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Full-Text Articles in Physical Sciences and Mathematics
John Horton Conway: The Man And His Knot Theory, Dillon Ketron
John Horton Conway: The Man And His Knot Theory, Dillon Ketron
Electronic Theses and Dissertations
John Horton Conway was a British mathematician in the twentieth century. He made notable achievements in fields such as algebra, number theory, and knot theory. He was a renowned professor at Cambridge University and later Princeton. His contributions to algebra include his discovery of the Conway group, a group in twenty-four dimensions, and the Conway Constellation. He contributed to number theory with his development of the surreal numbers. His Game of Life earned him long-lasting fame. He contributed to knot theory with his developments of the Conway polynomial, Conway sphere, and Conway notation.
Zn Orbifolds Of Vertex Operator Algebras, Daniel Graybill
Zn Orbifolds Of Vertex Operator Algebras, Daniel Graybill
Electronic Theses and Dissertations
Given a vertex algebra V and a group of automorphisms of V, the invariant subalgebra VG is called an orbifold of V. This construction appeared first in physics and was also fundamental to the construction of the Moonshine module in the work of Borcherds. It is expected that nice properties of V such as C2-cofiniteness and rationality will be inherited by VG if G is a finite group. It is also expected that under reasonable hypotheses, if V is strongly finitely generated and G is reductive, VG will also be strongly finitely generated. This is an analogue …
Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus
Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus
Electronic Theses and Dissertations
The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or …
Analyzing Common Algebra-Related Misconceptions And Errors Of Middle School Students., Sarah B. Bush
Analyzing Common Algebra-Related Misconceptions And Errors Of Middle School Students., Sarah B. Bush
Electronic Theses and Dissertations
The purpose of this study was to examine common algebra-related 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 algebra-related 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 …