Course meeting times: TTh 2:30-3:50pm, SAV 264
Instructor: Ivana Bozic
Office Hours: M 1:00-2:00pm, T 4:00-5:00pm LEW 306
Teaching Assistant: Rose Nguyen
Office Hours: T 10:00-11:00am, W 10:00-11:00am LEW 115
Course description: Introductory survey of applied mathematics with emphasis on modeling in terms of differential equations. Formulation, solution, and interpretation of results. The course consists of a series of independent topics in a wide variety of fields of application. No background in these areas are required.
Textbook: Topics in Mathematical Modeling, by K.K. Tung (available at the University Book Store).
Grading: Homework (60%), final project (30%) and class participation (10%).
Homework Policy: There will be 6 problem sets. Each problem set is weighted equally (100 points each). Homework should be submitted electronically through Canvas, and will be due at noon on the homework due date. Approximate due dates (subject to change): 1/18, 1/25, 2/1, 2/8, 2/15, 2/27. No late assignments will be accepted on the first problem set. For subsequent problem sets, each student has 2 late days to use for any reason throughout the quarter (either combined on one problem set, or split between two problem sets).
Final Project: Final project can be on any subject that is related to the topics covered in the course or in the book. The content of your project/term paper can be new and innovative research, or reviewing a few papers written by other scientists. A list of possible topics will be provided to you. A minimum of 10 pages without counting references and figures is required. One or two or three students can work on the same paper collaboratively, but no more than three. There should be more substantial material when more people are involved in a project.
A two page project proposal will be due on T 2/20. Final projects are due on the last day of class. Some useful guidelines for the final project, written by K.K. Tung, can be found here. Instead of a written paper, a final project can be presented orally in class, using projected slides (e.g. Powerpoint, Keynote).
Possible final project topics:
(1) Modeling vegetation patterns in Africa. Suggested papers: JA Bonachela et al. Science 2015, CE Tarnita et al. Nature 2017.
(2) Chaos. Suggested reading: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering by S. Strogatz.
(3) Synchronization. Sugested reading: Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life by S. Strogatz
(4) Nash Equilibrium, Prisoner's Dilemma. Suggested reading: Evolutionary Dynamics by MA Nowak.
(5) Dynamics of leukemia under treatment. Suggested papers: F Michor et al. Nature 2005., C Tomasetti Blood Cancer Journal 2011.
(6) Modeling HIV. Suggested reading: DIS Rosenbloom et al. Nature Medicine 2012.
(7) Modeling drug resistance in cancer. Suggested papers: C Tomasetti and D Levy Mathematical biosciences and engineering 2010, I Bozic et al. eLife 2013.
(8) Game theory and the Cuban missile crisis. Suggested reading: plus.maths.org/content/os/issue13/features/brams/index
(9) Cicadas and prime numbers: Campos et al 2004, Phys. Rev. Letters. Hoppensteadt and Keller 1976 Science.
(10) Modeling of social contagion. Suggested reading: AL Hill et al. PLOS Comp Bio 2010, AL Hill et al. Proc Royal Soc B 2010.