CME 181: Projects in Applied and Computational Mathematics
Course description: Teams of students use techniques in applied and computational mathematics to tackle problems of their choosing. Students will have the opportunity to pursue open-ended projects in a variety of areas: economics, physics, political science, operations research, etc. Projects can cover (but are not limited to!) topics such as mathematical modeling of physical systems, data-driven applications or analysis, or complex systems in engineering. Teams develop projects collaboratively in partnership with a graduate student mentor throughout the quarter.Course Information
CME 181Location: Encina West 202
Times: Tu / Th 2:15PM - 3:30PM
Instructor:
- Michael Minion (mlminion AT stanford DOT edu)
- Anil Damle (damle AT stanford DOT edu)
Course Objectives
Students will gain practical experience in how to identify key questions in a research project, to formulate models and choose an appropriate scope of inquiry, to find and incorporate relevant references, to collaborate efficiently and productively, and to communicate research findings effectively in both scientific reports and presentations.Example Projects
Climate Models
How should large scale complex models treat the behavior of certain specific phenomena that may impact the larger model? One potential project would be to choose one of these specific phenomena and work on a model for its behavior. For example, a team could investigate how volcanic activity affects the atmosphere. Furthermore, it may be interesting to assess the impact of changing how the larger scale models account for such phenomena, perhaps some of them are more or less sensitive to subtle differences in their treatment. Could an understanding the impact from a particular source lead to a geo-engineering remedy to global warming?Disease Spread
How do diseases spread in populations? This is a very interesting question that has been and continues to be the subject of active research. The scope of this question can vary dramatically. For example, the problem could be considered at the scale of an environment such as a university, where individual instances of disease contraction may be considered.Optimal Placement in Electrical Charging Stations
How should charging stations for the growing number of electrical cars be placed? What criteria should be used to determine a good distribution? How do uncertainties in future demand affect a placement strategy? How well does relying solely on market factors accomplish a good placement of resources (as in the location of Starbucks)?Water Waves
Waves in the oceans are controlled by a number of factors, some as large as gravitational fields, and others as small as local topography. How do these different forces and scales interact in oceans, gulfs, and bays? How does the formation of waves differ in shallow versus deep water? How could you model the formation and evolution of waves or some other phenomenon in water?Choose Your Own
What is of interest to you? If you have a question that you would like to tackle in a mathematical framework you can bring it into this class and make a project out of it.Short Lectures
In addition to working on projects, the course will contain a sequence of mini-lectures and discussions on an assortment of topics. Potential topics include- The formulation of mathematical models
- Validating models
- Assessing uncertainty in models, data, parameters, numerics
- Conducting numerical experiments
- Dealing with data, effective visualization
- Collaborative research, teamwork and leadership
- Document sharing, version control, project organization
- Creating effective scientific presentations and reports
- Finding and citing sources
- Publishing results, web pages and the peer review process
Prerequisites
CME 100/102/104 or equivalents, or instructor consent. It is recommended that students have taken CME 106/108 or the equivalent and have familiarity with programming at the level of CME192/193 or are taking either of these courses now.
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