Math3ma

Last week was the start of a mini-series on limits and colimits in category theory.

In recent months, several of you have asked me to recommend resources for various subjects in mathematics.

Next up on Good Reads: The Princeton Companion to Mathematics, edited by Fields medalist Timothy Gowers.

Over the past couple of years, I've been learning a little about the world of quantum machine learning (QML) and the sorts of things people are thinking about there.

It's hard for me to believe, but Math3ma is TEN YEARS old today.

In a bit of fun news, I've just launched a new video podcast with my coworker Adam Green.

The next episode in the fAQ video podcast is now up!

In the past few months, I've shared a few mathematical ideas that I think are pretty neat: drawing matrices as bipartite graphs, picturing linear maps as tensor network diagrams, and understanding the linear algebraic (or "quantum") versions of probabilit…

Quantum entanglement is, as you know, a phrase that's jam-packed with meaning in physics.

Today I'm excited to share a few new videos with you.

Recently on The Math3ma Institute's blog, I announced an upcoming event that will be hosted at The Master's University (TMU), which is a small private university in Santa Clarita, California.

Hello world!

Welcome to our third and final installment on the Yoneda lemma!

Today I'm happy to share that the Math3ma platform has recently grown in a small yet personal way.

I recently had the pleasure of chatting with Grant Sanderson on the 3Blue1Brown podcast about a variety of topics, including what first drew me to math and physics, my time in graduate school, thoughts on category theory, basketball, and lots more.

Welcome to the final installment of our mini-series on the new preprint "An Enriched Category Theory of Language," joint work with John Terilla and Yiannis Vlassopoulos (https://arxiv.org/abs/2106.07890).

Fatou's Lemma, the Monotone Convergence Theorem, and the Dominated Convergence Theorem are three major results in the theory of Lebesgue integration which, when given a sequence of functions $\{f_n\}$ answer the question, "When can I switch the limit symb…

Fatou's Lemma, the Monotone Convergence Theorem, and the Dominated Convergence Theorem are three major results in the theory of Lebesgue integration which, when given a sequence of functions $\{f_n\}$, answer the question, "When can I switch the limit sym…

Today we're chatting about the Borel-Cantelli Lemma.

Today I'd like to share some math connecting ideas from information theory, algebra, and topology.

Part 1 of this mini-series opened with the observation that language is an algebraic structure.

In the previous post I mentioned a new preprint that John Terilla, Yiannis Vlassopoulos, and I recently posted on the arXiv.

What is applied mathematics?

The TensorFlow channel on YouTube recently uploaded a video I made on some elementary ideas from linear algebra and how they're used in machine learning (ML).

Let's jump right in to where we left off in part 1 of our warm-up to enriched category theory.

It's no secret that I like category theory.

Over the years, the articles on this blog have spanned a wide range of audiences, from fun facts (Multiplying Non-Numbers), to undergraduate level (The First Isomorphism Theorem, Intuitively), to graduate level (What is an Operad?)

In the previous post, I described a simple way to think about matrices, namely as bipartite graphs.

Once upon a time, we embarked on a mini-series about limits and colimits in category theory.

Previously on the blog, we've discussed a recurring theme throughout mathematics: making new things from old things.

Some time ago, I started a blog series introducing the basics of category theory (categories, functors, natural transformations).

Recently I've been working on a dissertation proposal, which is sort of like a culmination of five years of graduate school (yay).

Today I'd like to share an idea.

In this article and the next, I'd like to share some ideas from the world of quantum probability.

Welcome back to our mini-series on quantum probability!

Last time I shared a light introduction to adjunctions in category theory.

Welcome to the last installment in our mini-series on adjunctions in category theory.

There are a couple of questions that I'm asked quite frequently these days: "How far along are you in graduate school?"

Hi all, just ducking in to help spread the word: the annual applied category theory conference (ACT2020) is taking place remotely this summer!

I've been collaborating on an exciting project for quite some time now, and today I'm happy to share it with you.

I'm happy to share that I've successfully defended my PhD thesis, and my dissertation—"At the Interface of Algebra and Statistics"—is now available online at arXiv:2004.05631.

Before introducing today's post, I'd like to first thank everyone who's reached out to me about my thesis and video posted last week.

Today I'd like to share with you a new paper on the arXiv [2007.03834]—my latest project in collaboration with mathematician Yiannis Vlassopoulos (Tunnel, IHES).

This is the official launch week of our new book, "Topology: A Categorical Approach," which is now available for purchase!

We know what it means to have a module $M$ over a (commutative, say) ring $R$.

Galois Theory is all about symmetry.

In the words of Dan Piponi, it "is the hardest trivial thing in mathematics."

After some exposure to group theory, you quickly learn that when trying to prove a group $G$ is abelian, checking if $xy=yx$ for arbitrary $x,y$ in $G$ is not always the most efficient - or helpful!

I hope you have enjoyed our little series on basic category theory.

Last week we began a discussion about the Yoneda lemma.