Essays about: "Galois field"
Found 5 essays containing the words Galois field.
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1. The Abel-Ruffini Theorem : The insolvability of the general quintic equation by radicals
University essay from Umeå universitet/Institutionen för matematik och matematisk statistikAbstract : This thesis explores the topic of Galois theory at a relatively introductory level with the goal of proving the Abel Ruffini theorem. In the first part algebraic structures are considered: groups, ring, fields, etc. Following this, polynomial rings are introduced and the attention is then turned to finite field-extensions. READ MORE
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2. Profinite groups
University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/MatematikcentrumAbstract : This thesis provides a comprehensive study of profinite groups, which are fascinating mathematical objects that have attracted significant interest in modern algebraic research. Profinite groups are infinite generalizations of finite groups and share many similarities with them. READ MORE
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3. 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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4. 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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5. Efficient Message Passing Decoding Using Vector-based Messages
University essay from Institutionen för systemteknikAbstract : The family of Low Density Parity Check (LDPC) codes is a strong candidate to be used as Forward Error Correction (FEC) in future communication systems due to its strong error correction capability. Most LDPC decoders use the Message Passing algorithm for decoding, which is an iterative algorithm that passes messages between its variable nodes and check nodes. READ MORE