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Teaching Topology with Code

This paper was written as part of a final project for MATH 412: Computational Topology, taught by Paul Bendich during the Falll 2014 semester at Duke University.

Click images for interactive demonstrations.

Vietoris-Rips ComplexSensor Networks

Abstract

The popular data visualization library D3.js was used to create illustrations of several key concepts covered in an undergraduate course in topology. Approaches for developing visualizations which augment the other learning resources found in undergraduate math courses are discussed. Three different visualizations focusing on the topics of height-functions, Rips-complexes, and dynamic sensor networks are offered as case studies in using code to illustrate abstract concepts. I give general suggestions for incorporating such learning tools into undergraduate math courses while analyzing the design of these interactive tools at a high level.

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Final paper written for MATH 412: Computational Topology, taught by Paul Bendich.

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