Networks

Lectures: 2 sessions / week; 1.5 hrs / session.

Recitations: 1 session / week; 1 hr / session.

Basic probability at the level of 6.041 Probabilistic Systems Analysis and Applied Probability or 14.30 Introduction to Statistical Methods in Economics. Since the course is aimed at developing a systematic understanding and analysis of networks and processes over networks, the students will be expected to work with mathematical models and analytical reasoning.

Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. But it is only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use web-like supply chains. Financial linkages, both among banks and between consumers, companies, and banks, also form a network over which funds flow and risks are shared. Systemic risk in financial markets often results from the counterparty risks created within this financial network. Food chains, interacting biological systems, and the spread and containment of epidemics are some of the other natural and social phenomena that exhibit a marked networked structure.

This course will highlight common principles that permeate the functioning of these networks and how the same issues related to robustness, fragility, and interlinkages arise in several different types of networks. It will both introduce conceptual tools from dynamical systems, random graph models, optimization, and game theory, and cover a wide variety of applications including: learning and informational cascades; economic and financial networks; social influence networks; formation of social groups; communication networks and the Internet; consensus and gossiping; spread and control of epidemics; and control and use of energy networks.

The final grade in the course is based upon our best assessment of your understanding of the material during the semester.

There will be bi-weekly problem sets. There will also be some computational assignments (Python / MATLAB). Problem set solutions will be handed out on the day it is due. Late problem sets will not be accepted. You may interact with fellow students when preparing your solutions. However, at the end, you must write up solutions on your own. Duplicating a solution that someone else has written or providing solutions to be copied is not acceptable. If you do collaborate on problem sets, you must cite, in your written solution, your collaborators.

There will be two exams in the subject. The exams will both be closed book. You will be allowed to bring two 8.5 x 11-inch sheets of notes (both sides) to the midterm exam, and four 8.5 x 11-inch sheets of notes to the final exam.

A project on a topic that overlaps with the course (potentially selected from a list of topics) is assigned. You will be expected to work in groups. The project will be due on the day of presentation, which will be held during the last lectures of the class.

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