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Hunter Rehm
United States
เข้าร่วมเมื่อ 1 มี.ค. 2020
This channel will be used to discuss various topics in mathematics. For more information about me (Hunter Rehm), check out my website at www.uvm.edu/~hrehm/ and email me if you have any questions!
วีดีโอ
Planar Graphs
มุมมอง 9122 ปีที่แล้ว
SUBSCRIBE if you enjoyed this! What is a planar graph? Thank you to John Ramsdell for the video idea and to @MeanSquaredError for the music.
The 4th Dimension
มุมมอง 7103 ปีที่แล้ว
SUBSCRIBE if you enjoyed this! This video is intended to give you some intuition as to how to think of the 4th dimension. The animation software was provided by @3Blue1Brown and the music was provided by Marcus Elia. Thank you!
Breadth First Search
มุมมอง 3303 ปีที่แล้ว
SUBSCRIBE if you enjoyed this! Here is the link for the example python code: github.com/Hunter-Rehm/Breadth-First-Search/blob/main/BFS.py Thank you to @3Blue1Brown for providing the animation software and Marcus Elia for providing the music!
Coin Flipping Paradox
มุมมอง 4143 ปีที่แล้ว
SUBSCRIBE if you enjoyed this! Is there a difference between the average number of heads in each trail and the total percentage of heads? Indeed. Thank you to @3Blue1Brown for the animation software, enjoy!
Incidence Matrix
มุมมอง 3.6K3 ปีที่แล้ว
SUBSCRIBE if you enjoyed this! Thank you to @3Blue1Brown for providing the mathematical animation software (Manim) to make this video. In this video, we discuss the incidence matrix of a graph and how to construct it. Enjoy! (:
Adjacency Matrix
มุมมอง 9643 ปีที่แล้ว
SUBSCRIBE if you enjoyed this! Thank you to @3Blue1Brown for providing the mathematical animation software (Manim) to make this video. In this video, we discuss how to input a graph into a computer by constructing the adjacency matrix. Enjoy!
What is Graph Theory?
มุมมอง 4.5K3 ปีที่แล้ว
SUBSCRIBE if you enjoyed this! Thank you to @3Blue1Brown for providing the mathematical animation software (Manim) to make this video. Before you enter your graph theory class, watch this video! We will discuss what a graph is and describe a situation for which they are useful.
Ramsey Theory Introduction
มุมมอง 38K3 ปีที่แล้ว
en.wikipedia.org/wiki/Ramsey's_theorem Avoiding triangles is not as easy as it may seem. SUBSCRIBE if you enjoy this video!
Section 5.5 Lecture Math 019 Spring 2020
มุมมอง 484 ปีที่แล้ว
We discuss the Fundamental Theorem of Calculus. Enjoy!
Generatingfunctionology S1.5 - Binomial Coefficients
มุมมอง 2544 ปีที่แล้ว
In this video we discuss how to find the formula for the binomial coefficients.
Generatingfunctionology S2.3 (Example)
มุมมอง 1354 ปีที่แล้ว
in this video we discuss and example that uses ordinary generating functions and exponential generating functions!
Generatingfunctionology S2.2 - The calculus of formal ordinary power series
มุมมอง 1434 ปีที่แล้ว
Generatingfunctionology S2.2 - The calculus of formal ordinary power series
Generatingfunctionology S2.1 - Formal Power Series
มุมมอง 9884 ปีที่แล้ว
Generatingfunctionology S2.1 - Formal Power Series
Generatingfunctionology S1.6 - Another two variable case
มุมมอง 1184 ปีที่แล้ว
Generatingfunctionology S1.6 - Another two variable case
Generatingfunctionology S1.1-An easy two term recurrence
มุมมอง 3604 ปีที่แล้ว
Generatingfunctionology S1.1-An easy two term recurrence
One of my olympiad competition requires this technique to solve the problem, thanks for that, love your content mayn, Jesus bless
already exactly what i need - thank u
Highest quality content
Great video
Banger video man I love math
Very direct and informative; I appreciate the upload!
Thank u sir love and support from Pakistan ❤
Such a great video
Glad you think so!
