Mihai Nica

Intro to Markov Chains and Reinforcement Learning W25 - YouTube

I taught a course for 4th year undergrads last term on RL, you can see the lecture recordings here (use the YouTube AI summary to get the topics easily!) youtube.com/playlist?lis... and GitHub here (probably more useful!) github.com/mcnica89/Mar...

Surprisingly accurate Google AI summary for those that want to know what it's about!

A Gaussian integral formula for the Hermite polynomials: Combinatorics, Asymptotics and Applications The Hermite polynomials are ubiquitous but can be difficult to work with due to their unwieldy definition in terms of derivatives. To remedy this, we showcase an underappreciated Gaussian integral for...

And here's the link to the arXiv paper arxiv.org/abs/2508.13910

The Hermite Polynomials & Probability | Lecture at Canadian Math Society 2025 YouTube video by Prof Mihai Nica

Recording of my talk on the Hermite Polynomials in Probability Theory at the Canadian Math Society meeting in Toronto this weekend. youtu.be/pD-lU_pj3zs?...

The *BEST* "Guess Who?" strategy (Beyond binary search) YouTube video by Dr Mihai Nica

My new video on how I found and proved the optimal strategy in the kids game "Guess Who?" youtu.be/_3RNB8eOSx0 . Turns out that viral Mark Rober video was not exactly correct....

Catapults in SGD: spikes in the training loss and their impact on generalization through feature learning In this paper, we first present an explanation regarding the common occurrence of spikes in the training loss when neural networks are trained with stochastic gradient descent (SGD). We provide eviden...

arxiv.org/abs/2306.04815

I agree it's not hard and could be taught. However I do think it's hard to motivate at that level: like you could easily teach HOW to multiply two matrices but motivating WHY it works the way it works and not some other way is trickier. So overall I think it makes sense to wait for the motivation!

I vote small at first glance! Looks intriguing :)

I like the ones about computer vision! (I don't know what I don't know so can't be more specific)

The Math of Rolling with Advantage; What is the average maximum of several dice rolls? - Mihai Nica's Notes - Obsidian Publish In the world of tabletop role-playing games like Dungeons & Dragons (D&D), the concept of "rolling with Advantage" is a popular mechanic. This works by rolling a 20-sided die *twice* and taking the m…

I'm experimenting in converting some of my YouTube math explainers to to blog form to see if there's any interest. Let me know what you think! publish.obsidian.md/nicam/YouTub...

Imagine the bombs are cards instead. The situation is equivalent to each player being dealt one card and whoever is dealt the bomb loses. (You could imagine also "dealing" each player their card only on their turn if you wish). It's completely symmetric.

Whatever you do, don't go to the restaurant AT the zoo.

"Never start a land war on Feranganar"

Once I was teaching a class and wanted to emphasize a strict inequality <, so my brain jumped to underlining it to make my point. (Answer to original question: Not significant, must be < )

Solidarity. I think the thing I was most confused about as a parent is why they use the word "cry" so often....scream is so much more common/accurate imo!

One of the greatest misnaming in all of mathematics is the "quadrilateral": it should be called a "tetragon"!

Edit to add that I just saw the secret endscreen and the connection to pi-with-blocks is even nicer than I thought.

Very nice video! It's incredible that the pi-with-blocks problem has a "real life" application. Btw, I had on my list to make a video of ordinary probability vs quantum probability and this video is sparking joy. Would it be ok with you if I used some clips/screenshots from your video in my video?

A Pentagon, a Random Walk, and... Fibonacci?! YouTube video by Dr Mihai Nica

New video on an unexpected appearance of the Fibonacci numbers in a probability problem about a random walk youtu.be/g8aA76pNBkg

I swapped it to do 25% of 70, which is 70/2/2 = 17.5

@hankgreen.bsky.social Love the new 4x3 word game! I thought of it as a Venn Diagram (see image). This way, you can make other patterns, e.g. I made an "outer square". I created an app where you can play & make more here marimo.app?slug=708we4 and a 6 minute YouTube tutorial youtu.be/VVunnwwupT4

Episode 1 of Parlor Room on @dropout.tv is an absolute triumph. Wavelength is one of my favourite games in real life, and I had just as much fun watching y'all as playing it myself. I was laughing nonstop the whole episode. Can't wait for the rest of the season Becca! @thebeccascott.bsky.social

Love it. Is there a name for this? I propose Cantor's Textbook Argument.

Tetragon >> quadrilateral. I'm starting a petition!

Is Square hiding in the present ready to jump out and surprise everyone?

Congrats! The amount you should celebrate this win is 1/epsilon

Genuinely, they might remember this as one of those wonderful days of childhood.

The generalized Alice HH vs Bob HT problem In 2024, Daniel Litt posed a simple coinflip game pitting Alice's "Heads-Heads" vs Bob's "Heads-Tails": who is more likely to win if they score 1 point per occurrence of their substring in a sequence ...

With Svante Janson and Simon Segert, we just posted out latest in the Alice HH vs BoB HT saga on the arxiv! arxiv.org/abs/2503.19035 We generalize to strings other than HH or HT. I also made a YouTube video a while ago giving the general idea youtu.be/_ufR0fOFO-E?...

π day 2025: Why is Pi in the Bell Curve? YouTube video by Dr Mihai Nica

Happy Pi Day!!! I made a probability proof of why Pi is in the bell curve. Along the way we find an interesting formula for the sum of squares X^2+Y^2 for two normal random variables. youtu.be/sN-ZQ3rohsY

No, but I do use the phrase "no scope 2pi" when I nail a trig problem on the first try