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Évariste Galois and his theory
Richter, Lukáš ; Kvasz, Ladislav (advisor) ; Jančařík, Antonín (referee)
TITLE: Évariste Galois and His Theory AUTHOR: Lukáš Richter DEPARTMENT: The Department of Mathematics and Teaching of Mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The first part of my thesis deals with the life of the significant French mathematician of the 19th century, Évariste Galois, the founder of modern algebra. It is focused on his school years, meetings with mathematics, unsuccessful entrance exams to university, expulsion from school, his mathematic works and his bad experiences with French Academy of Science. He had difficulties with law during his life twice, he was judged and imprisoned. At the end of his short life he fell in love unhappily and consequently was killed in a duel. The second part is devoted to the solution of polynomial equations of the first degree up to the fourth degree by the algebraic patters already known at the times of Galois. Each of the formula is derived by the method suitable even for the students of secondary schools and its usage is illustrated on the example. The third part contains the basics of the Galois Theory and the insolubility of polynomial equations of at least fifth degree is demonstrated. Some of the statements are introduced on examples. KEYWORDS: Évariste Galois, polynomial equations, field extensions, automorphism groups, Galois Theory
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