Researcher ORCID Identifier

0009-0006-8564-9803

Graduation Year

2025

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Bahar Acu

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Rights Information

© 2025 Charlotte N Richards

Abstract

Mathematics has clear benefits in education, from preparing students for future careers to teaching them how to problem-solve. While mathematics achievement has been falling in recent decades, students claim that the problem is not the mathematics itself, but the ‘boring’ classroom material that feels removed from real life. More advanced mathematics topics, such as topology, could offer a solution, as their applications lie in countless fields. However, topology has been restricted to upper-level mathematics, disregarding the potential benefits of making this material broadly reachable for a junior high-school audience. In this paper, we analyze five different proofs of the theorem concerning the Classification of Surfaces with this goal of accessibility in mind. Based on these findings, we will generate a more accessible, holistic proof of the Classification of Surfaces that is both rigorous and approachable for students experienced with single-variable calculus. Through this project, we aim to increase engagement in mathematics and place it into the real world.

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