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Articles 1 - 9 of 9
Full-Text Articles in Algebra
Matrix Product Structure Of A Permuted Quasi Cyclic Code And Its Dual, Perian Perdhiku
Matrix Product Structure Of A Permuted Quasi Cyclic Code And Its Dual, Perian Perdhiku
Dissertations
In my Dissertation I will work mostly with Permuted Quasi Cyclic Codes. They are a generalization of Cyclic Codes, one of the most important families of Linear Codes in Coding Theory. Linear Codes are very useful in error detection and correction. Error Detection and Correction is a technique that first detects the corrupted data sent from some transmitter over unreliable communication channels and then corrects the errors and reconstructs the original data. Unlike linear codes, cyclic codes are used to correct errors where the pattern is not clear and the error occurs in a short segment of …
On The Local Theory Of Profinite Groups, Mohammad Shatnawi
On The Local Theory Of Profinite Groups, Mohammad Shatnawi
Dissertations
Let G be a finite group, and H be a subgroup of G. The transfer homomorphism emerges from the natural action of G on the cosets of H. The transfer was first introduced by Schur in 1902 [22] as a construction in group theory, which produce a homomorphism from a finite group G into H/H' an abelian group where H is a subgroup of G and H' is the derived group of H. One important first application is Burnside’s normal p-complement theorem [5] in 1911, although he did not use the transfer homomorphism explicitly to prove it. …
A Dynamic F5 Algorithm, Candice Mitchell
A Dynamic F5 Algorithm, Candice Mitchell
Dissertations
Gröbner bases are a “nice” representation for nonlinear systems of polynomials, where by “nice” we mean they have good computation properties. They have many useful applications, including decidability (whether the system has a solution or not), ideal membership (whether a given polynomial is in the system or not), and cryptography. Traditional Gröbner basis algorithms require as input an ideal and an admissible term ordering. They then determine a Gröbner basis with respect to the given ordering. Some term orderings lead to a smaller basis, but finding them traditionally requires testing many orderings and hoping for better results. A dynamic algorithm …
Resolving Classes And Resolvable Spaces In Rational Homotopy Theory, Timothy L. Clark
Resolving Classes And Resolvable Spaces In Rational Homotopy Theory, Timothy L. Clark
Dissertations
A class of topological spaces is called a resolving class if it is closed under weak equivalences and homotopy limits. Letting R(A) denote the smallest resolving class containing a space A, we say X is A-resolvable if X is in R(A), which induces a partial order on spaces. These concepts are dual to the well-studied notions of closed class and cellular space, where the induced partial order is known as the Dror Farjoun Cellular Lattice. Progress has been made toward illuminating the structure of the Cellular Lattice. For example: Chachólski, Parent, and Stanley have shown that it …
The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales
The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales
Dissertations
The use of standards-based grading in American public schools is increasing, offering students, parents, and teachers a new way of measuring and communicating about student achievement and performance. Parents indicate an appreciation for this method of grading, and students at the elementary grades (K-6) have improved standardized test scores in reading and math as a result of its implementation. This study seeks to determine whether standards-based grading has the same effect on students at the high school level (grades 9-12) by comparing end-of-course test scores and posttest scores of Algebra 2 students enrolled in a standards-based graded classroom with to …
Weighted Shifts Of Finite Multiplicity, Daniel S. Sievewright
Weighted Shifts Of Finite Multiplicity, Daniel S. Sievewright
Dissertations
We will discuss the structure of weighted shift operators on a separable, infinite dimensional, complex Hilbert space. A weighted shift is said to have multiplicity n when all the weights are n x n matrices. To study these weighted shifts, we will investigate which operators can belong to the Deddens algebras and spectral radius algebras, which can be quite large. This will lead to the necessary and sufficient conditions for these algebras to have a nontrivial invariant subspace.
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 …
Assessing The Impact Of A Computer-Based College Algebra Course, Ningjun Ye
Assessing The Impact Of A Computer-Based College Algebra Course, Ningjun Ye
Dissertations
USM piloted the Math Zone in Spring 2007, a computer-based program in teaching MAT 101and MAT 099 in order to improve student performance. This research determined the effect of the re-design of MAT 101 on student achievements in comparison to a traditional approach to the same course. Meanwhile, the study investigated possible effects of the Math Zone program on students’ attitude toward studying mathematics.
This study shows that there was no statistically significant difference on MAT101 final exam scores between the Math Zone students and the Classroom students in Fall 2007, Spring 2008 and Fall 2008. At the same time, …
A Generalization Of Cayley Graphs For Finite Fields, Dawn M. Jones
A Generalization Of Cayley Graphs For Finite Fields, Dawn M. Jones
Dissertations
A central question in the area of topological graph theory is to find the genus of a given graph. In particular, the genus parameter has been studied for Cayley graphs. A Cayley graph is a representation of a group and a fixed generating set for that group. A group is said to be planar if there is a generating set which produces a planar Cayley graph. We say that a group is toroidal if there is a generating set that produces a toroidal Cayley graph and if there are no generating sets which produce a planar Cayley graph. Characterizations for …