The Technion offers many of its mathematics courses, such as infinitesimal calculus and algebra, at several levels, with each course aimed at a different audience. At the lowest level are courses aimed at the “soft sciences”, such as biology, which usually need only elementary, paractical calculations. In the middle sit the majority of the Technion’s … More Introduction to sandwich making
This post is about the basics of the “gradient descent” method for finding the minimum of a function. I started writing it mainly to review the optimization material of lectures by Sébastien Bubeck given in Seattle. All of the material can be found elsewhere (for example, Sébastien’s book), but I can assure you that in … More Descent into madness
I’m happy to say that I recently uploaded a paper to the arXiv under the title “A conformal Skorokhod embedding” (https://arxiv.org/abs/1905.00852). In this post, I’d like to explain what the Skorokhod embedding problem is, how I came across it, some previously known solutions, and my own tiny contribution. But really, all of this is just … More New paper on arXiv: A conformal Skorokhod embedding
Part 1: Archery Lately I’ve been interested in archery. The target of target archery is to shoot a circle square in the middle. The target is usually placed quite far away, some 70 meters in the case of the Olympic games, so it’s not always very easy. Here is one of my volleys from 18 … More Low-dimensional archers have it easy
Here is a silly little question that my friend Ori and I ran into. Let be a decreasing sequence of positive real numbers which tends to 0. Perhaps in a more decent universe, the sum would always equal some finite number, but already in kindergarten we learn that that’s not true: For example, the partial … More Converging Bernoulli Series
Last time I introduced a neat little question: Is it true that every infinite path in contains arbitrarily long arithmetic progressions? For example, in the following path, the squares colored in red have coordinates , which form an arithmetic progression of length 3, where every two consecutive points differ by . As it turns out, … More Arithmetic progressions in space!
Here is a neat question that I stumbled upon during my academic random walk. A sequence of vectors is called an arithmetic progression of length k if there exists a vector such that . In other words, an arithmetic progression in is exactly the generalization you would expect of your good ol’ high-school arithmetic progression … More Arithmetic progressions in space?