Topics in Applied Mathematics (Math 76)

Winter 2022

2A: Tues-Thurs 2:25-4:15, x-hour Fri 4:35-5:25 as needed

Instructor: Professor Dorothy Wallace

Office: 204 Kemeny

Office hours: T-Th 4:30 - 5:15 pm

Co-instructor: Xie He

Office: 220 Kemeny

Office hours: Tues 1:25-2:25 and by request

We will do half of the class on continuous models, particularly the nonlinear pendulum, the wave equation, and infectious disease models. The second half will be discrete network models. It will be as hands-on as we can make it and you will need a computer in class with Matlab and possibly other software. There will be a final project, ongoing presentations in class, and class participation expectations but no exams. The prerequisite is linear algebra (Math 22 or 24) but Math 23 is also helpful.

Syllabus

Week 1 Pendulum (ODE linear and nonlinear, 2D system, phase portrait, equilibrium, stability, simple control problem, rigid pendulum experiments)

Week 2Intro/review of linear systems of ODE’s, the nonlinear SIR models, Hartman-Grobman theorem,

Week 3 Wave equation for vibrating string, Fourier series solution, string experiments

Week 4 Higher dimensional wave equations, vibrating drumheads and other objects, Chladni plates

Week 5SIR metapopulation model, SIR on a network, intro to networks

Week 6Introduction to Network Science; SIR continue; ER model; small-world networks; community detection; SBM model; Preferential Attachment; Centrality; PageRank.

Week 7More possible topics such as graph matching; graph embedding

Week 8 Link prediction lecture, student project presentations

Week 9 Student project presentations

Grading: In both courses the grades will be based on class presentations, class participation (in the form of group work and questions), and a final project of your choosing. These three factors will be weighted equally. The instructors reserve the right to adjust the final grade based on improvement over the course of the quarter.

Attendance: Attendance is required, and we will use the x-hour as needed. Do not schedule other activities during this time.

Text: We will be using various online and other sources including research papers. These will be distributed as needed.

Honor principle: All authors must contribute substantially to any paper with their names on it. All sources must be appropriately cited. Any suspicion of plagiarism will be forwarded to the COS.

Religious observance: 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 before the end of the second week of the term to discuss appropriate accommodations.

Students with a diagnosed learning disability are encouraged to discuss with the instructor any appropriate accommodations that might be helpful. All discussions will remain confidential, although the Student Accessibility Services office may be consulted.