# Galois Theory explains Quintic Equation sans radical root

Get to appreciate the reasoning outline is enough, “the devil is in the details” for the Math grads in the 4th year Hons degree.

https://v.ixigua.com/ebAQRjJ/

https://v.ixigua.com/eqMxeoh/

https://v.ixigua.com/eqM4mya/

https://v.ixigua.com/eqMa3rw/

https://v.ixigua.com/eqMQXFT/

https://v.ixigua.com/eqMsXoq/

# 《Galois Theory》 – Coursera by Ecole Normale Supérieure

Complete Free COURSERA Course 《Galois Theory》 (French) from Ecole Normale Supérieure (ENS 巴黎师范) , the university which kicked out Galois as a student in1830, but apologized to him 150 years later.

Today ENS ranked top 3 globally (after Harvard, Princeton IAS) in Math research & education, producing 1/3 of the world’s Fields Medalists by a single university.

For English Text translation (choose Google translate)

https://www.coursera.org/learn/theorie-de-galois

# From Polynomial to Modern Algebra

Examples Polynomial with degree > 5

# Richard Dedekind

Julius Wilhelmina Richard Dedekind (6 Oct 1831 – 12 Feb 1916)

– Last student of Gauss at Göttingen
– Student and closed friend of Dirichlet who influenced his Mathematical education
– Introduced the word Field (Körper)
– Gave the first university course on Galois Theory
– Developed Real Number ‘Dedekind Cut‘ in 1872
– Accomplished musician
– Never married, lived with his unmarried sister until death
“Whatever provable should be proved.”
– By 1858: still yet established ?
$\sqrt{2}.\sqrt{3} = \sqrt{2.3}$
– Gave strong support to Cantor on Infinite Set.

http://www-history.mcs.st-and.ac.uk/Biographies/Dedekind.html