Course Syllabus
MATH 36 FALL 2024
Mathematical Models in the Social Sciences
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."
Instructor: Peter J. Mucha, Kemeny 240, peter.j.mucha@dartmouth.edu, https://mucha.host.dartmouth.edu.
Prerequisites: MATH 13 and MATH 20.
Lecture Information: 9L (MWF 8:50–9:55), Haldeman 028.
Please hold the 9LX hour (Thursdays 9:05–9:55) open for possible use including one-on-one and small group meetings. If possible, please also hold the corresponding Tuesday 9:05–9:55 time, which we might use instead (if you have a conflict at this time, let me know).
Full class meetings at the 9LX time or its Tuesday analogue will be held on Thursday 10/17, Thursday 10/24, Thursday 11/14 and Tuesday 11/19.
Office Hours: Tuesdays 1:15–2:15 and Thursdays 9–11 in Kemeny 240, and by appointment (a DM on the Dartmouth Slack will almost always get a faster response than email).
Course Objectives:
The course aims to consider a variety of mathematical modeling types frequently used in the social sciences, including cellular automata, 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, information, and/or opinions. 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.
Textbooks:
We will organize our explorations of different topics and methods using parts of different textbooks that are available to you online, either from the author or through the Dartmouth library, including
- A Short History of Mathematical Population Dynamics by Nicolas Bacaër;
- Introduction to the Modeling and Analysis of Complex Systems by Hiroki Sayama;
- Statistical Analysis of Network Data with R by Eric Kolaczyk and Gabor Csardi (second edition, 2020); and
- Networks, Crowds, and Markets by David Easley and Jon Kleinberg.
We will also consider some articles that will be listed in References (which you can also find under Pages in the left sidebar). Note that you do not need to purchase anything.
Assignments, Projects, and Grading:
Homework assignments will include short "daily assignments" and longer "weekly assignments". The "daily assignments" will be due by the next class meeting (unless indicated within 2 class meetings) and will typically be worth 1–3 points each. The "weekly assignments" will have longer times to their due dates, and will be worth more. 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. Possible topics include deep dives into another chapter in one of the textbooks or an appropriate journal article. The project will include multiple milestones assigned as regular assignments, as well as a separate set of project assignments (in lieu of an in-person final exam) including a poster (10 points), draft report (15 points) and final report (25 points).
The instructor reserves the right to modestly re-weight the separate components of the course (daily problems, weekly problem sets, project milestones, poster, final report) to ensure each contributes fairly to the overall course grade. 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 2 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 or other illness. For the health and safety of our class community please do not attend class when you are sick. If possible, please let me know in advance in a timely way if you are sick and believe you might miss an upcoming class.
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.
Religious Observances:
Dartmouth has a deep commitment to support students’ religious observances and diverse faith practices. 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 meet with me as soon as possible—before the end of the second week of the term at the latest—to discuss appropriate course adjustments.
Academic Honor Principle:
The Academic Honor Principle is an essential tenet of the Dartmouth community. For additional detail, see the Academic Honor Policy for Undergraduate Students in the Arts and Sciences. 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. You should also be sure to always fairly and completely cite your sources.
Use of Generative Artificial Intelligence:
As machine learning continues to advance, large language models (LLMs), such as ChatGPT, and other Generative AI (GAI) technologies are becoming more widespread. These models can at times be useful tools to accelerate productivity and understanding. Dartmouth has identified Guidelines on using Generative Artificial Intelligence for Coursework. The use of such technologies is permitted for the assignments in our course, so long as the following guidelines are adhered to:
- When using an LLM or other GAI to aid in completion of an assignment, all prompts and output should be saved and submitted as part of the assignment. This may be in the form of a screenshot, copy and paste, PDF, etc.
- The work that you submit should reflect your own understanding of the assignment.
- Copying the output from an LLM or other GAI and handing it in as your own work is not permitted, similarly to how copying a peer's work and submitting it as your own is not allowed.
Examples of situations where you might find it useful to use GAI in your work include when you know what kind of calculation you want to do but you don't know all of the details or syntax for how to code it, or you forgot an idea or concept from a previous class that is needed for the current item you are working on. Many other reasonable examples are surely possible; you are strongly encouraged to share your experiences using such tools. Please be aware that in many cases these technologies can give answers to a prompt that are completely incorrect (and sometimes wildly so). As such, you should always be skeptical of any GAI output you see and verify the veracity of the information contained within. If you have any questions about the use of GAI in the class, please reach out to the instructor.
Student Accessibility and Accommodations:
Students requesting disability-related accommodations and services for this course are required to register with Student Accessibility Services (SAS; Apply for Services webpage; student.accessibility.services@dartmouth.edu; 1-603-646-9900) 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 quarter 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:
Dartmouth is committed to maintaining a diverse and inclusive workplace and welcomes all members of Dartmouth's scholar-educator community to join in cultivating a culture that values and rewards teaching and welcomes diversity in its many aspects. I acknowledge that the distribution of authorship of the books, articles, and original materials referenced therein do not reflect that desired diversity, especially insofar as we consider historical references, but not only as such. 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_resources).
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.
| Week | Topics |
|---|---|
|
1 MWF |
A Very Brief History of Population Dynamics
|
|
2 MWF |
Cellular Automata
|
|
3 MWF |
Percolation
|
|
4 MWF |
Agent Based Models
Mean Field Approximation
|
|
5 WRF |
Networks No class on Monday 10/14
|
|
6 MWR |
Random Graph Models
No class on Friday 10/25 |
|
7 MWF |
Network Dynamics and Mean Field Approximations
|
|
8 MWF |
Heterogeneous Mean Field, Pair Approximation, and Approximate Master Equations
|
|
9 MWRF |
Wednesday, Thursday and Friday: Course project presentations |
|
10 MT |
Monday and Tuesday: Course project presentations |
Course Summary:
| Date | Details | Due |
|---|---|---|