As networking systems such as the Internet, wireless and mobile networks are becoming increasingly versatile and complex, mathematical methods for modeling, analysis, and design of computer networks and their protocols have become important. A wide variety of mathematical tools and techniques drawn from the areas of convex optimization, stochastic modeling, and control theory help to unify and to understand the key concepts of protocol design for optimum performance in computer networks. Concern for optimal operation of networks is quite often of crucial importance in protocol design due to the scarcity of resources such as wireless spectrum and battery lifetime.

In this course, some of the major mathematical concepts and techniques underlying modern network design are described in the setting of concrete examples drawn from network design problems such as congestion control, wireless scheduling, and multi-access protocols. The significance of these concepts and tools goes far beyond the setting of the specific examples in which they are presented. As the mathematical topics we use here are quite vast and varied fields by themselves, we focus on how these different tools are often brought together to provide an understanding of the given problem in network design. We do not develop the mathematics beyond what is necessary to understand the networking examples we consider.