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Discrete Mathematics and Combinatorics

Discrete mathematics is a broad subfield of applied mathematics that deals with the topic of enumerating and processing finite sets of objects. It draws on a wide variety of areas of mathematics, including geometry, algebra, and analysis, and in turn has a wide variety of applications from designing codes and circuits, to modeling computation, to algorithms for finding directions in a road network and finding good ways to do viral marketing. Researchers in CAM in this area work on topics such as studying incentives in online systems, designing algorithms to find near-optimal solutions to hard discrete optimization problems, to determining good ways to send information through networks, to figuring out how to organize and implement city-wide bike-sharing systems.