Dates: May 15-June 23, 2017
Number of students: up to four undergraduate students will be selected.
Participants will begin by learning to play a two-player mathematical game involving polynomials. Then they will try to find the optimal strategy for the game and prove that their strategy is correct. The same problem can be formulated in more general settings than polynomials. A sufficiently general solution will likely be publishable. Relevant background in algebra (Commutative Rings) and geometry (Algebraic Geometry) will be provided but not assumed.
Dates: June 5-July 26, 2017
Number of students: up to four undergraduate students will be selected.
The NU-UI Mathematics Summer REU program is a Research Experiences for Undergraduates (REU) program in mathematics for students from Nazarbayev University (NU) in Kazakhstan and the University of Illinois (UI). The program will be held at the University of Illinois campus in Urbana-Champaign from June 5 through July 26, 2017. Up to four UI students will be selected to participate in this program alongside students from Nazarbayev University. In addition to group research projects, the program includes a mini-course in applied probability and stochastic processes, a bootcamp in Mathematica programming, a variety of lectures and seminar talks, and workshops on building career skills and preparing for graduate school. For more details about the program and selection criteria, visit http://go.illinois.edu/mathreu
Dates: May 30-July 15, 2017
Number of students: up to four undergraduate students will be selected for the two projects Video as a Sensor and Visual Cliffs, Virtual Reality and Movement Disorders
The near future promises a rise in sensor-equipped vehicles. While machine learning is a core enabling technology, we believe that some models and context may provide additional benefits. Our goal is to compute some of the geometry of traffic surrounding the driver and understand how this affects driving decisions. Hopefully you will gain some expertise which is valuable in this exciting area (think Uber and Tesla). Solid coding ability is required. Video
Dates: May 30-July 15, 2017
Number of students: up to four undergraduate students will be selected for the two projects Video as a Sensor and Visual Cliffs, Virtual Reality and Movement Disorders
Virtual reality (VR) and Brain-Computer Interfaces (BCI) are entering into the public consciousness. In this project, which is a continuation of a Spring 2017 project, we want to further develop a VR-mechanics-BCI system for understanding the effect of fall-related anxiety in older adults with and without movement disorders. The VR component will be developed on an HTC Vive or similar VR platform, while the BCI component will involve a combination of signal processing, pattern recognition and machine learning on time series data from a mobile neuroimaging system (i.e., electroencephalography (EEG) or functional near-infrared spectroscopy (fNIRS)). Solid coding skills are needed. This project promises to be challenging, but will give you expertise in a number of exciting areas. Video
Dates: May 15 - June 23, 2017
Number of students: up to three undergraduate students will be selected
In quantum mechanics, the evolution of quantum states is described in terms of the solutions of the SchrÃ¶dinger equation, that depends on the Laplacian operator. Such interpretation can be adapted to the case in which the particle is confined to a finite graph. In this project we intend to use spectral graph theory to understand physical quantities (observables) associated to graph quantum mechanics, such as the total energy, entropy, etc and to compare them with properties of the graph such as connectivity, number of cycles, etc. Applications of this approach include diffusion of information on social networks, as well as a combinatorial analysis of the syntaxis of written texts.