A brief introduction to generating functions

[@CossZt6]

YES! The most intuitive explanation I've seen yet, beating that of my prof's. Thank you very much!

[@danielhasson6985]

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

[@yyahn]

Thank you very much your kind words! Very much appreciated!

[@rajeevkarunanayake]

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!

[@mahmoudabdalmaksoud8416]

wow ,that's really impressive , you have a unique skill at simplify concepts

[@eobardthawne6903]

Why would anyone dislike these videos? Amazing work sir!!

[@Mayank-mf7xr]

here from reddit. amazing explaination. keeping simple things simple. no overcomplexing. retained everything. nice work dude.

[@yyahn]

You can check out the second video talking about generating function and the Poisson distribution: kzbin.info/www/bejne/i4KToKSrjtBjrMU Also check out this video on Fibonacci numbers: kzbin.info/www/bejne/fp2ZYqCAra5_d5Y

[@EngineeringSolution321]

Very early reply

[@yyahn]

@@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.

[@stephaniegreen1214]

This was such a useful, intuitive, helpful and concise video! Thank you so much!

[@augustusr5671]

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 👍👍👍

[@noahniederklein8038]

Very nice video! Intuitive, clear, and concise. Great examples to demonstrate the power of generating functions. Keep it up!

[@cestlezooicimw]

thank you, I was looking again and again through videos who were barely explaining what the generating function is

[@gemini_537]

Great introduction to generating functions! Very easy to understand! Thank you!

[@adilghaznavi3948]

What a beautiful video! Thank you for posting this on reddit. And please continue to do so.

[@laibaaqureshi6228]

Explained so well , otherwise it was just a theory topic for me now I got practical insight. Thanks😊

[@stevenshi9012]

Understanding the functionality of Generating function really helps for learning combinatorics, thanks!

[@anwoybarua8213]

Thanks for precise introduction to generating functions. Would appreciate if you upload more stat-related contents on youtube.

[@stefan_eng]

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.

[@yyahn]

Indeed! 😬

[@mdorghammm]

Best video I’ve seen on generating functions.

[@Starcell170]

Easy to understand! You are good teacher!

[@manojmohite1982]

Very lucid explanation! Thank you so much.

[@dysfunctional_programming]

This is how maths should be taught! keep up the good work :)

[@WellWang-q3z]

This 7mins video is much better than my professor's teaching

[@adambkehl]

What a great explanation! Thank you so much.

[@Armcollector77]

Very high quality video. Thanks so much.

[@yunzheli8784]

It helped me a lot to understand better of moment generating function.

[@RobertWF42]

Ah, I just made the connection! So the moment generating functions I learned in statistics are a special example of generating functions.

[@Yeahmansingh]

you made it very easy to grasp idea of generating function, thanks

[@MasterBunnySan]

bless up brother. you saved my grade

[@squaidinkarts]

This is what should be in the freaking book!

[@jackobrien7073]

This video is SOSOSO useful for my 2nd year stats class

[@suchitabhalotia]

This is such a cool way to explain maths

[@jungbjun]

Beautiful Video 😉 It helped me a lot.

[@divyakumar8147]

amazing video thanks for such content

[@kir13y8]

Thank you, very concise & informative!

[@simateimotorworld]

Watching at the time of the pandemic, Amazing

[@Ebemelek]

Is it me only but there is no x^8 on 6:16

[@Hillis360]

Great explanation, Should consider making more videos.

[@michaelvendredi8274]

Great video bro!

[@hi_im_buggy]

Great intuitive explanation! Thanks!

[@ruizeng3076]

so clear about the proof in the first three minutes thanks !

[@agrajyadav2951]

omg this is soo coool!! And you are an amazing explainer. Thanks a lot!

[@yuangao7566]

Amazing explanation!

[@enno1162]

amazing explanation! just wondering what you said that the new generating function represents? 5:17 - 5:24. especially the last word.

[@yyahn]

The new generating function represents the probability of the "sum of values from the original generating functions" that are multiplied together.

[@DillonHuff]

Very informative video. Thanks for posting this!

[@m322_yt]

Cool, that was a concise motivation! Thank you :)

[@GladwinNewton]

thank you so much. you are awesome

[@rongliao9255]

Great tutorial 👍 Thanks a lot!!

[@zuggrr]

This is great ! Thank you so much

[@qiaohuizhou6960]

1:57 mathematical operations 3:24 analytical tool

[@seandunn8657]

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

[@yyahn]

Yes you're correct!

[@lopezramirezmonserrat5957]

Your explanation is incredible!! what do you do for a living?

[@yyahn]

Thanks! Professoring! 👀

[@drewkavi6327]

Brilliant video

[@iaquobe]

jo this video is great!!!! thanks a lot!

[@bhaskarmazumder5679]

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.

[@yyahn]

It is just an example of a mathematical operation that you can use. It's about taking a derivative and then multiply x.

[@bhaskarmazumder5679]

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....

[@dominicellis1867]

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?

[@yyahn]

I'm not sure... Maybe this video by 3b1b would be useful: kzbin.info/www/bejne/mIC7dH-IaLyln8U

[@shanemg16]

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?

[@yyahn]

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.

[@lolmes7473]

You are the best

[@robertleo3561]

For real you made it just click! Thank you

[@דניאל-ט9ד]

good video! thanks! helped me alot!

[@kreeesqeeel]

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!

[@yyahn]

A great question! It corresponds to the zeroth power of x (x^0) and represents the case of zero candy. :)

[@EngineeringSolution321]

Superb explanation

[@Bednesti38]

Great video!

[@kaursingh637]

excellent -excellent -excellent

[@da_lime]

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.

[@yyahn]

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.

[@da_lime]

@@yyahn wow, thank you!

[@VarunaXavier]

Excellent!!!!!

[@hassandanamazraeh5975]

Great 👍

[@rofiihamdi65]

Thankyou so much man

[@bakarandguladze]

Good job, buddy!

[@aidan-ator7844]

I don't understand why, in the first G(x), there is a different power ascribed to each probability. It does not seem to intuitively follow whatsoever

[@yyahn]

Yes, generating functions are not very intuitive at the beginning! I tried to explain it as a purely mathematical trick first to separate all the values from each other because trying to make sense of it often makes it harder to grasp.

[@aidan-ator7844]

@yyahn I like the deep explanations. I am a philosophical thinker so I don't mind abstract concepts

[@aidan-ator7844]

@yyahn I just struggle with sudden inferred results from theorems and ideas I don't understand.

[@kanewilliams1653]

You are a GOD. Are you a teacher?

[@yyahn]

Thanks! Yes

[@SevenRiderAirForce]

Nice!

[@lileggy9553]

the best

[@timelygoose]

Thank you sir

[@dr.alshadkb135]

How about pgf of continuous distributions?

[@yyahn]

Check out "factorial moment generating function".

[@Anonymous-s7j1y]

When I first see when you construct a generating function out of nowhere I thought the function looked ridiculous now Im like wow...

[@Anonymous-s7j1y]

What textbook or resource can I refer to if any?

[@yyahn]

@@Anonymous-s7j1y 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

[@botix2]

Very good

[@ScaryTimeTravel]

This was cool

[@pankajsinghrawat1056]

Why don't our professors tech us like u, the world would be all different.

[@saikrishna8871]

Golden nugget

[@vipnirala]

Just wow

[@didyoustealmyfood8729]

bruh your accent is hard to interpret.