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.
第一集：Abel’s & Galois’s tragic life
第二集：Solving equations of degree 2, 3, 4
第三集：Introduction to Group, Equation’s roots and their relation with the coefficients.
第四集：Group secret in a game (odd & even parity)
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)
Examples Polynomial with degree > 5
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 ?
– Gave strong support to Cantor on Infinite Set.