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Articles 1  9 of 9
FullText Articles in Education
Analyzing Common AlgebraRelated Misconceptions And Errors Of Middle School Students., Sarah B. Bush
Analyzing Common AlgebraRelated Misconceptions And Errors Of Middle School Students., Sarah B. Bush
Electronic Theses and Dissertations
The purpose of this study was to examine common algebrarelated misconceptions and errors of middle school students. In recent years, success in Algebra I is often considered the mathematics gateway to graduation from high school and success beyond. Therefore, preparation for algebra in the middle grades is essential to student success in Algebra I and high school. This study examines the following research question: What common algebrarelated misconceptions and errors exist among students in grades six and eight as identified on student responses on an annual statewide standardized assessment? In this study, qualitative document analysis of existing data was used ...
HilbertSamuel And HilbertKunz Functions Of ZeroDimensional Ideals, Lori A. Mcdonnell
HilbertSamuel And HilbertKunz Functions Of ZeroDimensional Ideals, Lori A. Mcdonnell
Dissertations, Theses, and Student Research Papers in Mathematics
The HilbertSamuel function measures the length of powers of a zerodimensional ideal in a local ring. Samuel showed that over a local ring these lengths agree with a polynomial, called the HilbertSamuel polynomial, for sufficiently large powers of the ideal. We examine the coefficients of this polynomial in the case the ideal is generated by a system of parameters, focusing much of our attention on the second Hilbert coefficient. We also consider the HilbertKunz function, which measures the length of Frobenius powers of an ideal in a ring of positive characteristic. In particular, we examine a conjecture of Watanabe and ...
Homology Of Artinian Modules Over Commutative Noetherian Rings, Micah J. Leamer
Homology Of Artinian Modules Over Commutative Noetherian Rings, Micah J. Leamer
Dissertations, Theses, and Student Research Papers in Mathematics
This work is primarily concerned with the study of artinian modules over commutative noetherian rings.
We start by showing that many of the properties of noetherian modules that make homological methods work seamlessly have analogous properties for artinian modules. We prove many of these properties using Matlis duality and a recent characterization of Matlis reflexive modules. Since Matlis reflexive modules are extensions of noetherian and artinian modules many of the properties that hold for artinian and noetherian modules naturally follow for Matlis reflexive modules and more generally for minimax modules.
In the last chapter we prove that if the Betti ...
Groups And Semigroups Generated By Automata, David Mccune
Groups And Semigroups Generated By Automata, David Mccune
Dissertations, Theses, and Student Research Papers in Mathematics
In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, selfsimilar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups ``expanding automaton semigroups''. We show that this class strictly contains the class of automaton semigroups, and we show that the class of asynchronous automaton semigroups strictly contains the class of expanding automaton semigroups. We demonstrate that undecidability arises in the actions of expanding automaton semigroups and semigroups ...
Annihilators Of Local Cohomology Modules, Laura Lynch
Annihilators Of Local Cohomology Modules, Laura Lynch
Dissertations, Theses, and Student Research Papers in Mathematics
In many important theorems in the homological theory of commutative local rings, an essential ingredient in the proof is to consider the annihilators of local cohomology modules. We examine these annihilators at various cohomological degrees, in particular at the cohomological dimension and at the height or the grade of the defining ideal. We also investigate the dimension of these annihilators at various degrees and we refine our results by specializing to particular types of rings, for example, Cohen Macaulay rings, unique factorization domains, and rings of small dimension.
Adviser: Thomas Marley
Epistemic Strategies For Solving TwoDimensional Physics Problems, Mary Elyse HingHickman
Epistemic Strategies For Solving TwoDimensional Physics Problems, Mary Elyse HingHickman
Physics Theses & Dissertations
An epistemic strategy is one in which a person takes a piece of knowledge and uses it to create new knowledge. Students in algebra and calculus based physics courses use epistemic strategies to solve physics problems. It is important to map how students use these epistemic strategies to solve physics problems in order to provide insight into the problem solving process.
In this thesis three questions were addressed: (1) What epistemic strategies do students use when solving twodimensional physics problems that require vector algebra? (2) Do vector preconceptions in kinematics and Newtonian mechanics hinder a student's ability to apply ...
Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette
Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette
Dissertations, Theses, and Student Research Papers in Mathematics
In this work, I offer an alternative presentation theory for C*algebras with applicability to various other normed structures. Specifically, the set of generators is equipped with a nonnegativevalued function which ensures existence of a C*algebra for the presentation. This modification allows clear definitions of a "relation" for generators of a C*algebra and utilization of classical algebraic tools, such as Tietze transformations.
Predictors Of Student Outcomes In Developmental Math At A Public Community And Technical College, Linda Darlene Hunt
Predictors Of Student Outcomes In Developmental Math At A Public Community And Technical College, Linda Darlene Hunt
Theses, Dissertations and Capstones
With the wide range of abilities of community college students, proper course placement is crucial. Therefore, having better predictors of success can help improve placement of students for their achievement. This study analyzed student predictors, instructor predictors, and classroom predictors in relation to student final exam score and student final grade in Elementary Algebra and Intermediate Algebra classes. Student predictors included gender, ACT math score, SAT math score, community college enrollment, math pretest score, and ASC grade. Instructor predictors included gender, employment status, Mozart music use, and ALEKS software use. Classroom predictors included time of day, number of class meetings ...
On The Betti Number Of Differential Modules, Justin Devries
On The Betti Number Of Differential Modules, Justin Devries
Dissertations, Theses, and Student Research Papers in Mathematics
Let R = k[x_{1}, ..., x_{n}] with k a field. A multigraded differential Rmodule is a multigraded Rmodule D with an endomorphism d such that d^{2} = 0. This dissertation establishes a lower bound on the rank of such a differential module when the underlying Rmodule is free. We define the Betti number of a differential module and use it to show that when the homology ker d/im d of D is nonzero and finite dimensional over k then there is an inequality rank_{R} D ≥ 2^{n}. This relates to a problem of Buchsbaum ...