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Full-Text Articles in Mathematics
An Introduction To Lie Algebra, Amanda Renee Talley
An Introduction To Lie Algebra, Amanda Renee Talley
Electronic Theses, Projects, and Dissertations
An (associative) algebra is a vector space over a field equipped with an associative, bilinear multiplication. By use of a new bilinear operation, any associative algebra morphs into a nonassociative abstract Lie algebra, where the new product in terms of the given associative product, is the commutator. The crux of this paper is to investigate the commutator as it pertains to the general linear group and its subalgebras. This forces us to examine properties of ring theory under the lens of linear algebra, as we determine subalgebras, ideals, and solvability as decomposed into an extension of abelian ideals, and nilpotency, …
Construction Of Finite Group, Michelle Soyeong Yeo
Construction Of Finite Group, Michelle Soyeong Yeo
Electronic Theses, Projects, and Dissertations
The main goal of this project is to present my investigation of finite images of the progenitor 2^(*n) : N for various N and several values of n. We construct each image by using the technique of double coset enumeration and give a proof of the isomorphism type of the image. We obtain the group 7^2: D_6 as a homomorphic image of the progenitor 2^(*14) : D_14, we obtain the group 2^4 : (5 : 4) as a homomorphic image of the progenitor 2^(*5) : (5 : 4), we obtain the group (10 x10) : ((3 x 4) : 2) …
Making Models With Bayes, Pilar Olid
Making Models With Bayes, Pilar Olid
Electronic Theses, Projects, and Dissertations
Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects …
Investigation Of Finite Groups Through Progenitors, Charles Baccari
Investigation Of Finite Groups Through Progenitors, Charles Baccari
Electronic Theses, Projects, and Dissertations
The goal of this presentation is to find original symmetric presentations of finite groups. It is frequently the case, that progenitors factored by appropriate relations produce simple and even sporadic groups as homomorphic images. We have discovered two of the twenty-six sporadic simple groups namely, M12, J1 and the Lie type group Suz(8). In addition several linear and classical groups will also be presented. We will present several progenitors including: 2*12: 22 x (3 : 2), 2*11: PSL2(11), 2*5: (5 : 4) which have produced the homomorphic images: …
Simple And Semi-Simple Artinian Rings, Ulyses Velasco
Simple And Semi-Simple Artinian Rings, Ulyses Velasco
Electronic Theses, Projects, and Dissertations
The main purpose of this paper is to examine the road towards the structure of simple and semi-simple Artinian rings. We refer to these structure theorems as the Wedderburn-Artin theorems. On this journey, we will discuss R-modules, the Jacobson radical, Artinian rings, nilpotency, idempotency, and more. Once we reach our destination, we will examine some implications of these theorems. As a fair warning, no ring will be assumed to be commutative, or to have unity. On that note, the reader should be familiar with the basic findings from Group Theory and Ring Theory.