Algebra

Articles and videos

Se repérer dans un labyrinthe (avec l'algèbre) - Frédéric Le Roux by Frédéric Le Roux (January 31^st, 2022) ► A basic introduction to algebraic topology: using group theory to study a bicolour graph (fundamental group, covering map…).
↪Un peu plus de topologie algébrique avec Frédéric Le Roux by Frédéric Le Roux (March 13^th, 2022) ► The continuation of the previous video.
Thomaths 16 : Transformations Linéaires et Matrices (algèbre linéaire 2) by Alexander Thomas (February 12^th, 2022) ► An introduction to matrices.
Thomaths 18 : Théorème du Rang (algèbre linéaire 3) by Alexander Thomas (August 19^th, 2022) ► The title says it all: the rank–nullity theorem.
Approaching the Yoneda Lemma • Attila Egri-Nagy • YOW! 2019 by Attila Egri-Nagy (December 24^th, 2023) ► A fast-paced introduction to algebra to developers.
The Frobenius Problem (and numerical semigroups) - Numberphile by David Eisenbud (January 10^th, 2025) ► The Frobenius Number, Sylvester’s proof for two integers, and the fact that we have no formula for three or more integers.
Baptiste Huguet - Le théorème de d'Alembert-Gauss... via le mouvement brownien by Baptiste Huguet (January 29^th, 2025) ► Using the Brownian Motion to prove the Fundamental Theorem of Algebra.
Clotilde Fermanian - Changeons l’addition pour mieux grimper ! by Clotilde Fermanian (March 6^th, 2025) ► I guess you need to already have some knowledge of this to understand this introduction to the work of Linda Rothschild and Élias Stein on Lie groups.
Mickaël Launay’s presentation
- Structures algébriques 1 (Introduction : Monoïdes, Groupes, Anneaux, Corps) by Mickaël Launay (October 6^th, 2013) ► What is an algebraic structure.
- ↪Structures algébriques 2 (Les magmas) by Mickaël Launay (October 7^th, 2013) ► The definition of a magma.
- ↪Structures algébriques 3 (Propriétés de l'opération) by Mickaël Launay (October 14^th, 2013) ► The definition of the commutativity, the associativity, and the identity element.
- ↪Structures algébriques 4 (Monoïdes : définition et exemples) by Mickaël Launay (October 26^th, 2013) ► The title says it all.
- ↪Structures algébriques 5 (Un théorème de la théorie des monoïdes) by Mickaël Launay (December 11^th, 2013) ► The proof that an invertible element is cancellable.
- ↪Structures algébriques 6 (Les groupes) by Mickaël Launay (December 12^th, 2013) ► The definition of a group.
- ↪Structures algébriques 7 (Exemples de groupes, rubik's cube et groupes de symétrie) by Mickaël Launay (December 16^th, 2013) ► The title says it all.
- ↪Structures algébriques 8 (Un résultat de la théorie des groupes appliqué au rubik's cube) by Mickaël Launay (December 17^th, 2013) ► The proof that by repeatedly composing an element with itself, we will reach the identity element.
- ↪Structures algébriques 9 (Les anneaux - Définition) by Mickaël Launay (December 18^th, 2013) ► The definition of a ring.
- ↪Structures algébriques 10 (Les corps - Définition) by Mickaël Launay (December 19^th, 2013) ► The definition of a field.
- ↪Structures algébriques 11 (Vocabulaire et conclusion...) by Mickaël Launay (December 20^th, 2013) ► The origin of the algebra terms.
Groups
- Monster Group (John Conway) - Numberphile by John Conway and Tim Burness (May 9^th, 2014) ► The classification of finite simple groups, the sporadic groups, and the Fischer-Griess Monster.
- ↪Monster Group (a little extra bit) by Tim Burness (May 10^th, 2014) ► The continuation of the previous video.
- Moonshine Link Discovered for Pariah Symmetries — A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory. by Erica Klarreich (September 22^nd, 2017) ► More links are discovered between symmetry groups and modular forms.
- Les groupes de Galois, révolution mathématique ( avec démonstration ) - Passe-science #31 by Thomas Cabaret (April 7^th, 2020) ► A short and fast introduction to Galois theory.
- Symétries - Myriogon #27 by Mickaël Launay (May 5^th, 2020) ► Ambigrams, mirrors, and groups.
