TED-Ed
TED-ED: How the K_nigsberg bridge problem changed mathematics - Dan Van der Vieren
You'd have a hard time finding the medieval city K_nigsberg on any modern maps, but one particular quirk in its geography has made it one of the most famous cities in mathematics. Dan Van der Vieren explains how grappling with...
3Blue1Brown
How pi was almost 6.283185...
A bit of the history behind how we came to use the symbol "pi" to represent what it does today, and how Euler used it to refer to several different circle constants.
TED-Ed
TED-Ed: Can you solve the multiverse rescue mission riddle? - Daniel Finkel
A bug in the superconductor system has trapped your team in 11 separate dimensions. Can you get them back home safely? -- It was a normal Tuesday at the superconductor, until a bug in the system caused your team to be trapped in 11...
Crash Course
Probability Part 2 Updating Your Beliefs with Bayes - Crash Course Statistics
Today we're going to introduce bayesian statistics and discuss how this new approach to statistics has revolutionized the field from artificial intelligence and clinical trials to how your computer filters spam! We'll also discuss the...
PBS
Making Probability Mathematical
What happened when a gambler asked for help from a mathematician? The formal study of Probability.
3Blue1Brown
Tattoos on Math
After a friend of mine got a tattoo with a representation of the cosecant function, it got me thinking about how there's another sense in which this function is a tattoo on math, so to speak.
3Blue1Brown
Where Newton meets Mandelbrot (Holomorphic dynamics)
How the right question about Newton's method results in a Mandelbrot set.
Bozeman Science
Practice 5 - Using Mathematics and Computational Thinking
Paul Andersen explains how mathematics and computational thinking can be used by scientists to represent variables and by engineers to improve design. He starts by explaining how mathematics is at the root of all sciences. He then...
Crash Course
Henrietta Lacks, the Tuskegee Experiment, and Ethical Data Collection - Crash Course Statistics
Today we’re going to talk about ethical data collection. From the Tuskegee syphilis experiments and Henrietta Lacks’ HeLa cells to the horrifying experiments performed at Nazi concentration camps, many strides have been made from...
Crash Course
Test Statistics - Crash Course Statistics
Test statistics allow us to quantify how close things are to our expectations or theories. Instead of going on our gut feelings, they allow us to add a little mathematical rigor when asking the question: “Is this random… or real?” Today,...
Crash Course
Statistics in the Courts - Crash Course Statistics
As we near the end of the series, we're going look at how statistics impacts our lives. Today, we're going to discuss how statistics is often used and misused in the courtroom. We're going to focus on three stories in which three huge...
Crash Course
What Is Statistics - Crash Course Statistics
Welcome to Crash Course Statistics! In this series we're going to take a look at the important role statistics play in our everyday lives, because statistics are everywhere! Statistics help us better understand the world and make...
TED-Ed
TED-Ed: What is a vector? - David Huynh
Physicists, air traffic controllers, and video game creators all have at least one thing in common: vectors. But what exactly are they, and why do they matter? David Huynh explains how vectors are a prime example of the elegance, beauty,...
3Blue1Brown
Limits | Chapter 7, Essence of calculus
What are limits? How are they defined? How are they used to define the derivative? What is L'Hospital's rule?
3Blue1Brown
Implicit differentiation, what's going on here? Essence of Calculus - Part 6 of 11
How to think about implicit differentiation in terms of functions with multiple inputs, and tiny nudges to those inputs.
3Blue1Brown
Differential equations, studying the unsolvable: Differential Equations - Part 1 of 5
What is a differential equation, the pendulum equation, and some basic numerical methods
Crash Course
P-Hacking - Crash Course Statistics
Today we're going to talk about p-hacking (also called data dredging or data fishing). P-hacking is when data is analyzed to find patterns that produce statistically significant results, even if there really isn't an underlying effect,...
PBS
Does Math Really Exist?
Math is invisible. Unlike physics, chemistry, and biology we can't see it, smell it, or even directly observe it in the universe. And so that has made a lot of really smart people ask, does it actually even EXIST?!?!
TED-Ed
TED-Ed: The paradox at the heart of mathematics: Gödel's Incompleteness Theorem | Marcus du Sautoy
Consider the following sentence: "This statement is false." Is that true? If so, that would make the statement false. But if it's false, then the statement is true. This sentence creates an unsolvable paradox; if it's not true and it's...
TED-Ed
TED-ED: The rise and fall of the Assyrian Empire - Marian H. Feldman
Before the sun never set on the British Empire; before Genghis Khan swept the steppe; before Rome extended its influence to encircle the Mediterranean Sea; there was ancient Assyria. Considered by historians to be the first true empire,...
3Blue1Brown
But what is a partial differential equation? Differential Equations - Part 2 of 5
The heat equation, as an introductory PDE.
PBS
The Multiplication Multiverse
What happens if you multiply things that aren't numbers? And what happens if that multiplication is not associative?
PBS
The Honeycombs of 4-Dimensional Bees ft. Joe Hanson
Why is there a hexagonal structure in honeycombs? Why not squares? Or asymmetrical blobby shapes? In 36 B.C., the Roman scholar Marcus Terentius Varro wrote about two of the leading theories of the day. First: bees have six legs, so they...
Crash Course
Plots, Outliers, and Justin Timberlake Data Visualization Part 2 - Crash Course Statistics
Today we’re going to finish up our unit on data visualization by taking a closer look at how dot plots, box plots, and stem and leaf plots represent data. We’ll also talk about the rules we can use to identify outliers and apply our new...