For the last four years I’ve been working on a book for programmers who want to learn mathematics. It’s finally done, and you can buy it today. The website for the book is pimbook.org, which has purchase links—paperback and ebook—and a preview of the first pages. You can see more snippets later in the book on the…
Markov chains, named after Andrey Markov , are mathematical systems that hop from one "state" (a situation or set of values) to another. For example, if you made a Markov chain model of a baby's behavior, you might include "playing," "eating", "sleeping," and "crying" as states, which together with other behaviors…
Vincent Chen is a student at Stanford University studying Computer Science. He is also a Research Assistant at the Stanford AI Lab. -------------------------------------------------------------------------------- It’s not entirely clear what level of mathematics is necessary to get started in machine learning…
This essay describes a number of strategies for studying college level mathematics. It has sections entitled
Disclaimer 2024-12-02 Since this rant is going viral again (again (again)), some disclaimers: I wrote this six years ago to “”“win”“” an ugly Twitter fight. I’m glad I anonymized the inciting tweet and hope I’m the only person still getting grief over this. The core interesting bit— why it’s mathematically valid to…
I wrote a program to clean up scans of handwritten notes while simultaneously reducing file size.
Early this year a software engineer, Shaun Gilchrist, reached out to me after reading a blog post of mine from many years ago, about my informal search for hidden patterns in the prime numbers. The Ulam Spiral revealed non-random patterns, but they didn’t quite match up. Both Shaun and I had long felt there was […]
Most of us last saw calculus in school, but derivatives are a critical part of machine learning, particularly deep neural networks, which are trained by optimizing a loss function. This article is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We…
Douglas Hofstadter's book Gödel, Escher, Bach: An Eternal Golden Braid is a classic text that's had a strong influence on countle...
A handy rule of thumb for creating a confidence interval for the probability of an event you haven't seen happen yet.
Graph theory represents one of the most important and interesting areas in computer science. But at the same time it’s one of the most…
Benedikt Bitterli's Portfolio
Recently I found a paper being presented at NeurIPS this year, entitled Neural Ordinary Differential Equations, written by Ricky Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud from the University of Toronto. The core idea is that certain types of neural networks are analogous to a discretized differential…
Using graph theory and Ryanair route data to find cheap multi-city flight loops through Europe.
You can find a PDF version of this blog post here . A weighted graph is a data structure consisting of some vertices and edges, and each...
The Sophos Blog
I recently posted a blog post about a new hash table, and whenever I do something like that, I learn at least one new thing from my comments. In my last comment section Rich Geldreich talks about h…
Hi, I wrote my new favorite hash table. This came about because last year I wrote the fastest hash table (I still make that claim) and this year one of the organizers of the C++Now conference asked…
It just became a lot easier to learn about applied category theory, thanks to this free book: • Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Cate…
Discovery of the 50th known Mersenne Prime.
Before I started doing research, I saw SAT solvers as academically interesting but without practical uses ouside of other academic applications. I've since then changed my mind, and I want to change yours, because modern SAT solvers are neat, fast and almost criminally underused by the industry.
[Note: There is a followup to this post .] There has been a lot written over the past decade (and even longer) about problems associated with null hypothesis statistical testing (NHST) and p values. Personally, I have found most of these arguments unconvincing. However, one of t
If you, like me, frequently commute via public transit, you may be familiar with the following situation:
I decided to write an article about a thing that is second nature to embedded systems programmers – low level bit hacks. Bit hacks are ingenious little programming tricks that manipulate integers in a smart and efficient manner. Instead of performing operations (such as counting the number of 1 bits in an integer)…
