Snarky Math
Snarky Math
  • Видео 3
  • Просмотров 675 206
Counting Integer Points in Polygons with Negative Numbers | A 'moral' Intro to Generating Functions
Turn on the subtitles for the BEST experience. :)
0:00 - Introduction
5:17 - Section 1: The What and Why of Generating Functions
15:18 - Section 2: Finding GFs for Lattice Counting Functions
34:11 - Section 3: Substituting Negative Numbers
47:46 - Section 4: The Finale
58:09 - Conclusion
I tried my best to motivate generating functions and give an insight to why the generating functions work the way they should. Why they are intimately connected to the structure of the objects we are counting and their relation with linear homogenous recurrence relations is explained. The ideas are illustrated along the lines of the proof of the Ehrhart polynomials and Ehrhart Macdonald reciprocity which is abou...
Просмотров: 1 464

Видео

Can you draw a Venn diagram for 4 sets? | Why Venn diagrams are not easy
Просмотров 613 тыс.3 года назад
You can turn subtitles on :), I am sorry about the low audio quality, for I don’t have a mic at the moment :(. Timestamps 00:00 - Problems with 4 sets 01:55 - Solution 05:12 - Why circles are bad 10:35 - You can’t stick to one curve 13:35 - How Venn did it Music used: Esther’s Waltz - Esther Abrami (from RUclips audio library) The pictures I used are from Wikipedia, survey of Venn diagrams, Pet...
This random graph fact will blow your mind | Rado graph and its godlike properties
Просмотров 61 тыс.3 года назад
You can turn subtitles on if you wish to! :) Timestamps: 00:00 - Section 0: A random surprise 02:21 - Section 1: An "innocent" graph 05:27 - Section 2: Something fishy 08:57 - Section 3: Everything comes together 14:58 - Reflection and goodbye MUSIC used OMORI title theme: ruclips.net/video/9d9e6XmNn9Q/видео.html Something that I went "woah" when I first encountered the theorem statement. Count...

Комментарии

  • @endnes.m
    @endnes.m 6 дней назад

    the captions are so silly

  • @Elan_Altair
    @Elan_Altair 8 дней назад

    Damn Ven diagrams are supposed to be the easy ones

  • @teosandev6116
    @teosandev6116 5 месяцев назад

    head hurts :D

  • @zhiychen1626
    @zhiychen1626 11 месяцев назад

    I saw this problem in the book Concrete Mathematics problem 1.5( the author put it in "warmup" section😅) . The explanation given in that book is too short and I couldn't figure that out until I saw your video. Thank you anyways

  • @r.a.6459
    @r.a.6459 Год назад

    The circle regions sequence: 2, 4, 8, 14, 22, 32, ... is a series, which can be made by adding even numbers to the sum: +2, +4, +6, +8, ...

  • @Smallpriest
    @Smallpriest Год назад

    Honestly, after watching the whole thing, I wonder why we don't just represent it in Binary form, 1 if it's in the set, 0 if it's outside the set. It's so much easier for big venn diagrams

  • @LiamOng-g1n
    @LiamOng-g1n Год назад

    Soo 7 is the AuBuCuD off all?

  • @peepee4080
    @peepee4080 Год назад

    i watched this video about the time that it came out and i was a junior in high school. Now i’m majoring in math in college. I don’t know where or who i would be if this video didn’t exist

  • @cheshire1
    @cheshire1 Год назад

    how do we know the number of terms in the summation at 14:06 doesn't grow faster with k than p^k shrinks with k?

  • @b.clarenc9517
    @b.clarenc9517 Год назад

    It's weird to abbreviate "vertices" as "vtx", given there is no "x". Is it a common abbreviation or is it your own?

  • @nils8950UTAUACC
    @nils8950UTAUACC Год назад

    when talking about the probability of a graph being isomorphic to some other graph, which probability space and which measure are we actually working with?

  • @RealShimSham
    @RealShimSham Год назад

    This is what Kamala Harris studies in her free time

  • @VilliageSquidiot
    @VilliageSquidiot Год назад

    How dare you make me learn!

  • @pawebielinski4903
    @pawebielinski4903 Год назад

    Just after rewatch, I cannot fully exress how much I lika and appreciate this video.

  • @georgebeckons539
    @georgebeckons539 2 года назад

    This is so cool, never knew venn diagrams could be so complex.

  • @AndyRoidEU
    @AndyRoidEU 2 года назад

    Nice, it helped me quite a lot

  • @ziba2660
    @ziba2660 2 года назад

    Jut ∆ super Because

  • @ziba2660
    @ziba2660 2 года назад

    Git T..S. Screen

  • @HelPfeffer
    @HelPfeffer 2 года назад

    I've finally found a use for this And… I couldn't remember how it was done :( I needed to watch the video again

  • @kohwenxu
    @kohwenxu 2 года назад

    For those who might think the function f(n) at 14:09 is weird, that is the Fibonacci numbers in an explicit formula. The n in the formula must be an integer to see the Fibonacci numbers.

  • @lexinwonderland5741
    @lexinwonderland5741 2 года назад

    This was absolutely fantastic! I can't wait to see more of your content!

