From the ORC: "Disciplines such as anthropology, economics, sociology, psychology, and linguistics all now make extensive use of mathematical models, using the tools of calculus, probability, game theory, network theory, often mixed with a healthy dose of computing. This course introduces students to a range of techniques using current and relevant examples."
Please hold the 9LX hour (Thursdays 9:05–9:55) open for possible use including one-on-one and small group meetings. Any full class meetings at the 9LX time will be indicated on the Calendar.
There will be no class on Friday October 21 (campus Day of Caring) or Wednesday November 9 (as I have an obligation with my primary professional society).
Office Hours: Mondays 3-4 and Thursdays 12-1:30 in Kemeny 240, or by appointment.
Course Objectives:
The course aims to consider a variety of mathematical modeling types frequently used in the social sciences, including cellular automata, dynamics on and of networks, and agent based models. We will use simple computational simulations as well as analytical techniques in developing a better understanding of these complex systems. Topics of particularly timely interest that may be considered in varying depth by different students include models for the spread of disease and/or information, and models of opinion dynamics and voting. The goal is for you to develop a broad overview understanding of a variety of these models and methods and, through the course project, a detailed expertise on a selected topic.
Homework assignments will include short "daily assignments" and longer "weekly assignments". The "daily assignments" are due by the next class meeting, or if indicated within 2 class meetings, and are worth 1 point each. The "weekly assignments" will have longer times to their due dates, and are worth 3 points each. Unless otherwise specified, all daily assignments are due by the start of the corresponding class period (8:50am) and all weekly assignments are due by the end of the day (11:59pm).
Each student will engage in a course project on a topic selected by the student in consultation with the instructor. The project will include multiple milestones assigned as weekly assignments, as well as a poster (4 points), in-class oral poster presentation (1 point), and final report (6 points, in lieu of an in-person final exam).
No fractional points will be awarded. Scores will be dropped from the two lowest daily assignments and two lowest weekly assignments (but not on the poster, poster presentation, or final report). The course grade will then be determined by a traditional 90/80/etc. scale from the final total.
Attendance Policy:
Class participation is essential to our exploration of the course material. Please reach out to me in a timely, responsible way to pre-approve any excused absences as needed. After 3 unexcused absences, each additional unexcused absence will be penalized by a 1 point deduction in determining the course grade.
You are expected to attend class in person unless you have made alternative arrangements due to, e.g., illness, medical reasons, or the need to isolate due to COVID-19. For the health and safety of our class community please do not attend class when you are sick, nor when you have been instructed by Student Health Services to stay home. If possible, please let me know in advance in a timely way if you are sick and believe you might miss an upcoming class.
Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please notify me well in advance to discuss appropriate accommodations.
There are many potential reasons to request an excused absence. Please just reach out to me ahead of time and follow up after to discuss how to best catch up on any course material that you miss. In short, be responsible.
Academic Honesty:
The Academic Honor Principle is an essential tenet of the Dartmouth community. Collaboration is strongly encouraged in this course. At the same time, ultimately, all assignments submitted must represent your own understanding of the material. Be generous and honest in your citing assistance and input from your fellow students.
Student Accessibility and Accommodations:
Students requesting disability-related accommodations and services for this course are required to register with Student Accessibility Services (SAS; Getting Started with SAS webpage; student.accessibility.services@dartmouth.edu; 603-646-9900) and to request that an accommodation email be sent to me in advance of the need for an accommodation. Then, students should schedule a follow-up meeting with me to determine relevant details such as what role SAS or its Testing Center may play in accommodation implementation. This process works best for everyone when completed as early in the term as possible. If students have questions about whether they are eligible for accommodations or have concerns about the implementation of their accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.
Mental Health:
The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including the undergraduate deans, Counseling Center, and Student Wellness Center. I encourage you to use these resources to take care of yourself throughout the term, and to speak to me if you experience any difficulties.
