French Math is unique in treating these 3 conic curves: (ellipse, parabola, hyperbola), always starts from the first principle – a la the Cartesian Spirit “I think therefore I am” (我思故我在).

“Catersian” Analytical Geometry was co-invented by two 17CE French mathematicians René Déscartes and Pierre de Fermat.

Note: The “elliptic curve” is a powerful geometry tool used in Number Theory (proved the 350-year-old Fermat’s Last Theorem in 1994 by Andrew Wiles), also in the most advanced Encryption algorithm.

This is the 1st / 2nd Year Commerce University Math (Cours Prépa).

You shall see the French lecture on Matrix diagonalisation is quite different from the MIT lecture. The French approach is abstract theoretical and more general, the American approach is more practical less theory.

[French translation]

Eigen Value = Valeur Propre

Eigen Vector = Vecteur Propre

Note: Eigen (german) = characteristic 真正的

The same lecture covers more in depth (below) is for Engineering students (Prépa):

In French, ‘coller’ (the verb of colle) is to ‘glue’ (on the blackboard) i.e. get stuck by the Oral Interrogation.

This tradition started from Napoleon time, even Victor Hugo (author of Les Misérables) got ‘colle’ in Lycée Louis Le Grand’s Classe Préparation (or Prépas in short, equivalent to 1st and 2nd year of undergraduate course, for French Top 10% Baccalaureat students, who aspire to enter the elite Grandes Ecoles after many competitive Concours Entrance Exams).

Every week in the 2 years of Prépas there are 2 of the 4 colles: Math & Physics, or, Chemistry & Second Language (English / Spanish / Russian / German).

This video is the session of a Math colle. The students are grouped in 3 (Trinôme), take the oral test after 6 pm by a professor from internal or external university.

It is a nightmare for Math colle. Not so much for Physics or Chemistry. English colle for Singaporean student is easy except the translation from English to French.

300 years ago till today the Colles are still the same. The French like tradition but this Prépas and the Colles are horrible to kill the young French like Evariste Galois and many more young talents.