- Group theory, abstraction, and the 196,883-dimensional monster by Grant Sanderson (August 19^th, 2020) ► An introduction to group theory and the monster group.
- Mathematician Disproves 80-Year-Old Algebra Conjecture — Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses. by Erica Klarreich (April 12^th, 2021) ► Kaplansky’s conjecture has been disproved by Giles Gardam.
- Galois Groups and the Symmetries of Polynomials — By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.↓ by Allison Whitten (August 3^rd, 2021) ► This presentation of Galois’ theory is unclear.
- What is Group Theory? — Group Theory Ep. 1 by "Nemean" (August 6^th, 2022) ► An introduction to group theory.
- Marc Abboud - Le problème de Burnside by Marc Abboud (July 5^th, 2023) ► The Grigorchuk group is a Burnside group.
- The Verhoeff-Gumm Check Digit Algorithm #SoME3 by Kevin Lubick (August 5^th, 2023) ► The title says it all.
- Thomaths 28 : Actions de groupe by Alexander Thomas (November 16^th, 2024) ► Using Burnside’s lemma to compute the number of possible cubes having n colours modulo the rotations.
- Lê Nguyên Hoang’s presentation
  - La théorie des groupes | Lê Nguyên Hoang by Lê Nguyên Hoang (November 21^st, 2017) ► The definition of a group.
  - Exemples de groupes | Lê Nguyên Hoang by Lê Nguyên Hoang (November 28^th, 2017) ► The title says it all.
  - Les groupes de transformations invariantes | Lê Nguyên Hoang by Lê Nguyên Hoang (December 5^th, 2017) ► The title says it all.
  - Tout groupe est un sous-groupe du groupe des permutations | Lê Nguyên Hoang by Lê Nguyên Hoang (December 12^th, 2017) ► A proof of Cayley’s theorem.
Rubik’s cube
- A simple trick to design your own solutions for Rubik's cubes by Burkard Polster (January 15^th, 2016) ► The title says it all.
- Cracking the 4D Rubik's Cube with simple 3D tricks by Burkard Polster (June 18^th, 2016) ► A presentation of Magic Cube 4D, a software simulating a 4D Rubik’s cube.
- ↪Cracking the 4D Rubik's Cube with simple 3D tricks Part 2: Magic Cube 4D by Burkard Polster (June 18^th, 2016) ► The continuation of the previous video.
- Can you solve THE Klein Bottle Rubik's cube? by Burkard Polster (October 8^th, 2016) ► A presentation of MagicTile, a software with hundreds of variations of Rubik’s cube.
- ↪Intro to MagicTile (Part 2 of Can you solve the Klein Bottle Rubik's Cube) by Burkard Polster (October 8^th, 2016) ► The continuation of the previous video.
- What's the Monkey number of the Rubik's cube? by Burkard Polster (June 10^th, 2018) ► What is the average number of twists for a monkey to solve the Rubik’s cube?
- Incredible 3x3x9 Rubik's Cube↓ by "CUBASTIC" (March 1^st, 2019) ► Another type of cube, but the video author is very annoying.
- Rubik's cube et théorie des groupes, avec Florence Porcel - Myriogon #13 by Mickaël Launay and Florence Porcel (April 7^th, 2020) ► Some simple facts about Rubik’s cubes.
- Le Rubik's cube et ses 43 252 003 274 489 856 000 positions - Myriogon #25 by Mickaël Launay (April 30^th, 2020) ► Counting the number of positions.
- [AVENT MATHS] : 20 est le nombre de Dieu🚫 by Jason Lapeyronnie (December 20^th, 2020) ► A Rubik’s cube can always be solved in 20 moves or less.
The 15 puzzle
- Why is this 15-Puzzle Impossible? - Numberphile by Steven Bradlow (April 21^st, 2020) ► The well-known criteria of the well-known puzzle.
The Futurama Theorem
- Deux (deux ?) minutes pour Futurama by Jérôme Cottanceau (January 21^st, 2015) ► A description of the theorem.
- The Futurama Theorem by Burkard Polster (April 30^th, 2015) ► A slightly more detailed description.
- ↪The parity of permutations and the Futurama theorem by Burkard Polster (August 15^th, 2015) ► A presentation of permutation parity.
- ↪The 15 puzzle - solving the unsolvable 19th century Rubik's square by Burkard Polster (February 12^th, 2016) ► Applying parity to the 15 puzzle and the Rubik’s cube.