UCLA Mathnet Login

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