Project: 6nimmt! and Neural Networks
Project supervisor: Benjamin Antieau
Description: 6nimmt! is a simple card game published by Amigo. Players (2-10) are dealt a random hand and aim to play through the hand while accumulating as few points as possible. This is difficult because the play is simultaneous. The aim of this project is to use basic techniques from neural networks, which have been successful in some other random games like Backgammon, to explore winning strategies for playing 6nimmt! Students will learn some game theory and play trial games in person of 6nimmt! After some discussion, they will then implement various strategies using pre-existing software to host virtual tournaments of 10,000s of games to study the success of these strategies in different environments.
Prerequisites: familiarity with card games and python a plus.
Project: Designing Metamaterials
Project supervisor: David Nicholls
Description: Metamaterials are assemblies of naturally occurring substances which exhibit unusual properties such as zero permeability and/or permittivity, or negative index of refraction. Applications include high sensitivity diagnostics, superresolution imaging, and cloaking. Professor Nicholls’ group has developed a set of algorithms for simulating layered media in the optical regime, and the goal of this project is to use an implementation of this to design metamaterials. This project will focus on utilizing an open source machine learning platform (such as TensorFlow) to identify metamaterials of interest to engineers.
Prerequisites: Calculus, linear algebra, ODEs. Math 480/481 and MCS 471 a plus. Coding experience required.
Project: Magnetic Waves
Project supervisor: Mimi Dai
Description: Magnetic fields are well known to be vitally important on the earth and in the whole universe. The Earth’s magnetic field protects our planet from the charged particles streaming out from the Sun in the form of the solar wind. Magnetic fields in outer space play a significant role in star formation. Magnetic fields are also extensively used in industry to control the motion of liquid metals. The study of the dynamics of magnetic fields in electrically conducting fluids, such as in plasmas, liquid metals, and salt water, is called magneto-hydrodynamics, or MHD for short. In this project, we will investigate a few mathematical MHD models and perform simulations to visualize different types of magnetic waves. The models involved are 1-dimensional or 2-dimensional.
Prerequisites: Math 220 and knowledge of Matlab programming.
Project: Visualizing triangulations and tessellations with 3D printing
Project supervisor: Teddy Einstein
Description: Triangulations of surfaces are useful for studying the topological properties of surfaces using combinatorial techniques. The goal of this project is to produce 3D models to help illustrate how surfaces can be tiled by triangles or other polygons. Objectives include learning how to plot 3D models of surfaces using software, 3D-printing these models, and producing tessellations by triangles and other shapes on these surfaces. These models will be used to further explore the geometry of surfaces and other related topics from geometry and topology, such as the combinatorial Gauss-Bonnet Theorem.
Prerequisites: Multivariable calculus, some familiarity with programming (e.g. Python) and/or Mathematica.