Appreciate the video sir, it’s perfect
My pleasure!
If I claim R(5,5) = 72 what can be used to prove it wrong?
beautiful video! just started learning this ,Thank you!
Thank you! I’ll be coming out with a new video soon I hope
i love the animations. i really like to see animation tutorials too :)
Thank you! Do you make videos too?
Thanks Hunter. Good video
You bet! Let me know if there is a topic you are interested in seeing. I can try to make something on it.
Great video
Thank you so much! Let me know if there is another topic that interests you!
I love how clear is the sound and calm + i understood it in just 2 min thank you ❤
Love to hear it! Anything else you would like to see?
Helpful!
Glad you think so!
Mathematician Paul Erdős once said that if aliens landed on Earth and demanded a precise Ramsey number for 5 or they'd destroy the planet, humanity should divert all of its computing resources to figure out the answer. But if they demanded the Ramsey number for 6, humans should prepare for war.
What a great quote! This is a great field of research. I haven't studied Ramsey numbers in particular, but I have looked in to Anti-van der Waerden numbers and Schur numbers!
@@hunterrehm6165 i don't understand how they don't know the ramsey numbers for 6, can't you just brute force the solution with programming? I mean, with enough computing power, you can surely make an algorithm to check every possiblity for each number.
Honey, you’d best get ready to hit the bad lands for that one.
wow, super underated. subscribing time!
Welcome aboard! I just finished my PhD, so I will be making video more now. What would you like to see? More videos like this one?
The central cube looks like an expanded version of a dot placed in a standard cube (the outer cube), so maybe it's like a space in a space really? Or...
Hmm interesting point. It is worth trying to see if that continues in the next iteration of the hypercube!
@@hunterrehm6165 Thank you! However, I am getting to think, that maybe the only way to represent the 4D is to reduce the angles between the axis. That'd definitely look weird and non-Euclidean, but everything is going to look simpler for our 3D perception of reality. I hope...
Great! Thanks a lot
Glad you liked it!
Is there another video you would like to see?
It truly is a great paradox
I think so too! Have you thought about this before?
Thank you! Now I understand!
Glad I was able to help! =D
thanks!!
Glad you enjoyed it! Let me know if there are any other topics you would like to see!
riveting 🧐
It doesn't get much better than this!
Great job with these videos... so quick and powerful to get an answer !
Thanks! I really liked making this video, the tesseract is saweeet.
awesome video!!
Glad to hear you enjoyed it! Are you interested in graph theory like me?
it seems very interesting! I don't know much about it just happened to come across your channel because we used it in analysis as part of a proof of Bolzano weierstrauss
@@maxdemuynck9850 Wow that is interesting. It has been a bit since I have seen Bolzano-Weierstrass, but I am surprised to here Ramsey theory was in the proof. Would love to hear more!
The reason total heads/total tails = 50% while avg of the runs =58% is that the runs are different sizes. If you use a weighted avg, it is 50%. There are 16 individual flips, run 1 = 2/4 heads and comprises 4/16 of the data. Multiply 2/4 * 4/16 = 0.125. Do this for all of the runs and add them up for a wtavg of 0.5 heads!
This is true! Great explanation. Are you a math enthusiast like me?
@@hunterrehm6165 Definitely! I don't know anyone else who watches this kind of interesting stuff on youtube xD.
Thanks for the simplest presentation.:)
Oh its my pleasure. Are you interested in graph theory?
@@hunterrehm6165 I've taught graph theory on my youtube channel already 😊
@@pcmtutorials Awesome! I just checked it out! Love it!
I feel like talking through the construction a bit more would be enlightening. Closeness = distance, sure! So we examine the distances from our central vertex to every other vertex in the graph. Then, we need a way to collect this data into a single statistic. Summing seems like a natural option as it allows each value to contribute its weight to the final answer. But wait! If we sum, then the vertices that are FARTHER from others will have a higher centrality measure! We want to invert this - allowing vertices that are CLOSER to have higher centrality measures. So, we take 1/sum to order it as we wish. A natural question might be "Why don't we invert the distances and then sum them?". This is a case where order of operations matters quite a bit to interpretation! If we invert first, then we are saying that we want the larger distances to contribute less to the final statistic than the smaller distances. So, our final sum will now represent the contribution of these inverted distances. If this seems interesting to you, take a look at this follow on: If we use Sum(1/d(u,v)) rather than 1/Sum(d(u,v)), does the order change? If so, what causes the differences in orders?
