! And you are an amazing explainer. Thanks a lot!
Great video bro!
Your explanation is incredible!! what do you do for a living?
Thanks! Professoring! 👀
This is a great video, thank you, For the "even red candies" polynomial, shouldn't x^8 be included as a term between x^6 and x^10? Thanks again
Yes you're correct!
Great tutorial 👍 Thanks a lot!!
Cool, that was a concise motivation! Thank you :)
This is great ! Thank you so much
thank you so much. you are awesome
In the final example, why is there a 1 in the red and green probability functions? I don’t think I quite understand where that is coming from. Other than that, very simple video to understand thanks!
A great question! It corresponds to the zeroth power of x (x^0) and represents the case of zero candy. :)
So a generating function is simply solving dif eq with power series. Is there a methodology when a power series solution is impossible i.e. a non analytical differential equation. Would this then warrant fractional derivatives to smooth out planes of discontinuity?
I'm not sure... Maybe this video by 3b1b would be useful: ruclips.net/video/bOXCLR3Wric/видео.html
jo this video is great!!!! thanks a lot!
For the last example, given the restrictions, wouldn't it be impossible to chose 6, 8 or 10 red candies? So why would they be incorporated in calculating the probability?
Yes, that'd be a smarter way to avoid unnecessary calculations! At the same time, what's shown in the video can be *mechanically* carried out.
1:57 mathematical operations
3:24 analytical tool
Great 👍
good video! thanks! helped me alot!
You are the best
When I first see when you construct a generating function out of nowhere I thought the function looked ridiculous now Im like wow...
What textbook or resource can I refer to if any?
@@Anonymous-kj6cu There's this book: www2.math.upenn.edu/~wilf/DownldGF.html I'm much more familiar with network science applications which are nicely covered in www.amazon.com/Networks-Mark-Newman/dp/0198805098
Great video!
excellent -excellent -excellent
Superb explanation
For real you made it just click! Thank you
Excellent!!!!!
Hi, thank you!
Could you give a few examples where it can be used in practice? Maybe it finds some applications in computer science or physics or robotics perhaps.
It's useful for many combinatorial problems in general. The area that I'm most familiar with is network science. It's one of the most basic tools to study the properties of a network. For instance, you can study how a disease may spread through a social network.
@@yyahn wow, thank you!
Thank you sir
Thankyou so much man
Nice!
Good job, buddy!
You are a GOD. Are you a teacher?
Thanks! Yes
How about pgf of continuous distributions?
Check out "factorial moment generating function".
Very good
Why don't our professors tech us like u, the world would be all different.
the best
Just wow
This was cool
Golden nugget
bruh your accent is hard to interpret.