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 was repeated in Spring of 2019 and Spring of 2021.
MATH-GA.2840-004, 3 Points
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.
First offered 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
Next offered as "Communication in the Mathematical Sciences: Teaching, Writing, and Oral Presentation" in Spring 2020, Wednesdays 1:25-3:15pm, WWH 512.
Co-instructors: Corrin Clarson and Miranda Holmes-Cerfon
Communication, both oral and written, is essential in academic careers and beyond. This course aims to help graduate students in mathematics develop skills to more effectively communicate their discipline and their research, through teaching, writing and oral presentation. Half of the course will focus on teaching, and will prepare students to teach their first course. Students will learn evidence-based techniques for teaching effectively in the classroom as well as best practices for assessment. We will also discuss strategies for handling the various challenging situations often faced by instructors. The other half of the course will focus on academic writing, and will help students understand the 'logic' of writing so as to construct clearer prose both at the sentence, paragraph, and article level. Throughout, the course will pay attention to how skills from both of these areas transfer to creating clearer, more engaging research presentations.
This seminar-style course will be highly interactive, with much of the learning occurring through feedback from other students. Students are expected to actively participate during the course time, and to complete several assignments including observing a class, teaching a short class, writing a research report and completing shorter writing exercises. The course is best suited for upper-level PhD students in all areas of mathematics, who have a little experience with teaching and writing in an academic setting but who wish to gain a more structured understanding.
This class was first created in Fall of 2018 and is co-taught by Professor Charles Peskin and Courant Instructor Charles Puelz. Professor Peskin taught the advanced undergraduate course "Modeling and Simulation in Science, Engineering, and Economics" again in Falls of 2019 and 2020.
Detailed lecture notes for this course are posted at:
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.