DiBeo's

The Language of Linear Algebra

Imagine we have 3 vectors in space. At first, they seem to be completely unrelated to each other, but look closely. When we define them with these specific coordinates, then (technically) we can observe a hidden structure. Can you tell which? Your answer, here, will show whether or not you have the necessary intuition to…
Read article →
$This Simple Problem Helps You Think Like Gauss$

This Simple Problem Helps You Think Like Gauss

Here’s a classic question that you probably heard of before. It’s simple, but we will look at it from a completely different perspective that will show whether you really know how to think about mathematics: What is 1 + 2 + 3 + … + 200 ? Now, stop right there. How long do you…
Read article →
How To Solve Differential Equations

Look at this differential equation: My challenge for you is to decide which one is the best method to solve it, based on its structure. It has a very common structure, but only a person with trained eyes can recognize the pattern and can tell what the method is! In this video, we will see…
Read article →
The Language of Calculus

Take a look at this equation: 1+sin⁡x+1−sin⁡x=3\sqrt{1+\sin x} + \sqrt{1-\sin x}=\sqrt{3} Now, think to yourself: “How would you go about solving it?” You don’t need to know Calculus to do it, but you do need a very strong foundation in the Language of Calculus. This is actually the main reason people struggle so much with…
Read article →
Learn Math More Effectively

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.– William Thurston This idea is at the heart of everything we make: we want you to learn math as effectively as possible by building real intuition. To do that even better, we’d love to ask you a few things — this will…
Read article →
What Spheres Tell Us About Higher Dimensions

Here’s an interesting question: take a 2-dimensional sphere inside of a 3-dimensional space. Any rotation you can think of, always leaves 2 points fixed . They are the only 2 points that don’t move. Now, increase the dimensions by 1: imagine a 3-dimensional sphere sitting inside of a 4-dimensional space. Do you think that the…
Read article →
Do Mathematicians Think Like Computers?

Here’s a very interesting philosophical question: How can our brain understand mathematics? Is it like a computer, or, does it work in a different way? Understanding the answer will give you the most effective way to learn mathematics, because if you know how your brain works, you know the most optimal way to teach it. …
Read article →
The Roadmap to Linear Algebra I Wish I Had

The PDF is accompanied by this video. If you find value in our videos and would like to support our work further, and get very useful info that is unavailable anywhere else, consider purchasing this Full PDF on Linear Algebra This PDF offers a clear overview of the core ideas of linear algebra. It will…
Read article →
$Can Two People Understand the Same Math Differently?$

Can Two People Understand the Same Math Differently?

If I asked you to understand a mathematical proof, you would approach it in 1 of 2 completely different ways. That’s because mathematicians Poincare and Hadamard discovered that there are 2 kinds of mathematical minds: let’s see which one you have, and which one is better at helping you learn mathematics. Let’s take a really…
Read article →
The 5 Main Oscillators in Differential Equations

The PDF is accompanied by this video. We’d like to keep our videos free of interruptions and sponsors, so that the sole focus is the subject at hand. If you find value in our videos and would like to support our work further, and get very useful info that is unavailable anywhere else, consider purchasing…
Read article →