Discrete Math, Operations Research, and Probability
Discrete mathematics is the study of objects that are fundamentally discrete (made up of distinct and separated parts) as opposed to continuous. It is an area of mathematics that has been increasing in importance in recent decades, in part because of the advent of digital computers (which operate and store data discretely), and in part because of the recent ubiquity of large discrete networks (social, biological, ecological, ...).
Among the many subfields that fall under the umbrella of discrete mathematics, there is combinatorics (the study of how discrete objects combine with one another), graph theory (the study of networks consisting of nodes, some pairs of which may be connected), and coding theory (the study of the transmission of data across potentially noisy channels); these are areas of active research here at Notre Dame. Please follow the links below to get more information about the specific research of faculty in discrete mathematics.
Faculty 

Areas of Research 
Leonid Faybusovich  Optimization  
David Galvin  Graph theory, combinatorics  
Liviu Nicolaescu  Probability  
Roxana Smarandache  Coding theory 