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Snarky Math
Гонконг
Добавлен 31 янв 2020
Welcome to my channel. I am a math undergrad doing math undergrad things, and I love recreational math. On this channel, I would like to post some of the topics, problems and proofs that I enjoyed, especially those which are not well-known on RUclips. Hopefully, you will enjoy them like I did. Cheers! :)
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...
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...
the captions are so silly
Damn Ven diagrams are supposed to be the easy ones
head hurts :D
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
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, ...
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
Soo 7 is the AuBuCuD off all?
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
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?
It's weird to abbreviate "vertices" as "vtx", given there is no "x". Is it a common abbreviation or is it your own?
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?
This is what Kamala Harris studies in her free time
How dare you make me learn!
Just after rewatch, I cannot fully exress how much I lika and appreciate this video.
This is so cool, never knew venn diagrams could be so complex.
Nice, it helped me quite a lot
Jut ∆ super Because
Git T..S. Screen
I've finally found a use for this And… I couldn't remember how it was done :( I needed to watch the video again
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.
This was absolutely fantastic! I can't wait to see more of your content!
The thumbnail can be more clickbaity :) Appreciate the 1-hour video effort. Impressive!
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!
Are generating functions a new idea? I watch a lot of math, and I don't remember seeing this until recently.
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.
@@SnarkyMath That makes sense. They just became popular recently. Good luck in the contest.
Ehrhart polynomials are so cool!
Ikr! Here, take a hart.
Can I ask the shorcut formula how to solve 5 or more circles venn diagram😇😇Plsss help Thank you😇!
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
Yeeeeeeeeeeeeeeees!
Yeeeeeeeeeeeeeeeeee
Yeeeeeeeeeeeeeeeeeeeet
I really appreciate the details being worked in time-lapse. It's a good touch.
Only 15 min in and this is extremely cool, thank you for making this video!!!
Woah I _just_ learned about this (and by "just" I mean "a few weeks ago")! That timing is crazy!
Hoo boy, I'll have an extremely enjoyable hour today :)
is the chord at the start out of the omori title theme just a coincidence?
after watching this further, yes it is so this question was unnecessary
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
yeeeeeeeeeeeeeeeeeeeeeeee
yeeeeeeeeeeeeeeeeeeeeeeee
Love from Morningside College 😘😘😍😍🥰🥰
1:36 dude really tried to sneak in durian 😳😳😳
so true
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.
4 set Ven Diagram: three circles, Two of them overlapping and the third not overlapping with the others.
What is the source for the diagram "How Venn did it"? @13:54
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! ^^
d- durian? huh?
tfw ovals
The PTSD experienced by anyone who's played KTANE at 4:35
I ,honestly, love what you are doing with this channel! Keep up the great work!!!
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 😂
How about a 4-set diagram but in 3 dimensions?
You could do it with a square vendiagram