Thank you, still helping students 5 years in the future.
@maybeyesterday
2 жыл бұрын
6
@deveshh1865
2 жыл бұрын
at 16:20 why for the blue brackets. (x^2^ x^3^ x^4...) he takes x^2 at the first so he starts at x^2 (x^0 ^x^1 x^2^...) why he starts at x^0 ....
@muhammadshayanusman5540
2 жыл бұрын
7
@MLRTrytonix13
Жыл бұрын
8
@dennisdong9097
5 ай бұрын
9
@NoName-qi7vx
4 жыл бұрын
My professor just said these are the genrating functions and then he went straight to examples. He never, not even once showed how these things actually generate the series. I tried plugging values for x and never got a reasonable output (obviously). He did not once say that you have to do polynomial division. So this entire topic just seemed like magic to me. Thank god you exist
@leogao6929
Жыл бұрын
i hate how shitty college professors are man
@Comand94
4 жыл бұрын
Dude, you're saving my quarantined ass with this, my online lectures on this topic were very lackluster, thank you.
@thegui999
7 жыл бұрын
I SHOULD MAKE A STATUE IN YOUR HONOR! Tell me, how does it feel to save people for their impending doom in some random tests around the globe? -Brazilian computer science student
@florianveliou
7 жыл бұрын
hahaha so true greek computer science student
@cosmosisdown962
7 жыл бұрын
yes! - Azerbaijani computer science student
@nathannelson2710
6 жыл бұрын
You nailed it on the head! Marine Corps, computer science student here!
@anonymousted7302
6 жыл бұрын
Canada computer science student here.
@flaviadeluce9099
6 жыл бұрын
Somehow it feels right to write here: Mathematics major, Turkey :)
@ZnCuNO3
7 ай бұрын
Basically saved my life. That's the explaination I searched for months. A great video
@nielsieboy19
3 жыл бұрын
Dude you're a legend, after watching your videos I believe I can actually pass my exam!
@zacharyjulian8861
4 жыл бұрын
Thank you so much. You explain things in a simple, easy to understand manner. Your videos are straight to the point so I'm not skimming through a week's worth of my lectures trying to understand this concept.
@zemnly
3 жыл бұрын
I love how lucid yet simple this was.
@Rajat-Sharma1
4 жыл бұрын
I have a test tomorrow and I have just started. Glad to find this video. A useful resource.
@programmer4047
2 жыл бұрын
In which class, you were at the time of writing this question? I don't think generating functions are taught in schools
@ffles
7 жыл бұрын
Wow, I wish my university taught like you did. Your simple use of real world problems abstracted mathematics was a very important (and missing) link that most of us don't get from a formal education.
@saipavan851
7 жыл бұрын
You are 100% correct,
@tman7022
9 жыл бұрын
you have helped me beyond what i can explain :) thanks
@TheMesoria
8 жыл бұрын
I hardly suq at english. Understood everything PERFECTLY. Subscription for being good at what you are doing!
@cornmasterliao7080
Жыл бұрын
Idk how but I feel like even the look of your words make things seem easier to understand. Better than my professor.
@kashishbakshi9877
6 жыл бұрын
This really helped me get my basics right. Thank You! Keep Uploading More.
@lydiahchepkemoi9464
3 жыл бұрын
I would recommend this to economics and statistics students big time
@vishalchovatiya1361
Жыл бұрын
Thanks very much stumbled on this video after 7-8. And this by far the best video to understand generating functions.
@basicnpcc
8 жыл бұрын
Yo TrevTutor, I would love if you made another video on just the proofs. The longer proofs like (NOTp v q) ^ NOT(NOTq v r) v ( NOTp v r) being equivalent to a tautology tend to mess me up with how the laws work in them. Thanks mate.
@muubisgiller
2 жыл бұрын
Thank you so much. I am sending thanks from Istanbul Technical University. I even read the Brualdi's Combinatorics book but I understand well now.
@sushmitanigam4979
7 жыл бұрын
my heartiest thanx to you. This is superb and the best. Seriously you are the best teacher.
@SuperRockcore
Жыл бұрын
I’m inspired to memorize these now!
@paraphoenix6188
6 жыл бұрын
Awesome Awesome Awesome... I tried reading a book to learn this subject but my mind just got crushed out... So simple and amazing
@JaspreetSingh-oo7ry
8 жыл бұрын
woooohh what a life saver! crisp and clear explanation on generating functions
@wangealork4768
7 ай бұрын
This is amazing. Good and appropriate examples.
@nafiulawal1443
8 жыл бұрын
Please can you create a playlist of your videos or numbering them so I can follow it as a course. Thank you for a helpful videos
@Trevtutor
8 жыл бұрын
Playlist already exists for Discrete 1 and Discrete 2 series.
