This class is an introductory undergraduate course about networks, which can be used to study complex systems of interacting entities. The study of networks — including theory, computation, and applications — is pervasive in physics, biology, sociology, computer and information science, and myriad other fields. The study of networks is also a major part of data science.
Some Motivating Questions: How should one describe the structure of social networks? How do diseases and rumors spread in different types of networks, and how does network structure affect the speed and pervasiveness of the spread of information, misinformation, and diseases? Using network structure only, how can one determine which Web pages drive recommendations? How do ‘physical distancing’ and vaccination prevalence affect the spread of a disease?
Learning Outcomes: Students will develop a sound knowledge and appreciation of some of the tools, concepts, and computations that are used in the study of networks. The study of networks is predominantly a modern subject, so the students will also be expected to develop the ability to read and understand current research papers in the field. They will also have a chance to explore a topic in depth in a final group project. Course topics include the basic structural features of networks, generative models of networks, centrality, random graphs, clustering, graph Laplacians, and dynamical processes on networks.
Prerequisites: Math 3A, Math 4A, Math 6A, PSTAT 120B with a grade of C or better; knowledge of Python programming is highly recommended. Once the quarter starts, instructor approval is required to maintain enrollment in the course, including if students do not have the listed pre-requisite courses completed.