Past Projects

Spring 2024

Jason Liu: Introduction to Algebraic Geometry

Jason Liu.pdf

Fiona Yang: The Strong Law of Large Numbers

Fiona Yang.pdf

Paris Yang: Smooth Manifolds

Paris Yang.pdf

Jinyu Yang: Application of Representation Theory and Character Tables for S4 and A4

Jinyu Yang.pdf

Eric Wai Chee Ching: Two approaches to show the Hairy Ball theorem

Eric Wai Chee Ching.pdf

Derek Zang: Point Vortex Interactions in a Bounded Domain

Derek Zang.pdf

Danielle Aylward: An Exploration of Lattice Based Cryptography

Danielle Aylward.pdf

Eamon Zhang: The Twenty-Seven Lines theorem

Eamon Zhang.pdf

Kimberly Horvat: How to Detect Holes in a Shape: An Introduction to the Fundamental Group

Kimberly Horvat.pdf

Elhussein Abdelhamid: Spectral theorem in quantum mechanics

Elhussein Abdelhmaid.pdf

Spring 2023

Sarah Aguiar: The Elusive Search for Electoral Inequality

Nicholas DeDonato: Fenchel's Theorem

Adam French: An Introduction to Riemann Surfaces and a Few Applications

William Lee: Group Actions and Representation Theory

Tina Li: Six Versions of the Axiom of Choice

Jenny Lin: Neural Networks and Deep Learning


Jacob Niyazov: Markov Chains

Zifan Wang: Circumference-Area Ratio of a Hyperbolic Disc

Paris Yang: Dihedral Groups

Shuhan Yang: The Fundamental Group of the Klein Bottle

Fall 2019

Alexander Agishtein: Convex Optimization; Or, How I learned to Love Iterative Descent Methods

Spencer Cattalani: Verification of the Hilali Conjecture in Dimensions up to 20

Brandon Gontmacher: The Worst Way to Prove Lagrange's Four Squares Theorem

Yanbing Gu: 2D Nonlinear Dynamical Systems and the Poincare-Bendixson Theorem

Julian Michele: Hausdorff Measure, Dimension of Fractal Sets, and Rectifiable Curves

Iftiar Rana: Machine Learning

Renyu Rao: Linear Programming

Daniel Waxman: Topology and Physics of the Hopf Map

Ajmain Yamin: Plane Conics

Spring 2019

Michael Dapolito: Understanding the Schwarzchild Metric

Amber Han: Hausdorff Measure and Dimension

D'Andra Millien: General Sum Games

Lauren Perrotta: Counting Integer Points in Rational Polytopes 

Matthew Stern: Brownian Motion

Ajmain Yamin: An Introduction to Homology Groups and the Hairy Ball Theorem