@yujiabing8820
6 жыл бұрын
so clear and easy to understand for me.
@AnyaPb
8 жыл бұрын
in the last question, shouldn't x1 be (x^2 + x^3 + .. + x^12) because it can only go as high as 12 right, not go on forever?
@Trevtutor
8 жыл бұрын
There's no difference in the end, since the coefficients will still be the same even if we allow it to go higher. (This doesn't generalize to all questions)
@ketrinasiagian1585
4 жыл бұрын
i actually don't really understand but it help a litle bit. thank you
@luthfibalaka8592
3 жыл бұрын
Awesome! Thanks for the video, it really helps me understand the topic
@praveenparasar8969
8 жыл бұрын
I FOUND A MISTAKE !!!! in the question of red,blue and white shouldn't the red be (1+x^2+x^4+x^6) that's it because we have to give atleast 14 to the blue one,then how the red can go upto ...+x^20 expecting a reply soon thanks :)
@Trevtutor
8 жыл бұрын
It doesn't make a different. In the end we look at the coefficient of x^20. Letting red go up to x^20 won't affect the overall coefficient of x^20 after multiplying all the terms out.
@praveenparasar8969
8 жыл бұрын
yes sir thanks
@harshitjoshi4561
6 жыл бұрын
Hey TrevTutor, at 3:19, shouldn't you end the red jellybeans at x^6 only as it cannot possibly exceed that. Or maybe it doesnot matter??
@justinzhao6814
2 жыл бұрын
the first 5 minutes of this vidfeo gave me more understanding than a whole ass online lecture
@hobbyhuman
7 жыл бұрын
You are saving my life at exam time here.
@mohityadav8383
6 жыл бұрын
You made my day! man
@AmberComer
8 жыл бұрын
at 12:40, you go from =0+1+2x+3x^2+4x^3... to (1,2,3,4,5,6,...) I'm not understanding this. How did you get (1,2,3,4,5,6,...)? Why doesn't it start with 0?
@Trevtutor
8 жыл бұрын
0+1=1. The coefficient of x^0 is 1.
@AmberComer
8 жыл бұрын
Thank you for the speedy response! I'd like to ask a follow up question about that. So, from: 0+1+2x+3x^2+4x^3... For our list of coefficients, we simply do not list 0. We obtain 1 from x^0. Then, we obtain 2 from the coefficient of x^1, obtain 3 from the coefficient of x^2, etc?
@Trevtutor
8 жыл бұрын
You do not list 0 because the first coefficient is the coefficient of x^0. 0x^0 + 1x^0 = 1x^0. If I had 2x^2 + 4x^2 then the list of coefficients would be (0, 0, 6, 0, 0, 0, ...)
@AmberComer
8 жыл бұрын
TheTrevTutor Thank you!!!!!
@amirhosseinsafari1662
6 жыл бұрын
YOU ARE A LIFE SAVER, Thank you man.
@tejassoni1687
8 жыл бұрын
Best on KZitem I think.
@jujoropo
Жыл бұрын
amazing teacher man
@eddiechen6389
5 жыл бұрын
Hi, Mr Trev, I have a question regarding the jellybean question.In the first conditon, it says even reds, but the second conditon says AT LEAST 14, does it give the restriction to the first condition? which in my assumption, its: 1 + x2 + x4 +x6. Corret me if I am wrong? thanks a lot
@unusualgaming8629
3 жыл бұрын
thats true, however, when you count the coefficient of x^20 none that had reds greater than x^6 included, so it doesnt affect the final solution
@unusualgaming8629
3 жыл бұрын
haha 2 years later
@eddiechen6389
3 жыл бұрын
@@unusualgaming8629 ....a question being answered after 2 years...lol
@iragoum
Жыл бұрын
@@eddiechen6389 and how can we count the coefficient of x^20 ?
@eddiechen6389
Жыл бұрын
@Abderrahim Mougari that’s 1
@satviktejas6085
2 жыл бұрын
great explanation sir
@ddiq47
Жыл бұрын
*clicks on video* this is exactly what I was looking for :)
@johnasty517
3 жыл бұрын
So, if I understand correctly, there are 12 ways to solve the first question where x1+x2+x3=12 with 0≤xi≤6. You said that there are 3+4+5 ways of solving the equation, so that would be 12 ways in total, right?
@ayushpainuly4530
7 жыл бұрын
you saved my life.....love from india
@rajeshdansena
7 жыл бұрын
How we are going to get coefficient of x^12 at 2:20 ? Can you please elaborate? Appreciate :)
@HsiehAnastasia
5 жыл бұрын
This video is really helpful Thanks a looooot for making this video!!!
