Essays about: "fundamental theorem of algebra"

Found 3 essays containing the words fundamental theorem of algebra.

  1. 1. An almost algebraic proof of the fundamental theorem of algebra

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : David Kamali; [2021]
    Keywords : algebrans fundamentalsats; Sylows satser; kroppteori; Galoisteori; fundamental theorem of algebra; group theory; Sylow theorems; Galois Theory; field theory; Mathematics and Statistics;

    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

  3. 2. The classification theorem for closed surfaces

    University essay from Lunds universitet/Matematik LTH

    Author : Filip Jonsson Kling; [2019]
    Keywords : Topology; algebra; surfaces; fundamental group; simplex; homotopy; homology; Mathematics and Statistics;

    Abstract : In this thesis we will study some basic concepts in algebraic topology such as the fundamental group, simplicial complexes and simplicial homology. These are then used together with a method called surgery to prove a complete topological classification of closed surfaces... READ MORE

  4. 3. On Intersections of Algebraic Curves and Applications to Elliptic Curves

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Karl Lindén; [2018]
    Keywords : Bezout s theorem; Max Noether s fundamental theorem; Pappus s theorem; Pascal s theorem; Chasles theorem; algebraic curves; elliptic curves; Mathematics and Statistics;

    Abstract : In this thesis we state and give elementary proofs for some fundamental results about intersections of algebraic curves, namely Bezout's, Max Noether's, Pappus's, Pascal's and Chasles' theorems. Our main tools are linear algebra and basic ring theory. We conclude the thesis by applying the results to elliptic curves.. READ MORE