3Blue1Brown
The Brachistochrone, with Steven Strogatz: Brachistochrone - Part 1 of 2
A classic problem that Johann Bernoulli posed to famous mathematicians of his time, such as Newton, and how Bernoulli found an incredibly clever solution using properties of light.
3Blue1Brown
The paradox of the derivative | Essence of calculus, chapter 2
An introduction to what a derivative is, and how it formalizes an otherwise paradoxical idea.
3Blue1Brown
Winding numbers and domain coloring
An algorithm for solving continuous 2d equations using winding numbers.
3Blue1Brown
The Brachistochrone, with Steven Strogatz
A classic problem that Johann Bernoulli posed to famous mathematicians of his time, such as Newton, and how Bernoulli found an incredibly clever solution using properties of light.
3Blue1Brown
But what is a partial differential equation? | DE2
The heat equation, as an introductory PDE.
3Blue1Brown
Visualizing the chain rule and product rule | Chapter 4, Essence of calculus
The product rule and chain rule in calculus can feel like they were pulled out of thin air, but is there an intuitive way to think about them?
3Blue1Brown
Dot products and duality | Essence of linear algebra, chapter 9
What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.
3Blue1Brown
Solving 2D equations using color, a story of winding numbers and composition
An algorithm for numerically solving certain 2d equations. Even though we described how winding numbers can be used to solve 2d equations at a high level, it's worth pointing out that there are a few details missing for if you wanted to...
3Blue1Brown
Cross products | Essence of linear algebra, Chapter 8
The cross product is a way to multiple to vectors in 3d. This video shows how to visualize what it means.
3Blue1Brown
What DO we know about turbulence?
A look at what turbulence is (in fluid flow), and a result by Kolmogorov regarding the energy cascade of turbulence.
MinutePhysics
Is the Universe Entirely Mathematical feat. Max Tegmark
Is the Universe Entirely Mathematical feat. Max Tegmark
PBS
When Pi is Not 3.14
You've always been told that pi is 3.14. This is true, but this number is based on how we measure distance. Find out what happens to pi when we change the way we measure distance.
3Blue1Brown
Solving Wordle using information theory
An exploration for writing a Wordle solver, with the challenge of not using the official list of Wordle answers (except as a test set), which is really just an excuse for an information theory lesson.
3Blue1Brown
The medical test paradox: Can redesigning Bayes rule help?
The medical test paradox: Can redesigning Bayes rule help?
PBS
The Mathematics of Quantum Computers
What is the math behind quantum computers? And why are quantum computers so amazing? Find out on this episode of Infinite Series.
3Blue1Brown
The Essence of Calculus - Part 1 of 11
An overview of what calculus is all about, with an emphasis on making it seem like something students could discover for themselves. The central example is that of rediscovering the formula for a circle's area, and how this is an...
3Blue1Brown
Gradient descent, how neural networks learn | Deep learning, chapter 2
An overview of gradient descent in the context of neural networks. This is a method used widely throughout machine learning for optimizing how a computer performs on certain tasks.
3Blue1Brown
But what *is* a Neural Network? | Chapter 1, deep learning
An overview of what a neural network is, introduced in the context of recognizing hand-written digits.
3Blue1Brown
Sneaky Topology | The Borsuk-Ulam theorem and stolen necklaces: Topology - Part 3 of 3
Solving a discrete math puzzle, namely the stolen necklace problem, using topology, namely the Borsuk Ulam theorem
3Blue1Brown
Differential equations, studying the unsolvable | DE1
What is a differential equation, the pendulum equation, and some basic numerical methods
3Blue1Brown
Why 5/3 is a fundamental constant for turbulence
A look at what turbulence is (in fluid flow), and a result by Kolmogorov regarding the energy cascade of turbulence.
3Blue1Brown
Music And Measure Theory
How one of the introductory ideas in a field called "measure theory" can be thought of in terms of musical harnomy and dissonance.
3Blue1Brown
Cross products in the light of linear transformations | Essence of linear algebra chapter 8 part 2
The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.