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 of 256 bits. One of these was in the context of digital signatures and the other in the context of a cryptographic hash function. For…

# Tag: 3 brown 1 blue

## Gradient descent, how neural networks learn | Deep learning, chapter 2

Last video I laid out the structure of a neural network I’ll give a quick recap here just so that it’s fresh in our minds And then I have two main goals for this video. The first is to introduce the idea of gradient descent, which underlies not only how neural networks learn, but how…

## This problem seems hard, then it doesn’t, but it really is

Every year, more than 100 countries send 6 of their brightest teenagers, or the occasional pre-pubescent prodigy, to represent them in the International Math Olympiad, commonly known as the IMO. Considering that each country has its own elaborate system of contests leading to their choice of 6 representatives, the IMO stands as the culminating symbol…

## Backpropagation calculus | Deep learning, chapter 4

The hard assumption here is that you’ve watched part 3, giving an intuitive walkthrough of the backpropagation algorithm. Here, we get a bit more formal and dive into the relevant calculus. It’s normal for this to be a little confusing, so the mantra to regularly pause and ponder certainly applies as much here as anywhere…

## Linear transformations and matrices | Essence of linear algebra, chapter 3

Unfortunately, no one can be told, what the Matrix is. You have to see it for yourself. – Morpheus Surprisingly apt words on the importance of understanding matrix operations visually Hey everyone! If I had to choose just one topic that makes all of the others in linear algebra start to click and which too…

## Cross products | Essence of linear algebra, Chapter 10

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 like to do the same thing for cross products, which also have a standard introduction along with a deeper understanding in the light of linear…

## Essence of linear algebra preview

Hey, everyone! So I’m pretty excited about the next sequence of videos that I’m doing. It’ll be about It’ll be about linear algebra, which—as a lot of you know—is one of those subjects that’s required knowledge for just about any technical discipline, but it’s also—I’ve noticed—generally poorly understood by students taking it for the first…

## Eigenvectors and eigenvalues | Essence of linear algebra, chapter 14

“Eigenvectors and eigenvalues” is one of those topics that a lot of students find particularly unintuitive. Questions like “why are we doing this” and “what does this actually mean” are too often left just floating away in an unanswered sea of computations. And as I put out the videos of the series, a lot of…

## Visualizing the Riemann hypothesis 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. Don’t worry, I’ll explain that animation that you just saw in a few minutes. A lot of people know about this function because there’s a…

## The Essence of Calculus, Chapter 1

[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 the next 10 days. The goal here, as the name suggests, is to really get the heart of the subject out in one binge watchable…