Networks are at the heart of some of the most revolutionary technologies in modern times. They permeate science, technology, business, and nature. We begin this course with an in-depth mathematical study of the network problems traditionally discussed in operations research, with emphasis on combinatorial approaches for solving them. Students will be introduced to efficient algorithms used in solving shortest path, maximum flow, minimum cost flow problems, and related problems. We next focus on mathematically describing different classes of networks – random, small-world, scale free, dynamic – and their applications in modern network science.
probability and statistics (EN.625.603 or similar course), linear algebra and experience with reading and writing proofs as found in EN.625.609 or similar course. While the course is primarily mathematical, students will be expected to work within at least one programming environment (Matlab or Python will be easiest, but Julia, R and others will also be acceptable).