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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 20 for “"abstract algebra"”.
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Understanding abstract algebra concepts
… discusses various theoretical perspectives on abstract concept formation. Students' reasoning about abstract objects is described based on theoretical proposition that abstraction is a shift from abstract to concrete. Existing literature suggested a theoretical framework for the study. The …
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Learning and understanding in abstract algebra
… learning and understanding in an undergraduate abstract algebra class were described using Tall and Vinner's notion of a concept image, which is the entire cognitive structure associated with a concept, including examples, nonexamples, definitions, representations, and results. Prominent …
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Relating Understanding of Inverse and Identity to Engagement in Proof in Abstract Algebra
… with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of iterative coding drawing on grounded theory methodology (Charmaz, 2000, 2006; Glaser and Strauss, 1967). In the first phase, I analyzed the participants' interview responses to …
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Prospective Teachers' Knowledge of Secondary and Abstract Algebra and their Use of this Knowledge while Noticing Students' Mathematical Thinking
… of connections between concepts in Abstract Algebra and high school Algebra, as well as their use of this understanding while engaging in the teaching practice of noticing students' mathematical thinking. I drew on the theory, Knowledge of Nonlocal Mathematics for Teaching, which …
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Geometric Constructions from an Algebraic Perspective
… at times seem so unrelated such as Geometry and Abstract Algebra. These two branches of math would seem unrelated at first glance. I will try to bridge Geometry and Abstract Algebra just a bit with the following topics. We can be sure that after we construct our basic parallel and perpendicular …
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Designing visually rich mathmatical investing tools for repetitive geometric artifacts
… geometry (low-dimensional Euclidean geometry), abstract algebra, theoretical computer science, and human-computer interaction (HCI). Geometry provides examples of rich visual artifacts that have many subtle properties. Abstract algebra provides a means and a framework for understanding and …
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On Emmy Noether and Her Algebraic Works
… mathematics and science community . Her work in algebra and more specifically, ring theory, are said to be foundations for much of the work done since then. Her developments in abstract algebra helped to unify topology, geometry, logic and linear algebra. Also, Noether's theorem is a widely used …
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Teachers' Reflection on Inquiry-Oriented Instruction in Online Professional Development
… their implementation of IOI materials covering Abstract Algebra topics in online work groups developed to support teachers in implementing IOI. I analyze both reflection and enactment through the components of IOI characterized through the Instructional Triangle. Analysis of the teachers' …
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Facilitating Instructional Change: A Case Study on Diffusion of Curriculum Innovation
… instructors teaching with the Inquiry-Oriented Abstract Algebra (Larsen et al., 2013) curriculum materials. I investigate the relationship between the intent of the instructional support model and the facilitator's beliefs and goals for the professional development, using video data collected …
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AN INTRODUCTION TO BOOLEAN ALGEBRAS
<p>This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered …
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A History of Complex Simple Lie Algebras
… mathematicians recognized this as a division of abstract algebra, the area became known as “continuous transformation groups," but we now refer to them as Lie groups.</p> <p>Patterns and structures emerged from their work, such as describing Lie groups in connection with their associated Lie …
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The Irreducible Representations of D2n
… most intuitive non-abelian group we encounter in abstract algebra. I will compute the representations and characters of D2n and my thesis will be an explanation of these computations. When n = 2k + 1 we will show that there are k + 2 irreducible representations of D2n, but when n = 2k we will see …
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Algebraic aspects of propositional logic
… we seek to examine the connection between abstract algebra and propositional logic. We start by considering the category Bool of Boolean algebras, the algebraic counterpart of classical propositional logic. We provide an algebraic definition of theories and models of classical logic and …
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Examining Connections among Instruction, Conceptual Metaphors, and Beliefs of Instructors and Students
… of instructors and students from two abstract algebra classes. This research takes the form of a case study in which I answer four research questions, each addressing a relationship between instruction and beliefs or conceptual understanding. Specifically, these research questions are: …
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On the foldability of rigid origami
… rigidity theory, graph theory, linkage folding, abstract algebra and computer science. (2) We develop the rigidity theory for rigid origami under the folding angle description, including the generic rigidity and local rigidity. Generic rigidity studies how the rigidity is determined from the …
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Learning Mixed Multinomial Logit Models
… existence of ϵ-close estimates using tools from abstract algebra and will show that there exists an algorithm that can learn a general K-MNL models with probability at least 1−δ, if identifiable, using polynomial number of data samples and polynomial number of operations (in 1 ϵ and 1 δ ), under …
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Banach algebras on groups and semigroups
This thesis concerns the theory of Banach algebras, particularly those coming from abstract harmonic analysis. The focus for much of the thesis is the theory of the ideals of these algebras. In the final chapter we use semigroup algebras to solve an open probelm in the theory of C*-algebras. …