College

Buchtel College of Arts and Sciences (BCAS)

Date of Last Revision

2020-05-04 14:17:55

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

Included in

Analysis Commons

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