The labs on this website are designed to accompany the Foundations of Applied Mathematics textbook series.[1] They provide hands-on experience with key mathematical and computational concepts, connecting theory to practical, real-world applications.

I’m a fifth-year Ph.D. student in the Department of Mathematics at The Ohio State University. I’m interested in algebraic topology, semigroup theory, and computer science.

via: https://www.youtube.com/watch?v=CxGtAuJdjYI

This is the kind of mathematics I was put on this earth to do. The equation explorer is also just a genuinely useful tool for looking up equations; did so earlier this year as part of preparations for a lecture I gave.

Such an aesthetic problem.

A counterexample is any exception to a generalization. Counterexamples  are often used in science (and philosophy), as a means to setting boundaries. In mathematics at large,  well-chosen counterexamples may  bound possible theorems, disprove certain conjectures. This conspectus is (mostly) meant to gather and share counterexample book references (on algebra, analysis, calculus, logic, philosophy, probability, statistics, topology).

In general, if you’re trying to prove something, you can think of the various techniques and tools you have much like chess moves or Hanabi lines. Just like in turn-based games, you’ll find there are dead ends, e.g. trying to apply so-and-so theorem to reduce the problem to proving X, but X turns out to be false. Or there will be lots of paths that look more promising, but you can’t see far enough into the future to completely evaluate them all, and then you have to use heuristics and intuition to prioritize between approaches.

Most of us are familiar with the Fibonacci sequence. What’s the largest Fibonacci number you can compute in 1 second? I’m not setting any world records, here; I don’t own a supercomputer.

Je trouve amusant de lire ce que Dikstra a pu trouver, le premier exercice ressemble à un truc que je pourrais vouloir résoudre

A very nerdy talk on baseball using analogies to logic and probability.

The Largest Collection of Interactive Geometric Puzzles

120 Levels: From Very Easy to Really Hard, 11 Tutorials, 10 Innovative Tools, Automatic Verification of Solutions, “Explore” Mode and Hints, Dynamic Geometry in Action

Mathematics and science Braille textbooks are expensive and require an enormous effort to produce — until now. A team of researchers has developed a method for easily creating textbooks in Braille, with an initial focus on math textbooks. The new process is made possible by a new authoring system which serves as a “universal translator” for textbook formats, combined with enhancements to the standard method for putting mathematics in a Web page. Basing the new work on established systems will ensure that the production of Braille textbooks will become easy, inexpensive, and widespread.

We introduce a versatile method for finding prime numbers that display surprisingly intricate visual patterns— hypothetically, any desired pattern is possible, with only mild distortion. We use this method to locate several examples of large prime numbers that are, in and of themselves, self-referential works of art.

Interesting website who seem (at least) half satirical imo, with an editorial line leftist “anti-woke” but with interesting take on technology

Zvezdelina Stankova discusses the raffle function - and her epic proof ends with an interesting connection.

Beautiful, beautiful problem. Abstract algebra, calculus, number theory, and combinatorics all wrapped up into a bow. :)

reminds me of pattern matching in OCaml