3Blue1Brown
Three-dimensional linear transformations: Essence of Linear Algebra - Part 5 of 15
How to think of 3x3 matrices as transforming 3d space
3Blue1Brown
The Essence of Calculus, Chapter 1
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
Abstract vector spaces: Essence of Linear Algebra - Part 15 of 15
What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.
3Blue1Brown
Thinking visually about higher dimensions
A method for thinking about high-dimensional spheres, introduced in the context of a classic example involving a high-dimensional sphere inside a high-dimensional box.
Crash Course
The Rise of the West and Historical Methodology: Crash Course World History
In which John Green talks about the methods of writing history by looking at some of the ways that history has been written about the rise of the West. But first he has to tell you what the West is. And then he has to explain the Rise of...
3Blue1Brown
What does area have to do with slope? | Chapter 9, Essence of calculus
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?
3Blue1Brown
Derivatives of exponentials | Chapter 5, Essence of calculus
What is the derivative of a^x? Why is e^x its own derivative? This video shows how to think about the rule for differentiating exponential functions.
3Blue1Brown
Visualizing the chain rule and product rule: Essence of Calculus - Part 4 of 11
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
Taylor series: Essence of Calculus - Part 11 of 11
Taylor series are extremely useful in engineering and math, but what are they? This video shows why they're useful, and how to make sense of the formula.
3Blue1Brown
Change of basis: Essence of Linear Algebra - Part 13 of 15
What is a change of basis, and how do you do it?
3Blue1Brown
Change of basis | Essence of linear algebra, chapter 13
What is a change of basis, and how do you do it?
3Blue1Brown
Euler's formula with introductory group theory - Part 1 of 4
Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.
3Blue1Brown
Thinking outside the 10-dimensional box
A method for thinking about high-dimensional spheres, introduced in the context of a classic example involving a high-dimensional sphere inside a high-dimensional box.
3Blue1Brown
Fractals are typically not self-similar
What exactly are fractals? A common misconception is that they are shapes which look exactly like themselves when you zoom in. In fact, the definition has something to do with the idea of "fractal dimension".
3Blue1Brown
How colliding blocks act like a beam of light...to compute pi: Colliding Blocks - Part 3 of 3
The third and final part of the block collision sequence.
TED Talks
What physics taught me about marketing - Dan Cobley
* Viewer discretion advised. This video includes discussion of mature topics and may be inappropriate for some audiences. Physics and marketing don't seem to have much in common, but Dan Cobley is passionate about both. He brings these...
3Blue1Brown
Fractals are typically not self-similar
What exactly are fractals? A common misconception is that they are shapes which look exactly like themselves when you zoom in. In fact, the definition has something to do with the idea of "fractal dimension".
3Blue1Brown
Visualizing the chain rule and product rule | Essence of calculus, chapter 4
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
So why do colliding blocks compute pi?
A solution to the puzzle involving two blocks, sliding fricionlessly, where the number of collisions mysteriously computes pi
Bozeman Science
AP Biology Practice 2 - Using Mathematics Appropriately
Paul Andersen explains how to use mathematics appropriately. He begins by emphasizing the important role that mathematics plays in the life sciences today and in that the future. He describes important mathematical equations in each of...
TED-Ed
TED-Ed: Newton's three-body problem explained | Fabio Pacucci
In 2009, researchers ran a simple experiment. They took everything we know about our solar system and calculated where every planet would be up to 5 billion years in the future. They ran over 2,000 simulations, and the astonishing...
3Blue1Brown
What does area have to do with slope? | Essence of calculus, chapter 9
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?
3Blue1Brown
But what is the Fourier Transform? A visual introduction.
An animated introduction to the Fourier Transform, winding graphs around circles.
3Blue1Brown
Dot products and duality | Essence of linear algebra, chapter 7
What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.