About three years ago I became the national coach of the United States International Math Olympian Team. I was very happy for a day thinking this is very interesting. But the next day I started to think that maybe I should do something with this. And I decided that I wanted to focus not only […]

# Tag: mathematics

## Understanding e to the i pi in 3.14 minutes | DE5

One way to think about the function e^t is to ask what properties it has. Probably the most important one, from some points of view the defining property, is that it is its own derivative. Together with the added condition that inputting zero returns 1, it’s the only function with this property. You can illustrate […]

## Derivative formulas through geometry | Essence of calculus, chapter 3

Now that we’ve seen what a derivative means, and what it has to do with rates of change. Our next step is to learn how to actually compute these guys, as in if I give you some kind of function with an explicit formula you’d want to be able to find what the formula for […]

## Theory of mind through the lens of algorithms | Andreea Diaconescu | TEDxZurich

Translator: Pik Yan Wong Reviewer: Denise RQ What if I told you that the brain could be described using just a set of mathematical equations? My fascination with a human brain began as a young student volunteering in a psychiatric ward. There I met a woman who had an incredible talent. She was able from […]

## MATH3411 Problem 9

– [Dr Thomas Britz] Hi and welcome to MATH 3411 Problem 9 in which we’ll be looking at the ISBN code or more particularly, the ISBN 10 code. It’s the code consisting of all the sequences like this. X, the code word there being equal to x_1 up to x_10 where each of these is […]

## Dot products and duality | Essence of linear algebra, chapter 9

Traditionally, dot products or something that’s introduced really early on in a linear algebra course typically right at the start. So it might seem strange that I push them back this far in the series. I did this because there’s a standard way to introduce the topic which requires nothing more than a basic understanding […]

## 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 […]

## Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2

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 two-dimensional vectors. Now, I imagine that vector coordinates were already familiar to a lot of you, but there’s another kind of interesting way to think […]

## 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 […]