Math 398 -- Math in the City
Fall 2008

Instructor:   Petronela Radu (Office: Avery Hall 239   Phone: 472-9130)
Office Hours: Monday 2:30 - 4:00 pm ; Tuesday 12:00 -2:00; or by appointment
Schedule of classes: MWF 1:30 -- 2:20  Oldfather Hall 204

This is a modeling course offered to math and non-math majors and it is run in collaboration with local
businesses, research or administrative centers in town. The course has two components: one which revolves
around the lectures (the homeworks and the exam will be based on this material) and the second is
the project
. In order to complete the course you need to perform well on each component.

The mathematical content of the course will revolve around modeling. Using simple analysis one can give
fairly good estimates to questions like: How tall can a mountain be? How many cobblers are in the United
States? How much warmer is a densely populated urban area than the surrounding countryside? (questions
solved in John Harte's books: Consider a Spherical Cow and Consider a Cylindrical Cow). In the process, we
will learn more on probablity and statistics, differential equations, linear optimization, physical sciences,
and even some programming (Maple).

The difficulty of the topics will be perceived differently by students; each of you will discover that it
depends a lot on your background, the way you think and communicate in mathematics. The discussions
will be more beneficial if you keep up with the material on a day-to-day basis. Do not hesitate to ask
questions in or outside the class whenever in doubt about an argument, notation, etc. At the end of this
course a successful student will not only have performed very well on the tasks during the semester,
but s/he will be able to approach other real life problems that involve mathematics with more confidence.

The course was awarded a University ITLE grant in 2007.

References for the course:
John Harte: Consider a Spherical Cow, A Course in Environmental Problem Solving
John Harte: Consider a Cylindrical Cow, More Adventures in Environmental Problem Solving

The Project: In partnership with the Jim Dyck and Deb Hansen from The Architectural Partnership we will focus
on qualitative and quantitative features in sustainable design. As models for our investigation we will use two
green buildings:  the Earth House from the Prairie Hill Learning Center and the Nature Center from the Pioneers Park.

The Nature Center:

The Costs/Savings Group:

The Green Group:
Miranda Chrastil
Jennifer Determan

Resources for the projects:
United States Green Building Council
Capital-E  - Costs and Benefits for Greening America's Schools

Before writing your final essay for the class you may wish to consult the following resources:

20 points for the mathematical content  - correct formulas and arguments, complete explanations
10 points for good/steady progress during the semester (accomplishing the tasks on time, meeting with your
colleagues every week to work on the project, full participation with remarks and questions during the
meetings will invariably lead to a very good turn out for your efforts)
15 points for esthetical aspect (use of graphs, diagrams, colors) and organization
5 points for presenting the novelty and the significance of the work (any research that was done on the
subject, new methods, programming skills that you learnt while working on the project, emphasize the
importance of the work).
Total: 50 points
Each project should have 3 parts. The Introduction will contain a project description, an outline of the
methods used, and the significance of the work. In the Main Body you will include the work: a set-up
of the problem, the hypothesis, the arguments, and the steps taken to solve the problem. The
conclusions will contain the final results and their interpretation. All participants in a group project will
get the same grade, so it is important that each person in the group participate fully and equally.

Homework: The homework will be announced in class and posted on the web. You are encouraged
to discuss the problems with your colleagues, but you have to write your own solutions.

Homework 1

Oral Presentations.  At the end of the semester students will be required to give a presentation of their
work. This will be a collective effort such that every person will have the chance to do a slide presentation
with the results of their project. These group presentations will be scheduled on the last week of classes and
will be free to the public (faculty, graduate, and undergraduate students will be invited).

Exam:
There will be a two-hour in-class exam for this course covering the topics discussed during the
lectures.

Assessment:  Your final grade will be computed based on the follwing scheme.
50 % Project
25 % Exam
15 % Homeworks
10 % Oral Presentations
Honor Code: Some of your work during the course will be done individually, while some will be