Math 168 (Winter 2020)

Introduction to Networks (Math 168, Winter 2020)

Instructor: Nina Otter
(lastname AT math dot ucla dot edu)

Class schedule: MWF 11-11:50 am, MS 6627

Discussion: Thu 11-11:50 am, MS 6627

Office Hours: W 2-3 pm and Fr 12-1 pm MS 7380.

Teaching Assistant: Abigail Hickok
(abigailhickok2 at gmail dot com)

TA Office Hours: Thu 12-1pm MS 3919.

Textbook: Mark Newman, Networks, Oxford University Press, Second Edition

Additional reading will be posted on this page over the quarter.

Grading: Homework: 15% + 5%, Midterm: 15%, Final: 15%, Project: 50%. The homework with the lowest grade will be dropped from the final grade.


This is a project-based course about networks. Networks can be used to study complex systems of interacting agents, and the study of networks in terms of theory, computation, and applications is pervasive in physics, biology, sociology, information science, and myriad other fields. The study of networks is also a major part of data science. We will cover selected book sections, as well as additional material from other sources. Class participation is very important.

Learning outcomes: 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. Course topics include basic structural features of networks, generative models of networks, centrality, random graphs, clustering, and dynamical processes on networks.

Approximate course content by weeks:


There will be two different types of assignments:

The exercise sheets will be posted here (on the course webpage) on Mondays, and will have to be uploaded to Gradescope by Tuesday of the following week at 11am. These sheets will be graded and count towards 15% of the final grade.

There will be four short essays assigned during the first four weeks of the course, and these are meant to be in preparation of the final project. For the short essays you will be asked to put into writing a discussion of some topic which will be posted here (on the course webpage) on Mondays. The essays will have to be typed in LaTex and you should upload a .pdf file to Gradescope by 11am on Tuesday of the following week. The essays should be maximum two pages in length, or equivalently contain maximum ca. 1000 words. Please do not exceed this! The short essays will be graded with a P/NP and count towards 5% of the final grade.

No late assignments will be accepted.

Exercise sheets:

Short essays:


The capstone part of the course will be a group project, which has a final submission in two forms: (1) a final report in the format of a paper for the scholarly journal PNAS (maximum 6 pages of main text + any amount of Supplementary Materials); and (2) a final presentation. During the first half of the quarter there will be preparatory work for the project, groups for the project will be formed in week 3, and the main part of the work will take place starting week 5. The final report is due on Sunday 15 March 2020 at 11:59pm. The presentations will take place in week 11. The final report should be submitted to me by e-mail and (in case of large file size) shared with me using Dropbox or something similar.

Some reading material..

..for generalisations of networks:

..about community structures: Communities in networks, Mason A. Porter, Jukka-Pekka Onnela, and Peter J. Mucha, Notices of the AMS, September 2009

..about network models: A Survey of Statistical Network Models, A. Goldenberg, A. X. Zheng, S. E. Fienberg, E. M. Airoldi, arXiv e-print, 2009

..about epidemic modelling on networks: Networks and epidemic models, Matt J. Keeling and Ken T. D. Eames, Journal of the Royal Society Interface, 2005

Exams and project presentations

Midterm: Monday 3 February 2020 in class. Practice Midterm   Solutions for practice midterm

Final: Monday 9 March 2020 in class. Practice Final  

The structure of the final will be similar to that of the midterm. The final be on the material that we covered in class and in the exercises after the midterm. We covered selected book sections, and additional other references. Thus, the best study reference are the notes you took in class, as well as during the discussion sections, and the exercise sheets. The book sections are roughly Chapters 11, 12 (with exclusion of generating function methods), 14.1-2, 16.1, 16.2, 16.5.

Project presentations: Tuesday 17 March 8-11 am

No makeup exams.

Last updated 6 March 2020