Mathematical Modeling: Exploring and Predicting Phenomena with
There will be no exams in this course, however there will be two team based projects: one due at the middle of the term and a ﬁnal project due at the end of the class. The ﬁnal project will involve an in-class presentation of approximately 45 minutes.
Projects (2) :
Final Project Presentation : 20%
Attendance and Classroom Participation : 20%
While lectures will focus on and explicate important concepts, the class format will emphasize group work and independent experimentation. As such, consistent attendance is necessary and thus attendance will be taken. We also note that successful group work does require that group members individually assume responsibility and expend proportionate eﬀort. To sign one's name to a group project while having not contributed is a violation of Wesleyan's Honor Code: see http://www.wesleyan.edu/studenthandbook/3 honorsystem.html.
|Materials to Purchase|
Towing Icebergs, Falling Dominoes, and other Adventures in Applied Mathematics by Robert B. Banks, Princeton University Press (1998), ISBN 0-691-10285-6 (paperback.)
The overarching theme of this course is that- from a certain perspective- mathematics can be regarded as a language for describing the world around us. It is a tool that facilitates our ability to interpret, predict and describe physical, biological and social phenomena.
We will use familiar mathematics in the service of modeling various real world problems drawn from economics, engineering, biology and (broadly interpreted) physics. Each problem will be a "real world" problem which has, in some form or another, likely touched each of our lives.
Our plan is to cover in the semester the ﬁrst ten chapters in Towing Icebergs, Falling Domi-noes, and other adventures in Applied Mathematics by R. B. Banks. We will cover roughly one chapter per meeting, and so it is important that students have perused the chapter before coming to class. Each class will contain a short review of the relevant mathematics to be used in the lecture.
A partial list of the mathematical tools to be worked with is: algebra, calculus, linear algebra, and certain other standard mathematical tools. We will assume no prior exposure to these concepts, and we will only develop them to the required depth for our investigations. These tools will be applied to problems such as:
* What is the optimal arrangement of leaves of a plant- from the point of view of capturing the most sunlight- around the stalk?
* How does one design a (safe!) parachute?
* How to decide whether we should be worried- or worse- given that a particular meteor is hurtling towards Earth.
* Is it practicable to harvest icebergs for fresh water?