Uploaded September 2021 | Updated September 2026, 2 weeks ago
There is a formula for the sum of the first n natural numbers, which is n(n+1)/2. But that's the same thing as n+1 choose 2! Why are those the same? In this video we give a proof of that connection!
Challenge Problems playlist: youtube.com/playlist?list=PLug5ZIRrShJGkzGsXMYQt8bi5ImYtiEMM
Subscribe to see more new math videos!
Music: OcularNebula - The Lopez
There is a formula for the sum of the first n natural numbers, which is n(n+1)/2. But that's the same thing as n+1 choose 2! Why are those the same? In this video we give a proof of that connection!
Challenge Problems playlist: youtube.com/playlist?list=PLug5ZIRrShJGkzGsXMYQt8bi5ImYtiEMM
Subscribe to see more new math videos!
Music: OcularNebula - The Lopez
![Matrix Invertibility With F[x]-Modules](https://i.ytimg.com/vi/xnZ2d6y8JmA/mqdefault.jpg "Matrix Invertibility With F[x]-Modules
Characteristic polynomial explanation: https://youtu.be/jCt6mR3QtPk
Ring & Module Theory playlist: https://youtube.com/playlist?list=PLug5ZIRrShJExMapwnaKTFXDYbKeWDXq7
In this video, we use F[x]-modules to prove that a matrix is invertible if and only if its determinant is nonzero. Another example of how F[x]-modules can be applied to a ton of things in linear algebra!
Subscribe to see more new math videos!
Music: OcularNebula - The Lopez")