@abhishekaggarwal4066
6 жыл бұрын
Awesome...Thanks for the video...
@anonkiddo
7 жыл бұрын
Thanks for the video, helped a lot! Stay Awesome!
@rajeshdansena
7 жыл бұрын
at 15:30 Why should we go higher then x^12 for x1??? since x1+x2+x3=12 and x1>=2 hence it should be x^2,x^3,x^4,x^5,x^6,x^7,x^8,x^9,x^10,x^11,x^12. Please clarify! Appreciate your response.
@Trevtutor
7 жыл бұрын
It's slightly simpler to write out functions that go on forever than cutting them off. It doesn't change the coefficients at all, so it's inconsequential if we go further or not.
@RealMcDudu
5 жыл бұрын
Regarding long division of polynomials - aren't you suppose to line them up in decreasing order, i.e. -x + 1 instead of 1-x. How does this affect the answer? Also the 1/(1-x) solution is only true for |x| < 1. Are we assuming this?
@haileyfiedler6411
2 жыл бұрын
THIS VIDEO IS AWESOME!!!!!
@shivakumarnarayanan1165
4 жыл бұрын
4:05 how do i find the coeff of x^20
@shivakumarnarayanan1165
4 жыл бұрын
Wdym by sequence of x^n
@yashuppot3214
4 жыл бұрын
But wouldnt you have to multiply the brakcets out before taking derivaitives
@dhruvabhat3261
6 жыл бұрын
Thank you soo much..
@lindadada-dadadal9864
6 жыл бұрын
thank you so much for your videos! Got a combinatorics puzzle. Could you please help me with it? Choose 6 numbers from 1 to 49 so that exactly two of them are consecutive. How many combinations?
@intom1639
8 жыл бұрын
It really helps a lot!!! Thanks!
@jasonmiller8407
7 жыл бұрын
For the final problem, why isnt the x_1 term (1-x^11)/(1-x)? Isnt it the sum of values from 1 to x^12 by the problem statement?
@siraa8438
6 жыл бұрын
So helpful
@snake1625b
6 жыл бұрын
Is the way you are using the exponent syntax different from the traditional definition of repeated multiplication?
@sagnik5511
3 жыл бұрын
@TheTrevTutor...at 9:47 shouldn't the first series have the formula (1-x^n)/(1-x) instead of (1-x^n+1)/(1-x) ....maybe theres a calculation error coz I rechecked using the G.P. summation formula
@zaoyun19920621
7 жыл бұрын
thank you very much for your help
@DrQlimakz
8 жыл бұрын
I really don't like discrete maths :D
@Trevtutor
8 жыл бұрын
+Qlimakz That's okay. It's an infinitely smaller subset of continuous math, so you're not hurting its feelings too much.
@ujjwalpawar5920
6 жыл бұрын
That why they call it "Dry Subject".Fucks with your logical part of your brain.
@ilyasabdullah5965
4 жыл бұрын
Yeah man...i wish it just dissapears...
@kapilkumarsharma4401
4 жыл бұрын
It's my favourite subject
@deuteriumtritium9700
4 жыл бұрын
@@kapilkumarsharma4401 Same
@jslee417
6 жыл бұрын
It is interesting function. I think the x range should have range. 1/(1-x) forms you explained in the long division but when we divide 1 by 1-x the remnant x must be smaller than 1-x therefore, the x range should fall x
@markzenith1441
3 жыл бұрын
What if I wanted to generate polynomials? For example find the partition of a polynomial in the form of a pair of polynomials?
@VishalSharma-hq5ti
5 жыл бұрын
what will be X^12 at 2:30?
@azra8366
4 жыл бұрын
Why for picking even ones we consider X^0 wich is 1 also as an even number? If we have an empthy set or something that is zero we consider it even?
@aviksarkar707
6 жыл бұрын
In the jellybeans example ,isn't the generating function (1+x^2+x^4+x^6)(x^14+x^15+x^16+x^17+x^18+x^19+x^20)(1+x+x^2+x^3+x^4),since we have at least 14 blue jellys ?
@joaopedrosa2246
5 жыл бұрын
you don't need to stop at x^6 in this first term because any number above 6 will never be chosen since we will need to add it to at least 14 in the second term
@VisheshBajpai1vish
7 жыл бұрын
you are simply awsome man !!!!
@AmitTiwariSixRealString
5 жыл бұрын
why do we need the coefficient of x^12, Im not getting this part, explain plzzzz
@jonathannissim2774
5 жыл бұрын
Thank great explanation
@jablkomieta01
8 ай бұрын
THANK YOU!!!!!!!!!!!
