Discrete Math 2 - Tutorial 16 - Generating Functions

First look at Generating Functions; another way of counting objects.

Please comment rate and subscribe.

for latest updates :

[RipleySawzen]

My professor SUCKS at lecturing! I didn't even understand the point of a power series and you basically covered that in the first few minutes!

[GagePeterson]

WOW! Your a lifesaver! This is so much better than my textbook!

[jimmyhashat]

This was a great video, thank you very much. I will definitely be watching the rest of your vids. I loved the way you simplified things.

[irondev]

Thanks a lot for this tutorial. It was really helpful. In the pennies example though, for case b, shouldn't the expression only go to x^31 instead of x^35 because each child must have at least one penny?

[bradleystoll]

If there are only 35 pennies, it seems to me that in the generating function you would have (1 + x + x^2 + ... + x^35)^5. x^36 would represent getting 36 pennies, correct? So, even with no restrictions, how could you go beyond x^35?

[Slorthe]

Wow, explicit and understandable examples and explanations. Thank you so much

[Bansenshukai]

Watched this video for three minutes and I feel dumb. I must be one of those humans that work on outdated mental software. I already felt obsolete before, this confirms it

[christophersewell]

At around 3:15, you wrote and said that there is no power series for part a). I feel it necessary to point out that you are wrong. Ordinary generating functions are all about power series regardless of if they are infinite. Power refers to exponentiation. Series means there are terms which are summed. Hence power ... series.

[coursehack]

x represents each penny; for a) u can have no pennies up to 35 pennies per child... therefore, u start from 1 + x + x^2 + x^3
picture the coefficient as being the number of pennies
b) each must have atleast 1 penny, therefore, u start from x, since 1 represents none.
same conclusion for c) the oldest child must get at least 10 cents, u start from x^10

finally, the coefficient around the x's is the number of children with that condition...
so, for c) 1 child gets 10 cents and 4 children get 1-25

[vivvpprof]

OK, this seems to work well if children are distinguishable, which is usually the case. But what if I want to — say — put 30 pennies into 5 indistinguishable moneyboxes and each box may contain no more than 8 pennies? What would be the generating function in this situation? :)

[flamurmustafa]

6:46 the coefficient does not go to infinity but at 30.

[QuiQui]

For the case: c1 + c2+ c3+ c4+ c5 = 30, wouldn't the upper bound for ci be 30?

[DeedeeFruits]

It's very well explain, thank you so much for making this video ! :)