AMATH 383 Introduction to Continuous Mathematical Modeling
SLN 10231 TTh 2:00-3:20 pm
Instructor: Professor Ka-Kit Tung firstname.lastname@example.org Lewis Hall Room 323
Office hours: T 3:30-4:30pm. Wed 10:00-11:00 am.
Teaching Assistant: Rose Nguyen email@example.com
Office hours: Th, 10:00-11:00am, Fri 3:00-4:00pm Lewis Hall Room 128.
Grading: 5 Homework Assignments, each counting 10% of the final grade.
1 Term paper, 40% of the final grade; due:final day of instruction. If you need W-credit, turn in a draft two weeks before the final due date. Instead of a paper, your work can be presented orally in class. Up to 3 students can collaborate on a term project, which can be either original research or a review of a few papers on the subject of the student's choice. 10% of the final grade is awarded for class participation, especially during student oral presentation and discussions.
Term Paper: A term paper can be on any subject that is related (however remotely) to the topics covered in the course or in the book. 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 paper should consist of the following:
Title, Authors, Indicate whether it is for W-credit
Abstract: A succinct summary of the project.
Introduction: Description of the problem and motivations. Some historical discussion if relevant. A discussion and review of previous work on the subject.
Problem formulation or Modeling: This is where you introduce the mathematics (equations etc.)
Solution or Results
Interpretation of the results of the model. Does your model address the problems or the phenomenon that you posed in the Introduction?
References: Each reference should be listed in the following order: Author(s), year, title, journal, volume, pages.
Figures with legends can be embedded in the main text or collected after references.
Oral Presentation: Instead of a written paper, a term project can be presented orally in class. For a single presenter, 30 minutes of the class time is allotted. 45 minutes are given to two presenters. Projected slides (e.g. Powerpoint) should be used. Colorful slides and videos are also encouraged.
Possible term paper topics:
(1) Sync: Book of the same title by Steven Strogatz
(2) Bridge Collapse: Millennium Bridge.
(3) Serial Dating Strategy, Dynamic Programming: Google
(4) Nash equilibrium, Prisoner’s Dilemma.
(5) Six Degrees of Separation: Google.
(6) Death of Language: Abrams and Strogatz, nature 2003.
(7) Zipf’s Law of Human Language: Least effort, PNAS 2003 Cancho and Sole 03.pdf
(8) Cicadas and prime numbers: Campos et al 2004, Phys. Rev. Letters. Hoppensteadt and Keller 1076 Science.
(9) Modeling of Combat, but no video games.
(10) Modeling of epidemics.
(11) AIDS modeling.
(12) Collapse of empires; predator-prey modeling Motesharrei et al 2014.pdf
(13) Game theory and the Cuban missile crisis: plus.maths.org/content/os/issue13/features/brams/index
Course description: Introductory survey of applied mathematics with emphasis on modeling physical and biological problems 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
Text Book: Topics in Mathematical Modeling, by K. K. Tung, Princeton University Press. (Recommended but not required). On reserve at Engineering Library (3 day checkout), and Odegaard Library (2 hour checkout).
1. Review of ODE. Radiative decay, age of the solar system; carbon dating.
2. Nonlinear ODE. Qualitative methods on the phase plane. Population models; Harvesting problems.
3. Discrete time logistic equation. Chaos.
4. Climate models. Snowball Earth. The greenhouse warming problem.
5. System of ODEs, dynamical systems. Predator and prey; competition models; models of combat and attrition. Marriage and divorce.
6. Other topics by request (Finance? Internet?)
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