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Articles 1 - 5 of 5
Full-Text Articles in Mathematics
A Comparison Of Cryptographic Methods, Christopher Gilmore
A Comparison Of Cryptographic Methods, Christopher Gilmore
Senior Honors Theses
While elliptic curve cryptography and quantum cryptography are significantly different branches of cryptography, they provide a suitable reference point for comparison of the value of developing methods used in the present and investing in methods to be used in the future. Elliptic curve cryptography is quite common today, as it is generally secure and efficient. However, as the field of cryptography advances, the value of quantum cryptography’s inherent security from its basic properties should be considered, as a fully realized quantum cryptosystem has the potential to be quite powerful. Ultimately, it is of critical importance to determine the value of …
Gödel's Incompleteness Theorems, Derick Swarey
Gödel's Incompleteness Theorems, Derick Swarey
Senior Honors Theses
The Incompleteness Theorems of Kurt Godel are very famous both within and outside of mathematics. They focus on independence and consistency within mathematics and hence a more thorough understanding of these is beneficial to their study. The proofs of the theorems involve many ideas which may be unfamiliar to many, including those of formal systems, Godel numbering, and recursive functions and relations. The arguments themselves mirror the Liar’s Paradox in that Godel constructs a statement asserting its own unprovability and then shows that such a statement and its negation must both be independent of the system, otherwise the system is …
The Traveling Salesman Problem: An Analysis And Comparison Of Metaheuristics And Algorithms, Mason Helmick
The Traveling Salesman Problem: An Analysis And Comparison Of Metaheuristics And Algorithms, Mason Helmick
Senior Honors Theses
One of the most investigated topics in operations research is the Traveling Salesman Problem (TSP) and the algorithms that can be used to solve it. Despite its relatively simple formulation, its computational difficulty keeps it and potential solution methods at the forefront of current research. This paper defines and analyzes numerous proposed solutions to the TSP in order to facilitate understanding of the problem. Additionally, the efficiencies of different heuristics are studied and compared to the aforementioned algorithms’ accuracy, as a quick algorithm is often formulated at the expense of an exact solution.
A Phenomenological Study Of Perceived Factors Influencing Math Teachers' Technology Self-Efficacy, Jenna Finnegan
A Phenomenological Study Of Perceived Factors Influencing Math Teachers' Technology Self-Efficacy, Jenna Finnegan
Doctoral Dissertations and Projects
The purpose of this study was to explore how a teacher's technology self-efficacy influences decisions they make about the use of technology in their classrooms. The factors influencing teachers' technology self-efficacy were examined through a qualitative transcendental phenomenological research design. This study's theoretical framework was based on the combination of social cognitive theory and self-efficacy theory; both provide insight into how external and internal factors can influence a person's perception of their abilities. Using these theories helped identify and describe the self-efficacy experiences of high school math teachers. This research was conducted during the 2020-2021 school year using a qualitative …
A Phenomenological Study: The Lived Experience Of Self-Described Math-Anxious Students Attending College Online, Toni Nicole Sawhill
A Phenomenological Study: The Lived Experience Of Self-Described Math-Anxious Students Attending College Online, Toni Nicole Sawhill
Doctoral Dissertations and Projects
The purpose of this transcendental phenomenological study is to describe the lived experience of mathematics anxiety for self-described math-anxious students who completed an undergraduate mathematics course online at a university in the Pacific Northwest part of the United States. The theory guiding this study is community of inquiry (COI) introduced by early pragmatist philosophers C. S. Peirce and John Dewey and further developed by D. Randy Garrison, Terry Anderson, and Walter Archer as mathematics anxiety is a learned behavior based on students’ experiences. This research study answers the central research question: What are the lived experiences of mathematics anxiety for …