Undergraduate Summer School 2016

The Undergraduate Summer School provides opportunities for talented undergraduate students to enhance their interest in mathematics. This program is open to undergraduates at all levels, from first-year students to those who have just completed their undergraduate education. There will be many organized activities, with some specifically targeted at students at the introductory level and others at more advanced students. There will also be time for study groups and individual projects guided by advisors, as well as other activities.

The 26th Annual PCMI Summer Session will be held June 30 – July 20, 2016.

Click HERE to apply to the Undergraduate Summer School program. 


2016 Course Descriptions:

Edward Aboufadel, Grand Valley State University

Data Analysis with Wavelets and Other Mathematical Tools

Prerequisites:  linear algebra, multivariable calculus, and at least one of calculus-based statistics, discrete mathematics, or college geometry.

Wavelets are a tool from mathematical analysis and a robust alternative to Fourier analysis.  It is suited for data that has jumps or edges, such as the grayscale intensity in digitized images.  Wavelets have been critical in the current digital revolution, finding applications in many areas such as video compression, pothole detection, medical image analysis, and the analysis and restoration of historical works of art.  This course will provide an introduction to wavelets and their application to data analysis and visualization, as well as other mathematics that can be used, such as geometry, approximation theory, and discrete mathematics.  The goal is to create innovative and unexpected techniques in order to intentionally simplify complex systems, answer new questions about the subject matter of the data, and present results in visually appealing, engaging, and meaningful ways.

 

Rebecca Nugent, Carnegie Mellon University

Visualizing and Learning the Structure in Data

What are the location and severity patterns of earthquakes off Fiji?  What characteristics of the purchases you make on Amazon determine what products they recommend?  Can we predict the presence of roads and infrastructure from images of the earth's surface? Which words should be flagged in emails as indicating spam? Or in Internet chatter indicating potential acts of terror?    Is divorce contagious among friends?  What about obesity?  What grocery store items tend to be purchased together? Beer and diapers?

All of these questions can be answered by discerning, visualizing, and learning the structure in data.  While data sets used to be limited in size by the cost of their collection, today's data analytics problems are large, complicated, and messy.  Mistakes in data entry and odd anomalies can derail analyses if not identified and addressed.  Often the real information in the data or "signal" is hidden in all the background noise.  Statistical learning methods are designed to learn, extract, and model the important information and features in a data set. These methods should always be coupled with appropriate graphical displays of the quantitative information. This course will serve to introduce the student to both the most common forms of graphical displays (and their uses and misuses) and different supervised and unsupervised learning techniques (i.e. "learning with and without labels") focusing on clustering and classification methodology. Students will also engage in projects using both graphical methods and learning models to understand data from real, interdisciplinary research problems.

 

There will be a lot of other mathematics going on at PCMI.  Participants in the UGSS  will have the chance to meet and interact with mathematicians and math teachers from around the world. The Undergraduate Summer School is for all undergraduates or recent graduates. The only prerequisite is a course in abstract algebra.

 

The Coordinators of PCMI’s Undergraduate Summer School are Steven Cox, Rice University, and Thomas Garrity, Williams College.