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.
3Blue1Brown
Cramer's rule, explained geometrically: Essence of Linear Algebra - Part 12 of 15
This rule seems random to many students, but it has a beautiful reason for being true.
3Blue1Brown
But how does bitcoin actually work?
How does bitcoin work? What is a "block chain"? What problem is this system trying to solve, and how does it use the tools of cryptography to do so?
3Blue1Brown
What they won't teach you in calculus
A visual for derivatives which generalizes more nicely to topics beyond calculus. Thinking of a function as a transformation, the derivative measure how much that function locally stretches or squishes a given region.
3Blue1Brown
Nonsquare matrices as transformations between dimensions | Essence of linear algebra, chapter 8
How do you think about a non-square matrix as a transformation?
3Blue1Brown
Cross products | Essence of linear algebra, Chapter 10
The cross product is a way to multiple to vectors in 3d. This video shows how to visualize what it means.
3Blue1Brown
Eigenvectors and eigenvalues | Essence of linear algebra, chapter 10
Eigenvalues and eigenvectors are one of the most important ideas in linear algebra, but what on earth are they?
3Blue1Brown
But what is a Neural Network? | Deep learning, chapter 1
An overview of what a neural network is, introduced in the context of recognizing hand-written digits.
3Blue1Brown
Who (else) cares about topology? Stolen necklaces and Borsuk-Ulam: Topology - Part 2 of 3
How a famous theorem in topology, the Borsuk-Ulam theorem, can be used to solve a counting puzzle that seems completely distinct from topology.
3Blue1Brown
Who (else) cares about topology? Stolen necklaces and Borsuk-Ulam
How a famous theorem in topology, the Borsuk-Ulam theorem, can be used to solve a counting puzzle that seems completely distinct from topology.
3Blue1Brown
But how does bitcoin actually work? Cryptocurrency - Part 1 of 2
How does bitcoin work? What is a "block chain"? What problem is this system trying to solve, and how does it use the tools of cryptography to do so?
3Blue1Brown
Ever wonder how Bitcoin (and other cryptocurrencies) actually work?
How does bitcoin work? What is a "block chain"? What problem is this system trying to solve, and how does it use the tools of cryptography to do so?
3Blue1Brown
Inverse matrices, column space and null space: Essence of Linear Algebra - Part 7 of 15
How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?
3Blue1Brown
Implicit differentiation, what's going on here? | Chapter 6, Essence of calculus
How to think about implicit differentiation in terms of functions with multiple inputs, and tiny nudges to those inputs.
3Blue1Brown
Vectors, what even are they? | Essence of linear algebra, chapter 1
What is a vector? Is it an arrow in space? A list of numbers?
3Blue1Brown
e^(iπ) in 3.14 minutes, using dynamics | DE5
A quick explanation of e^(pi i) in terms of motion and differential equations
3Blue1Brown
A few of the best math explainers from this summer
Announcement for the results of the first Summer of Math Exposition
3Blue1Brown
The three utilities puzzle with math/science YouTubers
A classic puzzle in graph theory, the "Utilities problem", a description of why it is unsolvable on a plane, and how it becomes solvable on surfaces with a different topology.
3Blue1Brown
Binary, Hanoi and Sierpinski, part 1
How couting in binary can solve the famous tower's of hanoi problem.
3Blue1Brown
The hardest problem on the hardest test
A geometry/probability question on the Putnam, a famously hard test, about a random tetrahedron in a sphere. This offers an opportunity not just for a lesson about the problem, but about problem-solving tactics in general.
3Blue1Brown
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
Divergence, curl, and their relation to fluid flow and electromagnetism
3Blue1Brown
The hardest problem on the hardest test
A geometry/probability question on the Putnam, a famously hard test, about a random tetrahedron in a sphere. This offers an opportunity not just for a lesson about the problem, but about problem-solving tactics in general.
3Blue1Brown
e to the pi i, a nontraditional take (old version)
The enigmatic equation e^{pi i} = -1 is usually explained using Taylor's formula during a calculus class. This video offers a different perspective, which involves thinking about numbers as actions, and about e^x as something which turns...