This is really great comment! I have not thought about sum(1/d(u,v)), very interesting. Let me do a little analysis and see what I find!
Harmonic Centrality !
very interesting topic with many diverse applications! I learnt about this in further maths (decision module) this was a good recap :) keep it up
Thank you! Glad you enjoyed it!
this is amazing
Thanks Fatima Zahra!
My boy is wicked smart
Thanks man. I appreciate you watching!
You spelled "cats" wrong
5:50 You forgot to put the link :(
I just added the link in the description! It's just the wiki page, but it does a good job summarizing the known values.
Where is the link below?
My bad. I just added the link to the wiki page in the description. There is a table there which summarizes the known values!
this explanation is simpler than the one i read on the book. thanks dude
Love to hear it!
Please use the regular way to show your text.thx
I will do this for future videos probably!
Beautiful animations and soothing voice - thank you!
Thanks @Arno Claude!
This reminds me of arguing with my teacher, who escalated the argument to the principal of my 2nd grade (elementary school) of the fact that a sphere has one side. It took a long time to convince me and I don't remember my argument. Now I know the world is flat. No, no just kidding.
Haha that hilarious, I don’t often think about how many sides 3D objects have 🤔
Well, I um. I'll try watching again without drink in my brain.
Haha let me know if you have any questions! Happy to help.
I don't understand how the pidgeon hole principle helps us with the coloring at 3:40
@hisocar I think of the colors as the bins and the edges as the pigeons. This way, by the (generalized) pigeonhole principle, three of the edges must be colored the same. Does that make sense?
The idea is that nobody forces you to pick 3 red and 2 blue, you can try doing 5 red 0 blue, but no matter what, there always will be at least 3 people connecting to first person, that have same color, lets call them A B and C. This allows constructing the white triangle, at which point we are helpless, no matter what you color the triangle, you either create same color edge between first person and 2 from ABC, or if you try to avoid this situation by not giving same color at all... the white triangle becomes what you wanted to avoid, it has only one color!
A bit late, but if you're still having trouble, I think I got what Rehm meant. So for 1 person knowing or not knowing 5 others, from their POV, they can only have any one of the following possible mutually exclusive options: 1. Know all 5 2. Know 4, and not know 1 3. Know 3, and not know 2 4. Know 2, and not know 3 5. Know 1, and not know 4 6. Not know all 5 At 3:19, Rehm claims that using Pigeonhole principle, that person knows at least 3 people or not know at least 3 people. You can go through all 6 options listed above and see that, in every case, Rehm's claim is true. I'm not fully sure how the Pigeonhole principle is used here, but the ultimate claim is correct.
Use extended form of Pigeonhole principle i.e. [(n-1)/m] +1...... n=5 and m=2 .. Therefore, [(5-1)/2] +1= 3
Very simple and clear explanation, thanks!
Glad you said something! It means a lot!
excellent clear explanation
I’m glad you thought so!
Why can't everyone not know eachother though? Ie, all blue?
The theorem states that with 6 people in a room, either 3 people know each other, or 3 people do not. So if 3 people do not know each other, then the theorem is satisfied and we should consider the next case. That proof really just shows that there will necessarily be a monochromatic K_3 in every 2-edge-coloring of a K_6.
This was so good and helpful, thankyou 😄
Love to hear it! I am currently getting my PhD so video production is slow, but I hope you subscribed!
Great video!! Nice to see people using the manim engine.
Thanks! Yeah it’s nice and easy to make some really great animations. Have you tried it?
@@hunterrehm6165 Not really. But its nice to see the community making good of it.
Mind blown
🤯
animations make videos whole lot cooler
I agree!
Awesome
Thank you!
very helpfull
Thank you! Stay tuned for more videos!