In the first example, when you go from 1 apple to 2 apples, the answer should be 11 instead of 7 because you missed a banana (and it doesn't make sense that you'd go from 10 ways in the 1 apple case to 7 ways in the 2 apples case). (1 + x + x^2)(1 + x)^4 = x^6 + 5x^5 + 11x^4 + 14x^3 + 11x^2 + 5x + 1, the coefficient for x^2 is 11.
Apparently, the teacher eliminated one type of element, keeping the same number of elements, perhaps with the intention of not complicating the algebraic process. Otherwise the result is correct.
Thank you for your videos Patrick(: they are very helpful and have helped me a lot in math. I watch everyone of your videos just for fun. Math is fun(: Also, do you know of any physics or engineering how to videos on TH-cam like your channel provides? Thank you. You help infinitely many people with the great subject of mathematics each and everyday.
I love it. Combinatorics was my hardest subject in undergrad. If you could please answer this question I'd greatly appreciate it: what is the difference between ordinary generating functions and exponential generating functions?
My favorite generating function is for the partition of integers. Would be neat if you could do a video on the basic proof where you do the foiling. Anyway, take care Patrick!
I just started learning this topic today for the first time. I could follow the examples in the book but I still felt like I didn't exactly 'believe' what they were doing worked. I appreciate you making the tables to show that you get the same result. It really helped prove to me that the concept makes sense. There is just one thing though - I am still not really clear on why anyone would have thought to do this in the first place or why exactly it works. Does it have anything to do with orthogonality? (that's just a wild guess) Also, why 'generating' functions? I don't understand why the term 'generating' makes sense in this context.
As only two people have pointed out: bananas are missing, so we would have to consider the coefficient of x^2 in the polynomial (1+x+x^2)*(1+x)^4. so, guys, everyone who got 11 as a result is correct. The assumption that a banana turned into an apple... isn’t logical.
In the second example we can't not to choose from the cheese and the raspberry because then it will be less than seven so shouldn't be like for cheese x+ x²+x³ And for raspberry x+x²+x³+x4!
Hey Patrick, can you please make a video on exponential generating functions, and also a video on finding the coefficient using polynomial identifies? Plz
Hi Patrick, do you think it is reasonable to skip a precalculus class at my high school and move from Enriched Algebra 2 & Trigonometry -> AP Calculus AB/BC? Thank you and happy holidays.
In the third example, the number to choose is 7. If you not choose any raspberry, the another two types total remaining amount only adds up to five, which is below the number initially stipulated. Then, when performing the numerical check, 3 is set as the maximum amount of raspberries. But it is possible to choose (4,3,0);(4,2,1);(4,1,2). Can someone clarify this doubt for me?
Why would knowing this be beneficial at all? Multiplying those polynomials is similarly computationally expensive than looping over all options. What am I missing?
Being able to combine generating functions from multiple different problems and save polynomials to come up with quick solutions to potentially difficult problems would be my guess.
Hi Patrick, please dear god make the second video. This video taught me more in 15 minutes than my prof did in about 3 hours :)
It taught me more than what I did in 1 years
Hey Patrick, I know it's been over 3 years since this video, but is there a chance you will still make a second video it would be a lifesaver!
In the first example, when you go from 1 apple to 2 apples, the answer should be 11 instead of 7 because you missed a banana (and it doesn't make sense that you'd go from 10 ways in the 1 apple case to 7 ways in the 2 apples case). (1 + x + x^2)(1 + x)^4 = x^6 + 5x^5 + 11x^4 + 14x^3 + 11x^2 + 5x + 1, the coefficient for x^2 is 11.
i wasted 30m trying to think why it's 7 and not 11 & then saw he forgot the banana
Apparently, the teacher eliminated one type of element, keeping the same number of elements, perhaps with the intention of not complicating the algebraic process. Otherwise the result is correct.
dood... this is how you teach this stuff, build an intuition and then define it formally. Thank you for this video
Merry xmas and a prosperous new year to the most valuable youtuber in the world. Blessings🙋
thanks :)
Patrick thankyou so much for such amazing and useful videos!! Could never thank you enough :) You're a hero
I always watch your videos so I'd like to take a moment and appreciate your hard work !!
