Taylor series | Chapter 11, Essence of calculus
When I first learned about Taylor series, I definitely didn’t appreciate how important they are. But time and time again they come up in math, physics, and many fields of…
But what is a Fourier series? From heat flow to drawing with circles | DE4
Here, we look at the math behind an animation like this, what’s known as a “complex Fourier series”. Each little vector is rotating at some constant integer frequency, and when…
Quaternions and 3d rotation, explained interactively
In a moment, I’ll point you to a separate website hosting a short sequence of what we’re calling “explorable videos”. It was done in collaboration with Ben Eater, who runs…
But what is a neural network? | Chapter 1, Deep learning
This is a three. It's sloppily written and rendered at an extremely low resolution of 28 by 28 pixels. But your brain has no trouble recognizing it as a three…
The essence of calculus
[INTRO MUSIC] Hey everyone, Grant here. This is the first video in a series on the essence of calculus. and I'll be publishing the following videos once per day for…
How secure is 256 bit security?
In the main video on cryptocurrencies, I made two references to situations where, in order to break a given piece of security, you would have to guess a specific string…
Visualizing the Riemann zeta function and analytic continuation
The Riemann zeta function. This is one of those objects in modern math that a lot of you might have heard of, but which can be really difficult to understand….
Solving the heat equation | DE3
We last left off studying the heat equation in the one-dimensional case of a rod the question is how the temperature distribution along such a rod will tend to change…