For over six years now, I've been studying mathematics on my own in my spare time - working my way through books, exercises, and online courses. In this post I'll share what books and resources I've worked through and recommend and also tips for anyone who wants to go on a similar adventure.
In 1931, a 25-year-old Kurt Gödel wrote a proof that turned mathematics upside down. The implication was so astounding, and his proof so elegant that it was...kind of funny. I wanted to share his discovery with you. Fair warning though, I’m not a mathematician; I’m a programmer. This means my understanding is…
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Sonstiges - Learn more about palindromic dates in 2020 and in the near future. 2020-02-02 (YYYMMDD) or 02.02.2020 (DDMMYYY) and others.
Despite two linear algebra classes, my knowledge consisted of "Matrices, determinants, eigen something something". Why? Well, let's try this course format:
If you read any personal finance forums late last year, there's a decent chance you ran across a question from someone who was desperately trying to lose money before the end of the year. There are a number of ways someone could do this; one commonly suggested scheme was to buy put options that were expected to expire…
To represent 3D rotations graphics programmers use Quaternions . However, Quaternions are taught at face value . We just accept their odd multiplication tables and other arcane definitions and use them as black boxes that rotate vectors in the ways we want. Why does $\mathbf{i}^2=\mathbf{j}^2=\mathbf{k}^2=-1$ and…
Starting from the “ones” position, we add 6 + 6 = 12, write down a 2 and carry a 1. We proceed to the left, one position at a time, until there are no more digits to add.
A few months ago I saw a blog post touting fancy new SSE3 functions for implementing vector floor, ceil, and round functions. There was the inevitable proud proclaiming of impressive performance an…
Probability problems come up a lot in systems programming, and I’m using that term loosely to mean everything from operating systems programming and networking, to building large online services, to creating virtual worlds like in games. Here’s a bunch of rough-and-ready probability rules of thumb that are deeply…
There's this rather nifty feature of modern web browsers (such as Firefox or Chrome ) where the browser will automatically warn the user if they happen to navigate to a " malicious " URL:
Excited to announce that my technical paper “ N-Dimensional Rigid Body Dynamics ” was accepted to SIGGRAPH 2020 ! Very proud to present research developed for 4D Toys & Miegakure at such a prestigious conference.
Linear algebra is to machine learning as flour to bakery: every machine learning model is based in linear algebra, as every cake is based in flour . It is not the only ingredient, of course. Machine learning models need vector calculus, probability, and optimization, as cakes need sugar, eggs, and butter. Applied…
Fourier transforms are a tool used in a whole bunch of different things. This is a explanation of what a Fourier transform does, and some different ways it can be useful.
Say we have some things, and we want to be able to store and look them up in order. We could just put them in a big sorted array:
The Fibonacci series is a famous example of an object with a simple mathematical description, but a nearly inexhaustable list of bizarre and complicated properties. Originally, the series was described by Fibonacci in the 15th century in connection with the following problem:
Like making engineering students squirm? Have them explain convolution and (if you're barbarous) the convolution theorem. They'll mutter something about…
I was struck the other day by the following: The cooking instructions on my Bob’s tri-colored quinoa package said to combine 2 cups of water with 1 cup of dried quinoa, which would ultimately create 4 cups of cooked quinoa. See image above. My first reaction was to believe …
Inspired by James McKee’s Trinity Hall prime, physics researcher Gilles Esposito-Farese (of the self-descriptive pangram) has worked out that this 2,258-digit prime number: 53084469288402965415857953902888840109250315594591772197851275320 59910735745658243457138160802170063601085186072703319516241231606…
Why models always get better when they are bigger and deeper, even when the amount of data they consume stays the same or gets smaller.
A playable disease simulation
In this course we explain how category theory—a branch of mathematics known for its ability to organize the key abstractions that structure much of the mathematical universe—has become useful for writing elegant and maintainable code. In particular, we'll use examples from the Haskell programming language to motivate…
Learn cryptography in Go by building ciphers, hashes, password security, and encryption tools. Understand security beneath the library call.
What does matrix multiplication mean? Here's a few common intuitions: This is useful when first learning about vectors: vectors go in, new ones come out.…
The famous fast inverse square root is some mysterious code not written by programming legend John Carmack to calculate a fast approximation of $1/\sqrt{x}$:
Rotate a cube by 90 degrees around the \(x\)-axis, then rotate it by 90 degrees around the \(z\)-axis. This is equivalent to a single rotation. What is the axis and angle of this single rotation?
MIT mathematicians and engineers have developed a mathematical model that predicts how stable a knot is, based on several key properties, including the number of crossings involved, and the direction in which the rope segments twist as the knot is pulled tight.
To celebrate being alive for a billion seconds, Daniel Bruin built a machine with 100 gears with a 10-to-1 gear ratio…meaning that the overall gear ratio is a g