Diversity and Inclusion:
I strongly agree with the sentiments expressed in this sample syllabus statement on diversity from Monica Linden, Senior Lecturer in Neuroscience at Brown University. In linking to this statement, rather than copying it, I aim to both acknowledge the source and, in asking you to follow the link, highlight the message therein. In particular, I would like to emphasize that we will make an effort to read papers from a diverse group of scientists, while acknowledging that limits still exist on this diversity. I encourage you to talk to me if anything in class or out of class makes you uncomfortable or if you have any suggestions to improve our environment or the quality of the course materials.
Title IX:
At Dartmouth, we value integrity, responsibility, and respect for the rights and interests of others, all central to our Principles of Community. We are dedicated to establishing and maintaining a safe and inclusive campus where all have equal access to the educational and employment opportunities Dartmouth offers. We strive to promote an environment of sexual respect, safety, and well-being. In its policies and standards, Dartmouth demonstrates unequivocally that sexual assault, gender-based harassment, domestic violence, dating violence, and stalking are not tolerated in our community.
The Sexual Respect Website at Dartmouth provides a wealth of information on your rights with regard to sexual respect and resources that are available to all in our community.
Please note that, as a faculty member, I am a mandatory reporter obligated to share disclosures regarding conduct under Title IX with Dartmouth's Title IX Coordinator. Confidential resources are also available, and include licensed medical or counseling professionals (e.g., a licensed psychologist), staff members of organizations recognized as rape crisis centers under state law (such as WISE), and ordained clergy (see https://dartgo.org/titleix_resourcesLinks to an external site.).
Should you have any questions, please feel free to contact Dartmouth's Title IX Coordinator. Their contact information can be found on the sexual respect website at: https://sexual-respect.dartmouth.edu.
Course Schedule:
Note future topics listed are tentative, undoubtedly moving around as time permits.
Week
Topics
1
Introductions, syllabus, how to read a scientific paper.
Cellular automata, simulations in PyCX, NetLogo, NetLogo Web, the "majority rule" CA (a.k.a. "Voting"), with slightly different state-transition functions.
Possible CA for infectious disease? Consider 1D. Forest fire CA (a.k.a. "Fire") analogous to spread of infectious disease (in 2D), phase transition, critical point (e.g., at basic reproductive number R0 = 1), running experiments using BehaviorSpace under Tools. Similar behavior in "Percolation" CA. Observe very big change in the critical point in Fire switching from von Neumann neighborhood ("neighbors4") to Moore neighborhood ("neighbors").
See Sayama Chapters 10 & 11.
2
Estimate critical points of phase transitions in Fire and Percolation CA: branching process arguments (Monday) and renormalization group calculations (Friday).
Finite-size effects in percolation.
See Sayama Section 12.4.
3
Stochastic state transitions: agent based models
Mean field approximations
See Sayama Section 12.3.
4
Compartmental models
Simulating disease dynamics on networks
See Sayama Sections 15.1 and 15.2 for a quick, general introduction to the basics of networks. If you are a Python user, see the rest of Chapter 15 for a quick introduction to the NetworkX module.
See Sayama Sections 16.1 and 16.2 for discussion of dynamics on networks.
See Porter & Gleeson Section 3 for an even more general discussion of different kinds of dynamics on networks.
5
Mean Field Analysis of Dynamics on Networks (SI & SIS)
Friendship Paradox
"Super spreaders"?: Different MF arguments for SIS on scale-free networks
See Sayama Sections 18.4–18.6 and Porter & Gleeson Section 4.3.
6
Heterogeneous Mean Field for SIS
Pair Approximations
Hierarchies and Moment Closures
Friday: No class
7
Pair Approximation for Voter Model
Co-evolving ("adaptive") Voter Model
Co-evolving Prisoner's Dilemma Games
See the "supporting information" of Durrett et al. (2012) for PA details.
See Sayama 16.4 about "Simulating Adaptive Networks" and (if you can) run the associated simulation codes to see the different kinds of behaviors possible.
See Fu et al. (2009) for the prisoner's dilemma system.
8
High-Accuracy Approximations for Binary-State Dynamics
Threshold Models
Bounded Confidence Models
See Porter and Gleeson Appendix A for a quick overview and Gleeson (2013) for details.
9
Monday: Review and final thoughts Wednesday: No class Friday: Course project presentations
