Masters Thesis
Learning Manifolds and Manifold Learning: From the Whitney Embedding Theorem to the Universal Approximation Theorem With Injective Neural Networks | With Matti Lassas & Jinpeng Liu | 5/5
In this thesis I provide an introduction to contemporary machine learning research from the perspective of geometry and topology. I trace the history of the manifold from its definition and importance in geometry, examined through the proof of the Whitney embedding theorem, followed by its significance in machine learning research in the manifold hypothesis and manifold learning. The thesis is concluded with a proof of the universal approximation theorem with injective neural networks, a new result. Available at
Helda.Bachelors Thesis
Klein Has Me In Stitches! (An Exploration of Mathematical Constructions of the Klein Quartic and Creation of Analogous Crochet Models) | With Jerry Shurman | B
In this paper I apply Daina Taimina’s hyperbolic crochet method to the Klein Quartic, a known hyperbolic surface. With this technique I examine the many symmetries of the object and discover how different model types demonstrate different symmetries. I also use the subject to introduce important concepts in the study of non-Euclidean, particularly hyperbolic, geometries. Available at
Reed Library.