@emanu9677
6 жыл бұрын
How about exponential generating functions?
@rhaq426
2 жыл бұрын
How can you use generating functions to find permutations?
@vishalreddy3531
8 жыл бұрын
dude Ur awesome...thanks for the help
@safeamiiir
7 жыл бұрын
thank You I really Enjoy That man :))))
@lydiahchepkemoi9464
3 жыл бұрын
Me too
@orochicken
7 жыл бұрын
Thank you so much!
@juanmarin6557
4 жыл бұрын
How is that (1-x) goes 1 time into 1, x times into x and x² times into x², I'm not getting the meaning of any of these yet you say it like it's super obvious
@zihongbowang7518
4 жыл бұрын
He's just matching the power of the (1) in (1-x) with the highest power of the polynomial. When the number is 1, you subtract a 1-x from 1 to get x. Then you subtract x(1-x) from x to get x^2. You continue this to reach the infinite series 1+x+x^2+x^3.... The principle is similar to long division, which is why it is called polynomial long division.
@juanmarin6557
4 жыл бұрын
Peter i was taking calc 2 when i asked the question a few months ago. I get it now, thanks
@NaraAIApp
7 жыл бұрын
I watching this vid two times ...then i realize ...its super easy 😂😂 ..my lecturer cant explain this like you do..😅
@paulmadeya5396
8 жыл бұрын
Why did you change the x^2 to to x^5 in the last example?
@Trevtutor
8 жыл бұрын
multiplied x^2 and x^3 together.
@ElifArslan-l9g
3 жыл бұрын
thank you
@entertainmentsmtv
5 жыл бұрын
Thanks a lot
@catalingoga6002
3 жыл бұрын
Hello, what software do you use for writing with the graphical tablet?
@harshitsharma4097
5 жыл бұрын
sir at 14:05 it will be 0,0,0,0,1,1,1,1....
@nadeemjq
5 жыл бұрын
Is there a intro video to this that I missed? None of this makes sense....
@razeer1232
4 жыл бұрын
It starts making sense after you watch the whole video.
@SANJANASINGH-gp3wh
7 жыл бұрын
This is super goood 😀😀
@hyleenpognaire8134
2 жыл бұрын
Hey sir, what software u used to write this?
@byrantoby9786
6 жыл бұрын
shouldn't the first part of the last question be (x^2 * (1-x^13)/(1-x)) instead?
@Arnius_Music
Жыл бұрын
15:40 would you please explain to me why does this go to infinity?? and not to x¹²?? i couldnt understand the exolanation of the video
@mulkarithvik6151
4 жыл бұрын
What is the use of 12 in the second line
@tusharpatil9774
5 жыл бұрын
17:54 how to solve it further. I have watched complete series of generating functions mentioned on your channel. Is it the case of partial fraction decomposition and solve for each a0/(1-ax)^n ? Please reply m stuck.
@slingshot7602
Жыл бұрын
At 6:02 you didn't show how to get the coefficients of x^n
@real-investment-banker
3 жыл бұрын
These are nothing but G.P. . Sum of infinte G.P = a/1-r, but for that we've to assume that |x| < 1. Can we do that , is it the legit way to do ? As x is a variable of no significance , can we assume its value and solve the G.P. ?
@Arnius_Music
Жыл бұрын
4:17 how can we have more than x^6 for red if we have at least 14 blue jellybeans?? wouldnt that make it more than 20?
@satishnetane5189
9 жыл бұрын
Thanks buddy
@pantelisvasileiadis2858
2 жыл бұрын
2:25 you're right about my exes mister
@tarsala1995
8 жыл бұрын
I don't like it, I love it, love it, love it, uh oh So good I found it!
@ActuatedGear
Жыл бұрын
I have no idea what's going on here. I can do the trick... but I don't get it. I'm gonna watch this again. I just don't understand combinatorics and number systems like this.
@mauropappaterra
9 жыл бұрын
what software do you use for your videos?
@Trevtutor
9 жыл бұрын
yogurt1989 Windows Journal to write, and either OBS or Camtasia to record the screen region.
@erkins8818
7 жыл бұрын
rolling a die 5 times how many ways we get sum of 18
@sparkindness
3 жыл бұрын
(1+x²+x⁴+....)⁷ we have got X^n coefficent please tell me sir
@paulmuaddib3761
Жыл бұрын
3:49 almost 🇫🇷
@rameshsaday34
2 жыл бұрын
Sir ek video our banakar KZitem par dal dijeye please sir chepter -logic and proof
@Mark-nm9sm
3 жыл бұрын
You just turned confusing things , into even more confusing things
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