Cross products | Chapter 10, Essence of linear algebra
Last video, I've talked about the dot product. Showing both the standard introduction to the topic, as well as a deeper view of how it relates to linear transformations. I'd…
But what is the Fourier Transform? A visual introduction.
This right here is what we're going to build to, this video: A certain animated approach to thinking about a super-important idea from math: The Fourier transform. For anyone unfamiliar…
Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra
In the last video, along with the ideas of vector addition and scalar multiplication, I described vector coordinates, where's this back and forth between, for example, pairs of numbers and…
Limits, L’Hôpital’s rule, and epsilon delta definitions | Chapter 7, Essence of calculus
The last several videos have been about the idea of a derivative, and before moving on to integrals, I want to take some time to talk about limits. To be…
Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra
As you can probably tell by now, the bulk of this series is on understanding matrix and vector operations through that more visual lens of linear transformations. This video is…
Limits, L’Hôpital’s rule, and epsilon delta definitions | Chapter 7, Essence of calculus
The last several videos have been about the idea of a derivative, and before moving on to integrals, I want to take some time to talk about limits. To be…
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 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…
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….