Galois Theory explains Quintic Equation sans radical root

总结:Field Extension 扩域

还是解释得很快,听得蒙是正常,因为 Cauchy, Fourier, Gauss, Poisson 等世纪大师都听不懂 20岁 Galois 讲’西咪’ ?

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/

科普: Icosahydron(正20面体)

第一集:Abel’s & Galois’s tragic life

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


第二集:Solving equations of degree 2, 3, 4

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


第三集:Introduction to Group, Equation’s roots and their relation with the coefficients.

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


第四集:Group secret in a game (odd & even parity)

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

第五集:Icosahydron unsolvable

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

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