Uploaded August 2020 | Updated September 2026, 1 week ago
Proofs of the multiplication rule: youtu.be/CzJ-i4z0I78
Video on the division algorithm: youtu.be/qEaxFxUK-es
The fundamental definition and properties of congruence modulo n. We talk about how modular arithmetic is related to remainders, as well as the rules for addition and multiplication of congruences!
Modular Arithmetic playlist: youtube.com/playlist?list=PLug5ZIRrShJHPX-OyMNLLCQfKXchdZKpE
0:00 Definitions
5:17 Equivalence Relation
8:50 Operations (mod n)
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Music: OcularNebula - The Lopez
Proofs of the multiplication rule: youtu.be/CzJ-i4z0I78
Video on the division algorithm: youtu.be/qEaxFxUK-es
The fundamental definition and properties of congruence modulo n. We talk about how modular arithmetic is related to remainders, as well as the rules for addition and multiplication of congruences!
Modular Arithmetic playlist: youtube.com/playlist?list=PLug5ZIRrShJHPX-OyMNLLCQfKXchdZKpE
0:00 Definitions
5:17 Equivalence Relation
8:50 Operations (mod n)
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")
