College
Buchtel College of Arts and Sciences (BCAS)
Date of Last Revision
2023-05-03 18:38:38
Major
Mathematics
Honors Course
Mathematics Honors Thesis
Number of Credits
2
Degree Name
Bachelor of Science
Date of Expected Graduation
Fall 2020
Abstract
This text explores elementary analysis through the lens of non-standard analysis. The hyperreals will be proven to be implied by the existence of the reals via the axiom of choice. The notion of a hyperextension will be defined, and the so-called Transfer Principle will be proved. This principle establishes equivalence between results in real and hyperreal analysis. Sequences, subsequences, and limit suprema/infima will then be explored. Finally, integration will be considered.
Research Sponsor
Dmitry Golovaty
First Reader
Curtis Clemons
Second Reader
J Patrick Wilber
Honors Faculty Advisor
Curtis Clemons
Recommended Citation
Cebula, Logan, "Elementary Hyperreal Analysis" (2020). Williams Honors College, Honors Research Projects. 1005.
https://ideaexchange.uakron.edu/honors_research_projects/1005