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Title
The Joy of Playful Matrices
Authors
Educational level
Secondary School, Higher Education
Level
easy
Description
This PowerPoint presentation is designed to motivate and facilitate learning with an approach close to “gamification” through experimentation as a pleasure for discovery. It explores the use of simple orthogonal matrices and their product with others, taking the opportunity to delve into the world of cryptography: “The Joy of Playful Matrices”. It does not use the standard notation of the permutation group, nor does it aim to provide rigorous proofs. The goal is to play and enjoy mathematical reasoning. It can serve as a good starting point for other topics: the theorem of permutation decomposition into transpositions, working with determinant properties to prove that these matrices always have a determinant of +1 or -1, proving that these matrices are orthogonal, encrypting and decrypting, studying a known plaintext attack (how many plaintext-ciphertext pairs are needed to break the cryptographic system?), etc.
Licence
CC-BY
Type
Game/Online Exercise
Category
Linear algebra – Matrix calculus
Keywords
Permutation matrices, Cryptography, Gamification
File
UPC-063-GAM-EN.pptx