  • @horacehung8373
    @horacehung8373 2 года назад

    The thumbnail can be more clickbaity :) Appreciate the 1-hour video effort. Impressive!

  • @rafiihsanalfathin9479
    @rafiihsanalfathin9479 2 года назад

    Cute animation and overall enjoyable video! Even thought im not really familiar with this kind of mathematics but i can follow it pretty well. Nice submission!

  • @PhilipSmolen
    @PhilipSmolen 2 года назад

    Are generating functions a new idea? I watch a lot of math, and I don't remember seeing this until recently.

    • @SnarkyMath
      @SnarkyMath 2 года назад

      No. If I'm not wrong, they were used since 1700s as a general problem solving technique applicable to many fields like number theory and probability theory. As for RUclips math, I haven't seen them a lot either. But Mathologer had made a video about them and they also made appearance in a recent 3Blue1Brown video.

    • @PhilipSmolen
      @PhilipSmolen 2 года назад

      @@SnarkyMath That makes sense. They just became popular recently. Good luck in the contest.

  • @johnchessant3012
    @johnchessant3012 2 года назад

    Ehrhart polynomials are so cool!

    • @SnarkyMath
      @SnarkyMath 2 года назад

      Ikr! Here, take a hart.

  • @archieeliot29
    @archieeliot29 2 года назад

    Can I ask the shorcut formula how to solve 5 or more circles venn diagram😇😇Plsss help Thank you😇!

  • @columbus8myhw
    @columbus8myhw 2 года назад

    30:30 Why a _quadratic_ of z? Wouldn't it be a cubic? EDIT: Oh, right, you don't count the top vertex of the parallelopiped

  • @umotoyu6435
    @umotoyu6435 2 года назад

    Yeeeeeeeeeeeeeeees!

  • @ArtArtisian
    @ArtArtisian 2 года назад

    I really appreciate the details being worked in time-lapse. It's a good touch.

  • @azimuth4850
    @azimuth4850 2 года назад

    Only 15 min in and this is extremely cool, thank you for making this video!!!

  • @columbus8myhw
    @columbus8myhw 2 года назад

    Woah I _just_ learned about this (and by "just" I mean "a few weeks ago")! That timing is crazy!

  • @helloiamenergyman
    @helloiamenergyman 2 года назад

    Hoo boy, I'll have an extremely enjoyable hour today :)

  • @il9375
    @il9375 2 года назад

    is the chord at the start out of the omori title theme just a coincidence?

    • @il9375
      @il9375 2 года назад

      after watching this further, yes it is so this question was unnecessary

  • @alexsere3061
    @alexsere3061 2 года назад

    I feel like the only potential issue with this video is stuff with infinity. You showed us procedures that work for finite amounts of points and then basically went "so it works for the limit", which I dont think its necesariliy true, but its an educational video so maybe its supposed to skip those pesky details

  • @umotoyu6435
    @umotoyu6435 2 года назад

    yeeeeeeeeeeeeeeeeeeeeeeee

  • @umotoyu6435
    @umotoyu6435 2 года назад

    yeeeeeeeeeeeeeeeeeeeeeeee

  • @kyawshinthant4237
    @kyawshinthant4237 2 года назад

    Love from Morningside College 😘😘😍😍🥰🥰

  • @sparklerabbit33
    @sparklerabbit33 2 года назад

    1:36 dude really tried to sneak in durian 😳😳😳

  • @RedStinger_0
    @RedStinger_0 3 года назад

    so true

  • @TheSabian321
    @TheSabian321 3 года назад

    First time I considered it I thought it was impossible to make a, diagram with 4 circles, but I just can't prove it. I was so stupid I never thought about counting regions lol.

  • @jeffking
    @jeffking 3 года назад

    4 set Ven Diagram: three circles, Two of them overlapping and the third not overlapping with the others.

  • @ct2034
    @ct2034 3 года назад

    What is the source for the diagram "How Venn did it"? @13:54

  • @fleursetvelo2561
    @fleursetvelo2561 3 года назад

    Well, right now im drunk but first time for me to use some feature of yt (back, repeat, subtitle(also english isn't my native)) to help me understand a concept, thank you for the hindsight and get that subs! ^^

  • @JonahWho
    @JonahWho 3 года назад

    d- durian? huh?

  • @WaddlingWaffle
    @WaddlingWaffle 3 года назад

    tfw ovals

  • @starburst7681
    @starburst7681 3 года назад

    The PTSD experienced by anyone who's played KTANE at 4:35

  • @rockydavis8705
    @rockydavis8705 3 года назад

    I ,honestly, love what you are doing with this channel! Keep up the great work!!!

  • @dovebair
    @dovebair 3 года назад

    I got a real kick out of the way that you showed us the most elegant solutions that are currently known, and then went back and called Venn's original solution a cheat haha 😂

  • @Franlu95
    @Franlu95 3 года назад

    How about a 4-set diagram but in 3 dimensions?

  • @hannahbobanana
    @hannahbobanana 3 года назад

    You could do it with a square vendiagram