In the video at 6:49, you may notice and the constant term of the generating function and the value at n=0 are different and here is why: Adding generating function taking the 'or' literally. Meaning it will count construction 1 and 2 differently even when they might look the same. In this case, we have 2 in generating function because it says there are two way to pick 0: 0 shirt or 0 sock. I know it's odd, but that how it works. :-(
Thanks for making this video! My understanding is that the concept of generating functions is foundational in Analytical Combinatorics (I think it's called), a subject that seems pretty interesting, from what I've seen. This was a good, easy-to-understand introduction to the concept of generating functions!
Super cool! At the start I was like, huh? what's the point? But after those explanations this seems really useful. The clothing options was a good example.
Generating functions are more general than nCr. You can use generating functions to represents sequences that would be a lot harder or impossible to represent in terms of nCr for some n and r. This is simply an example of using generating functions to count, but you can also use generating functions to represent recurrence relations such as fibonacci. More importantly, generating functions can be used to find closed form solutions to many recurrence relations, which would be very difficult just using nCr.
This is the real way to teach. Thank you so much. I can't wait for the next.
I am so glad you find it useful!
Glad someone actually took the time to explain the intuition behind and not just fucking algebra
In easy problems it's just a logic, but in classical algebraic problems you need to learn advanced theories first.
In the video at 6:49, you may notice and the constant term of the generating function and the value at n=0 are different and here is why: Adding generating function taking the 'or' literally. Meaning it will count construction 1 and 2 differently even when they might look the same. In this case, we have 2 in generating function because it says there are two way to pick 0: 0 shirt or 0 sock. I know it's odd, but that how it works. :-(
Thanks for making this video! My understanding is that the concept of generating functions is foundational in Analytical Combinatorics (I think it's called), a subject that seems pretty interesting, from what I've seen. This was a good, easy-to-understand introduction to the concept of generating functions!
Thank you for your kind words!!
Super cool! At the start I was like, huh? what's the point? But after those explanations this seems really useful.
The clothing options was a good example.
Thank you! I am glad you find it useful!
Your video is very interesting and easy to understand. You just helped me in my Discrete mathematics class. THX
OMG! Thank you so much! You explained the concept so clearly!!!!
I am glad you find it useful!
Thanks so much for these joyful moments! :))))))
I love generating functions! When does part 2 come out?! I'm on the edge of my seat!
It will be next Friday!
lol chill
Thank you for the video! Your didacts and enthusiasm really helps to approach such an intricate topic! Regards
I am glad you like it!
the final problem is unexpected, but it helped me, many thanks to you!
So much effort in the video why this channel is not blowing up :( i subbed though
Excellent presentation! You are the anti-math.SE in tone and friendliness!
Thank you, this is an excellent explanation
Yo man, uuh gave me the idea to think in a new way about generation functions. 🙏
best video i found on the topic. thank you.
It was very helpful for me. Thank you.
I like this guy's attitude.
I like you too!
Fantastic explanation! Thank you so much for the effort. Really appreciate it
Glad it was helpful!
great video. thank you brother
Glad you like it!
Well why can't we use nCr instead of using the function?
Isn't this just application of fundamental theorem of counting?
Generating functions are more general than nCr. You can use generating functions to represents sequences that would be a lot harder or impossible to represent in terms of nCr for some n and r.
This is simply an example of using generating functions to count, but you can also use generating functions to represent recurrence relations such as fibonacci. More importantly, generating functions can be used to find closed form solutions to many recurrence relations, which would be very difficult just using nCr.
That was really good!
Great video; thanks!!
So never seem to want to solve X, do we
Plss make a playlist on number theory or combinatorics plzzzz plzzzz plzzz it is much needed plzzzzz plzzz
Well done!! Thank you.
thanks
Thanks so much!!
clean
Is it 18 or 19
18
helll yeah
Cute🤪