Nine years ago, I wrote a July 4th blog post about matroids called A Celebration of Independence. Today, I’d like to talk about independence’s lesser-known sibling. In particular, I want to describe a characterization of matroids due to Paul Vaderlind that I feel ought to be better known. In most books and articles on matroid […]| Matt Baker's Math Blog
In celebration of Pi Day 2024, I would like to explain how the “Arithmetic-Geometric Mean” of Gauss and Legendre can be used to give a rapid method for computing the digits of . By “rapid” here, I mean that the algorithm exhibits quadratic convergence: the number of correct digits roughly doubles with each iteration. I […]| Matt Baker's Math Blog
In honor of Pi Day 2023, I’d like to discuss Hilbert’s 7th Problem, which in an oversimplified (and rather vague) form asks: under what circumstances can a transcendental function take algebraic values at algebraic points? The connection with is that Lindemann proved in 1882 that the transcendental function takes transcendental values at every nonzero algebraic […]| Matt Baker's Math Blog
Let’s call a function $latex f : {\mathbb Z} \to {\mathbb Z}$ a near-endomorphism of $latex \mathbb Z$ if there is a constant $latex C>0$ such that $latex |f(a+b)-f(a)-f(b)| \leq C$ for al…| Matt Baker's Math Blog
