This NSF-funded RTG includes the development and teaching of two new project-based courses based on modeling and simulation. The undergraduate course will be addressed to advanced undergraduate students, and student teams will be supervised by RTG graduate students. The graduate course will be addressed to beginning graduate students, with student teams supervised by an RTG postdoc, and each research project evolving from lab experiments to mathematical modeling and simulation. We will also develop a new graduate student class that helps graduate students improve their teaching as well as technical oral and written presentation skills. This course will be co-taught by a clinical faculty with expertise in pedagogy and RTG faculty, and will give students supervised opportunities to lecture and write about topics of common interest.
This graduate course was first offered in the Spring of 2017 and will be repeated in Spring of 2019.
Spring 2019, MATH-GA.2840-004, 3 Points, Tuesdays 9:00-10:50AM
Advanced Topics In Applied Math: Modeling And Experiment In Fluid Dynamics
Instructor: Leif Ristroph
This course will explore how applied mathematics, math modeling and simulations can productively interact with the experimental sciences and with real world observations and data. The course will involve projects in fluid and solid dynamics, each of which has an experimental system in the Applied Math Lab. Students will work in small groups to gather experimental data, with an emphasis on discovery and characterization of phenomena, and they will formulate mathematical models and/or computational simulations to account for these observations and make testable predictions. Assignments will include journal-style papers and conference-style talks. The projects will be drawn from research and will explore questions relevant to the life and earth sciences as well as engineering: What role does fluid dynamics play in bird flocks and fish schools, How does erosion by water or wind sculpt landforms and landscapes, and What are the principles underlying flow control networks and circuits?
Modeling Topics for Spring 2019:
- network flows, capillary siphoning, the Feynman sprinkler, gliding plates and hula hooping.
This class is being offered for the first time in Spring of 2018 as MATH-GA.2840-004, 3 Points, Wednesdays, 11:00-12:50PM
Special Topics in Applied Mathematics: Written and Oral Presentation
Co-instructors: Aleksandar Donev and Mutiara Sondjaja
This course will provide graduate students preparing for teaching and research careers with several skills and tools for more effective professional oral and written presentation. It will also provide a platform for supervised teaching practice. Students from all fields of mathematics are welcome, both pure and applied. The first part of the course, taught primarily by Prof. Mutiara Sondjaja, will focus on teaching pedagogy and effective class management. The second part of the course, co-taught with Prof. Aleks Donev, will focus on scientific writing, from abstracts to complete papers. Students will practice both by writing a review article or lecture notes on a topic from their field of study, aimed at their peers and not at specialists. They will deliver lectures to the class on the chosen topic and get feedback from the instructors and other students. The use of LaTex or tools based on LaTex such as LyX or sharelatex/Overleaf will be strongly encouraged. We will also have some guest lectures from professional writers and career service professionals, and will provide, as time permits, help with basic job search skills like writing CVs, teaching and research statements, and cover letters. Students will be encouraged to help each other and learn from peers.
Textbook: "Handbook of writing for the mathematical sciences" by Nicholas J Higham, published by SIAM, any edition, strongly recommended. We will also use other optional more general sources such as "Stylish Academic Writing" by Helen Sword or Strunk and White's "The Elements of Style."
This class was created in Fall of 2018 and is co-taught by Professor Charles Peskin and Courant Instructor Charles Puelz. The class materials are hosted on the Modeling and Simulation github repository.
Prerequisite: MATH-UA.0262 Ordinary Differential Equations. Experience in computer programming (or willingness to learn in a hurry) is highly recommended.
Description: This is a project-oriented course in which students work individually or in teams on computer simulation projects that they write up and present to the class as a whole. Topics that will be taught in class, from which projects may be drawn, are: (1) Vibrations of structures, including the stability of buildings and bridges in earthquakes and high winds; (2) Rotational motion including gyroscopes and spinning tops, and effects of the rotating earth such as the Foucault pendulum and the gyrocompass; (3) Chemical kinetics including deterministic and stochastic simulation methods, enzyme kinetics, and molecular dynamics; (4) Synchronization and chaos in interacting nonlinear oscillator systems; (5) Electrical circuits including operational amplifiers and analog simulation, AM and FM modulation, and logic gates as the building blocks of computers; (6) Dynamic simulation of market forces and price equilibrium in economics; and (7) The use of information technology as a means to improve traffic flow.
Each student works on two projects during the semester, in teams of up to two students, each team being advised by a graduate student. No two students may work together on both projects. Projects begin with a written proposal, and also involve a presentation and a written report. Presentations will be accompanied by class discussion that may motivate additional work and follow-up presentations.
Class Projects for Fall 2018 included: nuclear fusion in a thermal box, circadian oscillators and synchronization, shooting a basketball, gyroscopes, ride-sharing and traffic flow modeling, options pricing, growth of skeletal muscles, contact of balls with the ground, circulation modeling in congenital heart defects, axial flow in a compliant tube, gyrocompass modeling, spreading of infections, double slit experiment, chemical reactions in cells, double pendulum, biomolecular motors, fruit growth and nutrient flow, biased coins, robotic arms, dynamics of structures with controllers, stability of an Icelandic clock tower, minimal surfaces approximated by faceted surfaces, enzyme kinetics, calcium release, rotating wheels with friction, structural stability and earthquakes, suspension bridges, parachute modeling, Coulomb scattering.