3Blue1Brown
Higher order derivatives | Essence of calculus, chapter 10
What is the second derivative? Third derivative? How do you think about these?
3Blue1Brown
Sneaky Topology | The Borsuk-Ulam theorem and stolen necklaces
Solving a discrete math puzzle, namely the stolen necklace problem, using topology, namely the Borsuk Ulam theorem
3Blue1Brown
Limits, L'Hôpital's rule, and epsilon delta definitions | Essence of calculus, chapter 7
What are limits? How are they defined? How are they used to define the derivative? What is L'Hospital's rule?
3Blue1Brown
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
Intuitions for divergence and curl, and where they come up in physics.
3Blue1Brown
How to count to 1000 on two hands
How to count in binary, and how this lets you count to 1023 on two hands.
3Blue1Brown
How to count to 1000 on two hands
How to count in binary, and how this lets you count to 1023 on two hands.
3Blue1Brown
What is backpropagation really doing? Deep learning - Part 3 of 4
An overview of backpropagation, the algorithm behind how neural networks learn.
3Blue1Brown
Visualizing turbulence
A look at what turbulence is (in fluid flow), and a result by Kolmogorov regarding the energy cascade of turbulence.
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Matrix multiplication as composition | Essence of linear algebra, chapter 4
How to think about matrix multiplication visually as successively applying two different linear transformations.
3Blue1Brown
The other way to visualize derivatives
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 - Part 8 of 15
How do you think about a non-square matrix as a transformation?
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How to lie using visual proofs
Time stamps: 0:00 - Fake sphere proof 1:39 - Fake pi = 4 proof 5:16 - Fake proof that all triangles are isosceles 9:54 - Sphere "proof" explanation 15:09 - pi = 4 "proof" explanation 16:57 - Triangle "proof" explanation and conclusion
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But what is a convolution?
A small correction for the integer multiplication algorithm mentioned at the end. A “straightforward” application of FFT results in a runtime of O(N * log(n) log(log(n)) ). That log(log(n)) term is tiny, but it is only recently in 2019,...
3Blue1Brown
Linear combinations, span, and basis vectors: Essence of Linear Algebra - Part 2 of 15
Some foundational ideas in linear algebra: Span, linear combinations, and linear dependence.
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Cross products: Essence of Linear Algebra - Part 10 of 15
The cross product is a way to multiple to vectors in 3d. This video shows how to visualize what it means.
3Blue1Brown
Olympiad level counting: How many subsets of {1,…,2000} have a sum divisible by 5?
Timestamps 0:00 - Puzzle statement and motivation 4:31 - Simpler example 6:51 - The generating function 11:52 - Evaluation tricks 17:24 - Roots of unity 26:31 - Recap and final trick 30:13 - Takeaways
3Blue1Brown
Who cares about topology? (Inscribed rectangle problem)
This is an absolutely beautiful piece of math. It shows how certain ideas from topology, such as the mobius strip, can be used to solve a slightly softer form of an unsolved problem in geometry.
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But WHY is a sphere's surface area four times its shadow?
Two proofs for the surface area of a sphere
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What does genius look like in math? Where does it come from? (Dandelin spheres)
A beautiful proof of why slicing a cone gives an ellipse.
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Researchers thought this was a bug (Borwein integrals)
Correction: 4:12 The top line should not be there, as that integral diverges Timestamps 0:00 - The pattern 4:45 - Moving average analogy 10:41 - High-level overview of the connection 16:14 - What's coming up next
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Hilbert's Curve: Is infinite math useful?
Drawing curves that fill all of space, and a philosophical take on why mathematics about infinite objects can still be useful in finite contexts.
3Blue1Brown
Oh, wait, actually the best Wordle opener is not “crane”…
Contents: 0:00 - The Bug 3:31 - How the best first guess is chosen 8:54 - Does this ruin the game?
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Derivative formulas through geometry: Essence of Calculus - Part 3 of 11
Introduction to the derivatives of polynomial terms and trigonometric functions thought about geometrically and intuitively. The goal is for these formulas to feel like something the student could have discovered, rather than something...