Math 398 -- Math in the City
Fall 2006

Instructor:   Petronela Radu (Office: Avery Hall 239   Phone: 472-9130)
                    Office Hours: 11:30 - 1:00 pm Mondays and Wednesdays or by appointment
Schedule of classes: MWF 1:30 -- 2:20  Avery Hall 111

Final Exam - November 27, 12:30-2:30 - Review topics

Info about the course:
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.
On Mondays and Wednesdays we will have lectures which will cover topics from Matrix Algebra, Statistics,
Differential Equations, and Maple. These topics will concern modeling issues from different areas of science.
On Fridays we will meet and discuss your work on the project.

The mathematical content of the course is diverse. 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 is partially supported by a University ITLE grant through December 2007.

Maple:    Examples  (UPDATED)  Part 1 (integration, differentiation, plots, solving DEs, linalg, iterations)
                Examples Part 2 (surfaces and curves, iterations)
                Homework #4 -problem 2 - Discrete Dynamical Systems (origin=repellor)
Projects: This semester there will be two projects:

 -- Traffic in Lincoln - This project will be conducted with the help of Mark Lutjeharms from the Schemmer
    Associates and it concerns the traffic in the city of Lincoln. Some of the questions we will look at are: How
    does traffic on one street affect the traffic in an intersection? Derive a relationship between the density of
    traffic and the speed of the traffic for different areas inside and outside the city limits. Given data for traffic
    at a given time, determine the traffic at later times on a highway with no entrances or exits. If time permits,
    we will look at additional topics, like efficiency for fuel consumption.
    City of Lincoln Traffic Operations
    The 2002-2003 City Traffic Report by the Schemmer Associates pdf 
    Data 1 (zip file)

-- Housing in Lincoln - During the last decade prices for houses have risen nationwide with a double digit
    increases every year in some areas. This appreciation has been observed for the Lincoln real estate market,
    but so far this increase has not been quantified. Using statistical analysis (and the SPSS package) students
    will work to answer the following questions: How can the price of a house be computed
    (ok, approximated) knowing the location, square footage, size of the lot,  etc.?  By how much did home
    values appreciate in Lincoln over the past ten years? This project will be run in collaboration with
    Michelle Slack from the Lincoln County Assessor.
    Guidelines for grading the project:

    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
        Friday 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.
   References: For the material taught in class you may use in addition to the notes given in class, any
   textbook in Linear Algebra, Differential Equations, and Statistics. You may have to find and read
   references for the project that you will choose to work on during the semester.
  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 (due September 18)
  Homework 2 (due October 2)
  Homework 3 (due October 20)
  Homework 4 (due November 1)
  Homework 5 (due November 17)

  Oral Presentations. Each student will give at least two oral presentations. The first one will be
  an individual presentation in front of her/his team members on a topic closely related to the project.
  The second presentation will be a collective effort and it will be done at the end of the semester. At
  that time each group will put together a poster and a slide presentation of their work. 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
  Assessment:  Your final grade will be computed based on the follwing scheme.
                        15 % Homeworks
                        50 % Project
                        25 % Exam
                        10 % Oral Presentations
  Honor Code: Some of your work during the course will be done individually, while some will be
  collaborative. I expect you to acknowledge the help you have received from your colleagues, outside
  friends, or me on homework assignments. I will assume that you will adhere to the UNL Policy on
 Academic Honesty.