Thank you !! Keep it up and merry Christmas !
Got surprised you made a video about Generating Functions, really expanding your range
Thank you so much for all your videos!! You helped me get a high grade in algebra! Happy Holidays!!:)
Where did the banana go in the second part?
It became an apple ;)
Eaten by him!!
Thank you for your videos Patrick(: they are very helpful and have helped me a lot in math. I watch everyone of your videos just for fun. Math is fun(:
Also, do you know of any physics or engineering how to videos on TH-cam like your channel provides? Thank you. You help infinitely many people with the great subject of mathematics each and everyday.
i know there are quite a few of each out there, but i don't have anyone to personally recommend!
I love it. Combinatorics was my hardest subject in undergrad.
If you could please answer this question I'd greatly appreciate it: what is the difference between ordinary generating functions and exponential generating functions?
Thank you for this life saver
My favorite generating function is for the partition of integers. Would be neat if you could do a video on the basic proof where you do the foiling. Anyway, take care Patrick!
Thank you sooo much!!! Very useful to know how and why these are important in terms of counting.
Thanks for the video. You said this is an intro, is there a second part for it ?
Beautiful and elegant...Thank you so much!
yes i am! thank you for noticing!
Very great video. More like this!
I just started learning this topic today for the first time. I could follow the examples in the book but I still felt like I didn't exactly 'believe' what they were doing worked. I appreciate you making the tables to show that you get the same result. It really helped prove to me that the concept makes sense.
There is just one thing though - I am still not really clear on why anyone would have thought to do this in the first place or why exactly it works. Does it have anything to do with orthogonality? (that's just a wild guess)
Also, why 'generating' functions? I don't understand why the term 'generating' makes sense in this context.
As only two people have pointed out: bananas are missing, so we would have to consider the coefficient of x^2 in the polynomial (1+x+x^2)*(1+x)^4. so, guys, everyone who got 11 as a result is correct. The assumption that a banana turned into an apple... isn’t logical.
how can get equation in 10:25?
In the second example we can't not to choose from the cheese and the raspberry because then it will be less than seven so shouldn't be like for cheese x+ x²+x³
And for raspberry x+x²+x³+x4!
*Awesome explanation....*
Great explanation bro, what's the name of the video where you explain this in more detail? (The following video) Thsnks
Can we see more of these PLEASE?!
Hey Patrick, can you please make a video on exponential generating functions, and also a video on finding the coefficient using polynomial identifies?
Plz
Hi Patrick, do you think it is reasonable to skip a precalculus class at my high school and move from Enriched Algebra 2 & Trigonometry -> AP Calculus AB/BC? Thank you and happy holidays.
It could be done. But I'd suggest you take precalculus first. There's no reason to rush things.
Hello, how can we find the # of permutations with gen func?... For example set = {GGGBP} how many 2-letter strings can be produced?
When will second part be released?? I have exam soon, so hurry up!!!
In the third example, the number to choose is 7. If you not choose any raspberry, the another two types total remaining amount only adds up to five, which is below the number initially stipulated. Then, when performing the numerical check, 3 is set as the maximum amount of raspberries. But it is possible to choose (4,3,0);(4,2,1);(4,1,2). Can someone clarify this doubt for me?
Why would knowing this be beneficial at all? Multiplying those polynomials is similarly computationally expensive than looping over all options. What am I missing?
Being able to combine generating functions from multiple different problems and save polynomials to come up with quick solutions to potentially difficult problems would be my guess.
You can reduce to the infinite series, and you gain a lot of computational time. You can write 1+x+...+x^6=
(1-x^7)/(1-x) for example.
Wait a sec..... thank you for the video but..... how do you do that polynomial multiplication and simplification in one step?
I watched this before one of my exams and I wouldn't have gotten one of the questions at all if I hadn't. Thanks!
how is he expanding those things so fast?
Where is the second part?
i love you thankyouuuuuuuuuu
please make a video on complex numbers
Wow!!
Thanks
How to make that table 😨
thanks😙😙😙😙😙
statistical methods seems like the more efficient method.
You sound like Tarantino :0
shikachus
so much confusion....