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.

Congratulations. You have taught me an intuitive understanding of something my lecturer did no manage to communicate across for the duration of the module.

[@cestlezooicimw]

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

[@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 👍👍👍

[@gemini_537]

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

[@noahniederklein8038]

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

[@adilghaznavi3948]

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

[@stevenshi9012]

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

[@laibaaqureshi6228]

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

[@anwoybarua8213]

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

[@Armcollector77]

Very high quality video. Thanks so much.

[@mdorghammm]

Best video I’ve seen on generating functions.

[@adambkehl]

What a great explanation! Thank you so much.

[@manojmohite1982]

Very lucid explanation! Thank you so much.

[@Yeahmansingh]

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

[@Starcell170]

Easy to understand! You are good teacher!

[@WellWang-q3z]

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

[@suchitabhalotia]

This is such a cool way to explain maths

[@squaidinkarts]

This is what should be in the freaking book!

[@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.

[@MasterBunnySan]

bless up brother. you saved my grade

[@jackobrien7073]

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

[@dysfunctional_programming]

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

[@divyakumar8147]

amazing video thanks for such content

[@kir13y8]

Thank you, very concise & informative!

[@simateimotorworld]

Watching at the time of the pandemic, Amazing

[@hi_im_buggy]

Great intuitive explanation! Thanks!

[@jungbjun]

Beautiful Video 😉 It helped me a lot.

[@Hillis360]

Great explanation, Should consider making more videos.

[@ruizeng3076]

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

[@DillonHuff]

Very informative video. Thanks for posting this!

[@yuangao7566]

Amazing explanation!

[@GladwinNewton]

thank you so much. you are awesome

[@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! 😬

[@Ebemelek]

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

[@agrajyadav2951]

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

[@drewkavi6327]

Brilliant video

[@michaelvendredi8274]

Great video bro!

[@rongliao9255]

Great tutorial 👍 Thanks a lot!!

[@m322_yt]

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

[@zuggrr]

This is great ! Thank you so much

[@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....

[@iaquobe]

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

[@lopezramirezmonserrat5957]

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

[@yyahn]

Thanks! Professoring! 👀

[@qiaohuizhou6960]

1:57 mathematical operations 3:24 analytical tool

[@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.

[@lolmes7473]

You are the best

[@robertleo3561]

For real you made it just click! Thank you

[@hassandanamazraeh5975]

Great 👍

[@דניאל-ט9ד]

good video! thanks! helped me alot!

[@timelygoose]

Thank you sir

[@EngineeringSolution321]

Superb explanation

[@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!

[@kanewilliams1653]

You are a GOD. Are you a teacher?

[@yyahn]

Thanks! Yes

[@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 😆

[@VarunaXavier]

Excellent!!!!!

[@Bednesti38]

Great video!

[@kaursingh637]

excellent -excellent -excellent

[@rofiihamdi65]

Thankyou so much man

[@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. :)

[@lileggy9553]

the best

[@SevenRiderAirForce]

Nice!

[@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.

[@bakarandguladze]

Good job, buddy!

[@botix2]

Very good

[@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.

[@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

[@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!

[@pankajsinghrawat1056]

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

[@dr.alshadkb135]

How about pgf of continuous distributions?

[@yyahn]

Check out "factorial moment generating function".

[@ScaryTimeTravel]

This was cool

[@vipnirala]

Just wow

[@saikrishna8871]

Golden nugget

[@didyoustealmyfood8729]

bruh your accent is hard to interpret.