# Math 168: General Course Outline

## Catalog Description

**168. Introduction to Networks.** (4) Lecture, three hours; discussion, one hour. Requisites: courses 115A, 170A or Electrical and Computer Engineering 131A or Statistics 100A. Introduction to network science (including theory, computation, and applications), which can be used to study complex systems of interacting agents. Study of networks in technology, social, information, biological, and mathematics involving basic structural features of networks, generative models of networks, network summary statistics, centrality, random graphs, clustering, and dynamical processes on networks. Introduction to advance topics as time permits. P/NP or letter grading.

## Course Information:

Students will develop a sound knowledge and appreciation of some of the tools, concepts, and computations 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 project. Topics include basic structural features of networks, generative models of networks, centrality, random graphs, clustering, and dynamical processes on networks.

## Textbook

Mark E. J. Newmn, *Networks: An Introduction*, 2010 [primary text]

Mason A. Porter and James Gleeson, *Dynamical Systems on Networks: A Tutorial*, 2016

Supplementary material from survey, review, and tutorial articles.

## Schedule of Lectures

Lecture | Section | Topics |
---|---|---|

1-3 |
Newman 1-6, 8 |
Introduction and Basic Concepts |

4-6 |
Newman 7.9, 15.1 |
Small-World Networks |

7-10 |
Newman 14 |
Models of Network Formation |

11-13 |
Newman 7 + supplementary material |
Network Summary Statistics |

14-17 |
Newman 12-13 |
Random Graphs |

18-21 |
Newman 11 + supplementary articles |
Clustering in Networks |

22-25 |
Newman 16-18; Porter & Gleeson |
Dynamical Processes on Networks |

26-27 |
Introduction to Advanced Topics |