Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Entire DC Network
Boolean And Profinite Loops, Benjamin Andrew Phillips
Boolean And Profinite Loops, Benjamin Andrew Phillips
Dissertations
A Quasigroup G consists of a set G together with a binary operation ∗ : G × G → G such that, for any elements a, b ∈ G there are unique solutions to the equations a ∗ x = b and y ∗ a = b within G. A loop is a quasigroup which also contains a 2-sided identity element. More heuristically, loops are essentially non-associative groups. However, without an associative binary operation, some of the familiar properties found in groups, such as 2-sided inverse, need not be present in loops.
The study of quasigroups and loops emerges …
Characterizing And Supporting Change In Algebra Students' Representational Fluency In A Cas/Paper-And-Pencil Environment, Nicole L. Fonger
Characterizing And Supporting Change In Algebra Students' Representational Fluency In A Cas/Paper-And-Pencil Environment, Nicole L. Fonger
Dissertations
Representational fluency (RF) includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students’ RF in learning environments that utilize both computer algebra systems (CAS) and paper-and-pencil. The purpose of this research was to: (a) characterize change in ninth-grade algebra students’ RF in solving problems involving linear equations, and (b) determine conditions of a CAS and paper-and-pencil learning environment in which those students changed their RF.
Change in RF was measured by comparing results from initial to …
Rank-Based Estimation And Prediction For Mixed Effects Models In Nested Designs, Yusuf K. Bilgic
Rank-Based Estimation And Prediction For Mixed Effects Models In Nested Designs, Yusuf K. Bilgic
Dissertations
Hierarchical designs frequently occur in many research areas. The experimental design of interest is expressed in terms of fixed effects but, for these designs, nested factors are a natural part of the experiment. These nested effects are generally considered random and must be taken into account in the statistical analysis. Traditional analyses are quite sensitive to outliers and lose considerable power to detect the fixed effects of interest.
This work proposes three rank-based fitting methods for handling random, fixed and scale effects in k-level nested designs for estimation and inference. An algorithm, which iteratively obtains robust prediction for both scale …
Variations On A Graph Coloring Theme, Bryan Phinezy
Variations On A Graph Coloring Theme, Bryan Phinezy
Dissertations
Historically, the subject of graph colorings has been the most popular research area in graph theory. There are many problems in mathematics and in real life that can be represented by a graph and whose solution involves finding a specific coloring of this graph. Our research consists of two parts: (1) combinatorial problems and vertex colorings and (2) distance-defined colorings. In this research, we show that certain combinatorial puzzles and problems can be placed in a graph coloring setting and graph colorings can be defined in terms of distance in graphs that are useful in applications.
Two vertices u and …