You’ve been chosen as a champion to represent your wizarding house in a deadly duel against two rival magic schools. Your opponents are fearsome. From the Newt-niz school, a powerful sorcerer wields a wand that can turn people into fish, but his spell only works 70% of the time. And from the Leib-ton school, an…

# Tag: math

## Orbitals, the Basics: Atomic Orbital Tutorial — probability, shapes, energy; Crash Chemistry Academy

This tutorial is about orbitals. We’re going to look at what orbitals are, what they represent, how electrons go in orbitals, the order electrons go in orbitals, and the shapes of orbitals. So we know that atoms are made out of electrons, protons, and neutrons. Electrons are very important. The arrangement of electrons dictates how…

## 🖥️ WRITING MY FIRST MACHINE LEARNING GAME! (1/4)

Today I have a very exciting episode for you all because as the title suggests It’s about machine learning But before we get into that I’d like to quickly share my history with machine learning so far Back when I was a kid I’ve always had an interest with AI I remember seeing the famous…

## Taylor series | Essence of calculus, chapter 11

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 engineering because they’re one of the most powerful tools that math has to offer for approximating functions. One of the first times this clicked for…

## Visualizing the sphere and the hyperbolic plane: five projections of each

The point to this video is to illustrate five different projections of the sphere to the plane and then in the second part 5 completely analogous projections the so-called hyperbolic plane. I’ll try to emphasize the similarities between spherical or elliptic geometry and hyperbolic geometry. Let me start with a simple segment showing a rotating…

## Matrix multiplication as composition | Essence of linear algebra, chapter 4

It is my experience that proofs involving matrices can be shortened by 50% if one throws matrices out. — Emil Artin Hey everyone! Where we last left off, I showed what linear transformations look like and how to represent them using matrices. This is worth a quick recap, because it’s just really important. But of…

## Claude Hagège at MIT, 2001 – English as Global Language: Real or Imagined Threat?

PRESENTER: CBBS, which is the Center for Bicultural Bilingual Studies at MIT, has kindly asked me to introduce Professor Hagege to you this afternoon. And I feel extremely honored and privileged to do so. So some of you may have listened to him last night. And if you have, and have come back, it’s because…

## Change of basis | Essence of linear algebra, chapter 13

If I have a vector sitting here in 2D space we have a standard way to describe it with coordinates. In this case, the vector has coordinates [3, 2], which means going from its tail to its tip involves moving 3 units to the right and 2 units up. Now, the more linear-algebra-oriented way to…

## Three-dimensional linear transformations | Essence of linear algebra, chapter 5

[classical music] “Lisa: Well, where’s my dad? Frink: Well, it should be obvious to even the most dimwitted individual who holds an advanced degree in hyperbolic topology that Homer Simpson has stumbled into … (dramatic pause) … the third dimension.” Hey folks I’ve got a relatively quick video for you today, just sort of a…

## Implicit differentiation, what’s going on here? | Essence of calculus, chapter 6

Let me share with you something I found particularly weird when I was a student first learning calculus. Let’s say you have a circle with radius 5 centered at the origin of the xy-coordinate plane, which is defined using the equation x2 + y2=52. That is, all points on this circle are a distance 5…