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Full-Text Articles in Number Theory
An Overview Of Monstrous Moonshine, Catherine E. Riley
An Overview Of Monstrous Moonshine, Catherine E. Riley
Channels: Where Disciplines Meet
The Conway-Norton monstrous moonshine conjecture set off a quest to discover the connection between the Monster and the J-function. The goal of this paper is to give an overview of the components of the conjecture, the conjecture itself, and some of the ideas that led to its solution. Special focus is given to Klein's J-function.
The Examination Of The Arithmetic Surface (3, 5) Over Q, Rachel J. Arguelles
The Examination Of The Arithmetic Surface (3, 5) Over Q, Rachel J. Arguelles
Electronic Theses, Projects, and Dissertations
This thesis is centered around the construction and analysis of the principal arithmetic surface (3, 5) over Q. By adjoining the two symbols i,j, where i2 = 3, j2 = 5, such that ij = -ji, I can produce a quaternion algebra over Q. I use this quaternion algebra to find a discrete subgroup of SL2(R), which I identify with isometries of the hyperbolic plane. From this quaternion algebra, I produce a large list of matrices and apply them via Mobius transformations to the point (0, 2), which is the center of my Dirichlet domain. This …
New Theorems For The Digraphs Of Commutative Rings, Morgan Bounds
New Theorems For The Digraphs Of Commutative Rings, Morgan Bounds
Rose-Hulman Undergraduate Mathematics Journal
The digraphs of commutative rings under modular arithmetic reveal intriguing cycle patterns, many of which have yet to be explained. To help illuminate these patterns, we establish a set of new theorems. Rings with relatively prime moduli a and b are used to predict cycles in the digraph of the ring with modulus ab. Rings that use Pythagorean primes as their modulus are shown to always have a cycle in common. Rings with perfect square moduli have cycles that relate to their square root.
Winnability Of The Group Labeling Lights Out Game On Complete Bipartite Graphs, Christian J. Miller
Winnability Of The Group Labeling Lights Out Game On Complete Bipartite Graphs, Christian J. Miller
McNair Scholars Manuscripts
For an arbitrary graph, we can play Lights Out on it if we assign a number label to each of the vertices of a graph G, representing states of on/off in the original Lights Out game, with the edges connecting those vertices representing the buttons that are adjacent to each other. This project is focused on a slightly modifed version of the game's original rules, with the labels for the vertices coming from the group Zn. It is not always possible to win the game. We will be investigating the values of n for which this group labeling "Lights Out!" …
A Study Of Finite Symmetrical Groups, May Majid
A Study Of Finite Symmetrical Groups, May Majid
Theses Digitization Project
This study investigated finite homomorphic images of several progenitors, including 2*⁵ : S₅, 2*⁶ : A₆, and 3*⁵ : C₅ The technique of manual of double coset enumeration is used to construct several groups by hand and computer-based proofs are given for the isomorphism types of the groups that are not constructed.
Enumeration And Symmetric Presentations Of Groups, With Music Theory Applications, Jesse Graham Train
Enumeration And Symmetric Presentations Of Groups, With Music Theory Applications, Jesse Graham Train
Theses Digitization Project
The purpose of this project is to construct groups as finite homomorphic images of infinite semi-direct products. In particular, we will construct certain classical groups and subgroups of sporadic groups, as well groups with applications to the field of music theory.
Symmetric Generation, Lisa Sanchez
Symmetric Generation, Lisa Sanchez
Theses Digitization Project
The purpose of this project is to conduct a systematic search for finite homomorphic images of infinite semi-direct products mn : N, where m = 2,3,5,7 and N <̲ Sn and construct by hand some of the important homomorphic images that emerge from the search.
Symmetric Generation Of M₂₂, Bronson Cade Lim
Symmetric Generation Of M₂₂, Bronson Cade Lim
Theses Digitization Project
This study will prove the Mathieu group M₂₂ contains two symmetric generating sets with control grougp L₃ (2). The first generating set consists of order 3 elements while the second consists of involutions.