2014 Math Course from Coursera: Galois Theory
Coursera is a free Online University Class taught by professors from 20+ world’s top universities, co-founded by a Singapore-born Stanford Professor Dr. Andrew Ng (ex-Rafflesian student and Computer scientist in Artificial Intelligence) with Dr. Delphne Koller.
Galois Theory is taught in the Honors / Masters Math Course in NUS (National University of Singapore, ranked the Top Asian University and 9th in the world for Mathematics in 2013)
Ecole Normale Superieure is the ‘Teacher College’ equivalent to NTU (NIE) in Singapore. It is the top Research University in the World, producing 1/3 of the world’s Fields medalists for Math and many French Nobel Prize scientists. Évariste Galois was its student during Napoleon Revolution, after having failed the entrance exams (Concours) of Ecole Polytechniques (X) in 2 consecutive years.
However, the 19-year-old math genius Galois was expelled too by Ecole Normale Supérieure for involving in the Revolution against the French King. Watch the latest movie “Les Misérables” by Victor Hugo, in the Parisian street barricade of student riots against the King’s soldiers, Galois was one of the student leaders.
Galois was sadly killed at 20 in a duel by his girl friend’s fiancé – a good mathematician is not ‘necessary and sufficient condition’ to be a good shooter. The night before he died (knowing well he would be killed by a marksman), Galois wrote down the theory in 60 pages, repeatedly scribbled at the margin, “Je n’ai pas le temps” (I have no time). He asked his brother to send the papers to Jacobi and Gauss to confirm its importance. But Gauss hated Napoleon and the French, who occupied his Germany and killed his King, refused to study the papers. Only 14 years later a X Prof Louisville discovered the Galois Theory and Group.
Galois Theory is the most advanced theory in Algebra. The famous Fermat’s Last theorem (x^n + y^n = z^n) was proved after 350 years using Galois Theory by the Cambridge Prof Andrew Wiles in 1994.
Another Good Math course:
French touch of graduate Math by the Engineering Ecole Centrale of Paris, the alma mater of the inventors of cars Renault, Citroën, Tower Eiffel / New York Status of Liberty.