The undergraduate component of the RTG includes an extensive summer research program, as well as several new undergraduate courses.

Summer Undergraduate Research Program

Each summer, up to 10 qualified Duke undergraduates will be selected for a 9-week research program, with generous stipends provided. Students will work in small groups (3-4 students in each group) on projects of both theoretical and applied interest, and will be mentored by faculty from several departments, including Mathematics, Statistics, Electrical Engineering, Biology, and Computer Science.

For more information about this year's projects and to apply, click here.

New Courses

There will be a new First-Year Seminar offered each spring, meant to give incoming students a gentle introduction to many of the modern data analysis techniques, as well as to the general problems presented by high-dimensional, massive, and/or noisy data. The catalog course description is as follows:

The Emerging Science of Complex Data

Introduction to a new scientific problem/opportunity: large amounts of
complex and poorly understood data which must be analyzed. Survey of classical and modern data analysis techniques: factor analysis, wavelets, diffusion geometry, topology, among others. Many applications, including finance, image analysis, high-energy physics, and genomics. Discussion of past and current use of data analysis in social policy. Needed mathematical background will be provided. Opportunities for summer research.

There will also be three regularly-offered foundational courses, aimed at third and fourth year undergraduate students. Their catalog descriptions are as follows:

Geometric and Diffusion-based methods for the Analysis of Data Sets

Data sets are often modeled as point clouds in high-dimensional spaces. The geometry of such point clouds may be used for many tasks, such as constructing dictionaries for data, denoising, modeling, and inference. This course will focus on techniques for analyzing quantitatively geometric properties, for constructing dictionaries for the data, and for using both to perform inference tasks such as regression or classification. Themes for the course include multiscale quantitative analysis of point clouds, diffusion-based techniques, and computational considerations. (offered by the math department)

Computational Topology

Introduction to topology from a computational viewpoint, with a focus on applications. Themes include: basic notions of point-set topology, persistent homology, finding multi-scale topological structure in point cloud data. Algorithmic considerations emphasized. (offered by math, cross-listed with computer science)

Stochastic Geometry and Statistical Inference

Traditionally stochastic geometry has been the study of random spatial patterns including spatial point processes and random measures. Modern perspectives
include distribution theory or stochastic measures on algebraic and geometric objects such as the Grassman and Stiefel manifolds and tree spaces. This course will develop probability theory on these geometric objects and illustrate how to use this for inference and stochastic modeling. Inference problems include: dimension reduction, inference of higher-order dependencies between variables, inferences of strata and manifolds, and inference of gradients and critical points. Application domains include computational biology, machine learning and data mining, non-parametric inference, and computational geometry. (offered by statistics, cross-listed with math)