Essays about: "Modern algebra"
Showing result 1 - 5 of 10 essays containing the words Modern algebra.
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1. Persistent Homology : A Modern Application of Algebraic Topology in Data Analysis
University essay fromAbstract : Topological data analysis emerged as a field in the 2000s and has proven very useful for examining the shape of data sets. Using persistent homology as their main methodology researchers has succesfully applied the theory presented in this paper to study as varied subjects as robot motion, brain connectivity, network theory, finger print analysis and computer vision. READ MORE
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2. 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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3. Pairing-Based Cryptography in Theory and Practice
University essay from Umeå universitet/Institutionen för matematik och matematisk statistikAbstract : In this thesis we review bilinear maps and their usage in modern cryptography, i.e. the theoretical framework of pairing-based cryptography including the underlying mathematical hardness assumptions. The theory is based on algebraic structures, elliptic curves and divisor theory from which explicit constructions of pairings can be defined. READ MORE
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4. Scheme Theory & Weak Mordell-Weil for Elliptic Curves Over Number Fields
University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)Abstract : We provide an introduction to scheme-theoretic algebraic geometry, which studies spaces that are in essence locally solutions to systems of polynomial equations, and prove the weak Mordell-Weil theorem. The weak Mordell-Weil theorem states that for an elliptic curve $E$ over a number field $K$, the quotient $E(K)/mE(K)$ is finite for all $m\geq 2$. READ MORE
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5. 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
