Essays about: "Galoisteori"
Found 4 essays containing the word Galoisteori.
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1. An almost algebraic proof of the fundamental theorem of algebra
University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)Abstract : By the results of the Sylow theorems, algebraic extension theorems and Galois theory, we shall prove the fundamental theorem of algebra, which states that the set of complex numbers is algebraically closed. This process of abstraction will provide an almost algebraic proof of the theorem and thereby supply us with a tool in solving many questions within the field of mathematics. READ MORE
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2. An Exploration of Galois Theory with some Classical Results
University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematik LTHAbstract : Galois theory unites field theory and group theory to solve some field theoretical problems. The aim of this thesis is to provide a concise introduction to the topic, culminating in the proof of the insolubility of the general quintic equation by radicals. READ MORE
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3. The étale fundamental group, étale homotopy and anabelian geometry
University essay from KTH/Matematik (Avd.)Abstract : In 1983 Grothendieck wrote a letter to Faltings, [Gro83], outlining what is today known as the anabelian conjectures. These conjectures concern the possibility to reconstruct curves and schemes from their étale fundamental group. Although Faltings never replied to the letter, his student Mochizuki began working on it. READ MORE
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4. Solubility of Polynomials of the Form x^6-ax+b
University essay from Matematiska och systemtekniska institutionenAbstract : This thesis is an attempt to find a criterion of when a sixtic equation of the form x^6-ax+b=0, with a,b belonging to Z, is soluble. To do this we use Galois theory and a theorem by Frobenius. We state some different criteria of the coefficients, a and b, which make the sixtic soluble. . READ MORE
