Holden Swindell

Writing

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I have informally written on a number of topics in mathematics. You can find most of this writing below.

If you notice any errors or have any suggestions or ideas you want to share, you can contact me using the information here.

Research Projects

• "Approximating the Uniform Norm via Discrete Sampling" (REU 2023) (PDF)

Short Notes

Short notes on assorted topics, including proofs, observations, ideas for further theory, and resources for students — essentially mathematical versions of GitHub's gists.

• "A Proof of Induction" (PDF)
• "A Proof of the Fundamental Theorem of Calculus" (PDF)
• "Homomorphisms and Generating Sets" (PDF)
• "Redundancy in the Axioms for a Topology" (PDF)
• "Using Connectedness to Show Constancy" (PDF)