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Full-Text Articles in Set Theory
Orientable Quadrilateral Embeddings Of Cartesian Products Of Graphs, Matthew Farnsworth, Max Goskie, Adrian Volpe, Jackson Sayre
Orientable Quadrilateral Embeddings Of Cartesian Products Of Graphs, Matthew Farnsworth, Max Goskie, Adrian Volpe, Jackson Sayre
SPARK Symposium Presentations
In the spirit of Pisanski (1989) we consider orientable quadrilateral embeddings of Cartesian products of cycles on surfaces. We offer a constructive example of such an embedding of three low-order cycles. Then we show more generally that such embeddings exist for the product of a 2-cycle, and even cycle, and an arbitrary third cycle. We represent our graphs using rotation schemes to show this existence. Use of rotation schemes led to the ultimate characterization of our findings visually, providing conjectures for generalizations of products of three cycles.
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy
Honors Scholars Collaborative Projects
This thesis evaluates the function of the current history of mathematics methodologies and explores ways in which historiographical methodologies could be successfully implemented in the field. Traditional approaches to the history of mathematics often lack either an accurate portrayal of the social and cultural influences of the time, or they lack an effective usage of mathematics discussed. This paper applies a holistic methodology in a case study of Kurt Gödel’s influential work in logic during the Interwar period and the parallel rise of intellectual modernism. In doing so, the proofs for Gödel’s Completeness and Incompleteness theorems will be discussed as …