I just gave a talk at the Canadian Math Society meeting in Toronto that I recorded and am planning to post. I recorded both my screen and me (like: me the human, waving hands, pointing at things etc). Which option is the best for format to post? Leave a comment if you have any other ideas!
A random walk on a k sided polygon takes on average E[T]=k steps to return to where it started. But how does the variance depend on the number of sides? Explanations of these facts in my latest video https://youtu.be/nXBZR1ARPZU
If you liked my video on Reinforcement Learning for Triangle Creatures using GRPO, you might like this video by Jia-Bin Huang. It covers a ton of other details that I didn't cover in my video on how the DeepSeek actually works. Great video Jia-Bin!
A spider goes for a random walk on a k-sided polygon. How many steps on average until he gets back to his house for the first time? ICYMI: The probabilities for a k=5 pentagon were the subject of my previous video https://youtu.be/g8aA76pNBkg.
Solution to this problem will be in my next video!
On the latest Triangle Creatures video someone commented saying it'd look cool if there was a bunch of them crawling on a manifold, so I ran this over the weekend: its a bunch of them crawling on a torus! They remind me of a school of jellyfish. ( If you haven't seen how they are trained yet using the DeepSeek GRPO algorithm, check out the original video at https://youtu.be/wXEvvg4YJ9I )
Thanks to everyone who voted in my video topics poll from a few days ago! By popular demand, I started working on a video explaining what Brownian motion is. To test out the animations, I made a little teaser video of infinetly zooming into Brownian motion. Stay tuned for the full video coming soon^{tm}!
Some people have been asking me for more "Probability Ninja" proofs (like my last video about the maximum of dice). One thing ninja proofs have in common is thinking about relationships between **random variables**. A classic one is the no-calculus-only-ninja-tricks proof of how Pi appears when throwing straight spaghetti on a square grid by looking at the relationship between straight and curvy noodles! I made a video about this for 3 Blue 1 Brown's Summer of Math Exposition #1 back in 2021 (I was a runner up in the contest!)
If you roll a 20-sided dice 2 times and take the maximum value (aka "rolling with advantage" in Dungeons & Dragons), a good approximation for the average is to take 2/3 of the maximum possible roll and add 0.5: i.e. Average Maximum ~= 2/3 * 20 + 0.5 = 13.8333.... . But why is this estimate true? And is it an underestimate or an overestimate for the true average value?
Prof Mihai Nica
Prof Mihai Nica
I just gave a talk at the Canadian Math Society meeting in Toronto that I recorded and am planning to post. I recorded both my screen and me (like: me the human, waving hands, pointing at things etc). Which option is the best for format to post? Leave a comment if you have any other ideas!
3 weeks ago | [YT] | 4
View 1 reply
Prof Mihai Nica
Finishing up my latest video for SoME4. Which title would you be most likely to click on? Leave a comment if you have any other suggestions!
4 months ago | [YT] | 5
View 6 replies
Prof Mihai Nica
A random walk on a k sided polygon takes on average E[T]=k steps to return to where it started. But how does the variance depend on the number of sides? Explanations of these facts in my latest video https://youtu.be/nXBZR1ARPZU
6 months ago | [YT] | 11
View 0 replies
Prof Mihai Nica
If you liked my video on Reinforcement Learning for Triangle Creatures using GRPO, you might like this video by Jia-Bin Huang. It covers a ton of other details that I didn't cover in my video on how the DeepSeek actually works. Great video Jia-Bin!
7 months ago | [YT] | 14
View 1 reply
Prof Mihai Nica
A spider goes for a random walk on a k-sided polygon. How many steps on average until he gets back to his house for the first time? ICYMI: The probabilities for a k=5 pentagon were the subject of my previous video https://youtu.be/g8aA76pNBkg.
Solution to this problem will be in my next video!
7 months ago | [YT] | 9
View 6 replies
Prof Mihai Nica
On the latest Triangle Creatures video someone commented saying it'd look cool if there was a bunch of them crawling on a manifold, so I ran this over the weekend: its a bunch of them crawling on a torus! They remind me of a school of jellyfish. ( If you haven't seen how they are trained yet using the DeepSeek GRPO algorithm, check out the original video at https://youtu.be/wXEvvg4YJ9I )
10 months ago | [YT] | 0
View 0 replies
Prof Mihai Nica
Thanks to everyone who voted in my video topics poll from a few days ago! By popular demand, I started working on a video explaining what Brownian motion is. To test out the animations, I made a little teaser video of infinetly zooming into Brownian motion. Stay tuned for the full video coming soon^{tm}!
11 months ago | [YT] | 5
View 0 replies
Prof Mihai Nica
Which video should I make next? Feel free to comment if you have another probability themed video idea you think I should do!
11 months ago | [YT] | 9
View 6 replies
Prof Mihai Nica
Some people have been asking me for more "Probability Ninja" proofs (like my last video about the maximum of dice). One thing ninja proofs have in common is thinking about relationships between **random variables**. A classic one is the no-calculus-only-ninja-tricks proof of how Pi appears when throwing straight spaghetti on a square grid by looking at the relationship between straight and curvy noodles! I made a video about this for 3 Blue 1 Brown's Summer of Math Exposition #1 back in 2021 (I was a runner up in the contest!)
11 months ago | [YT] | 10
View 0 replies
Prof Mihai Nica
If you roll a 20-sided dice 2 times and take the maximum value (aka "rolling with advantage" in Dungeons & Dragons), a good approximation for the average is to take 2/3 of the maximum possible roll and add 0.5: i.e. Average Maximum ~= 2/3 * 20 + 0.5 = 13.8333.... . But why is this estimate true? And is it an underestimate or an overestimate for the true average value?
1 year ago | [YT] | 23
View 1 reply
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