Math 398 -- Math in the City
Spring 2006

Section 003
Instructor:   Petronela Radu
                    Office: AVH 239
                    Phone: 472-9130
                    Office Hours:   2:30 - 4:00 pm Mondays and Wednesdays or by appointment
Graduate Teaching Assistant: 
              Sawanya Sakuntasathien   
              Office Hours: TuTh 10:00 -- 12:00   or by appointment

Nebraska Research Expo (Cornhusker Marriott, March 2006)
Poster:  Tell-Tale Heart Attack    photo 1 - Nikki, Jackie, Tigh, Julianne
                                                      photo 2 - Nikki, Jackie, Tigh, Sawanya, Petronela
     Poster:  Lake McConaughy, Is Your Water Gonna Stay?
                                                     photo 1 - Caleb, Eric, Melissa
                                                     photo 2 - Caleb, Eric, Melissa, Petronela
Schedule of classes:
MWF 12:30 -- 1:20  Avery Hall 110
Syllabus (tentative):
Week  01/09 - 01/13   Project descriptions; Introduction to Linear  Algebra
           01/16 - 01/20   Linear Algebra: matrices, linear systems
           01/23 -01/27    Statistics: Random variables, expected value, variance, special distributions, Introduction to Maple
           01/30 - 02/03   Statistics: The t and chi-square distributions, confidence intervals
           02/06 - 02/10   Statistics: Hypothesis testing, Linear regression
           02/13 - 02/17   Multiple Linear Regression, Multiple Logistic Regression
           02/20 - 02/24   DE: Substitution Methods in DE, Modelling with DE
           02/27 - 03/03   Existence and Uniqueness Issues for DEs, Euler's Method
           03/06 - 03/10   Qualitative Methods for DE and for systems of DEs
           03/13 - 03/17   Spring Break - No classes!
           03/20 - 03/24   Nonlinear DE

           03/27 - 03/31   DE: Fourier Transform
           04/03 - 04/07   Review for Exam
           04/10 - 04/14   Review for Exam (Exam is on 04/12)
           04/17 - 04/21  
Mathematics for your future
           04/24 - 04/28   Poster presentations and discussions
Project: As part of the coursework in this class groups of 3-4 students will work on a project designed
in collaboration with a local bussiness or research center. You may design your own project, however you need
to get the instructor's approval for your choice before starting any work on it. Some possible choices are:
        -- Medical Trial Analysis -- in collaboration with Professor Jane Meza from Nebraska Medical Center, Omaha
               Project Description
               Data for the project
        -- Water Levels in Nebraska: model to predict future levels for lake McConaughy, NE -- in collaboration
              with Dr. Shuhai Zheng from the Department of Natural Resources
              Data Set 1 (Elevation/Storage/Surface Area)
              Data Set 2 (Date/Elevation/Storage)

Guidelines for grading the project:
    30 points for the mathematical content  - correct formulas and arguments, complete explanations
    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).
   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.
  On a separate piece of paper, each student should summarize the work that he/she did on the project.

For the material taught in class you may use as additional references besides 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 chose 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 01/30)
Homework 2 (due 02/10)
Homework 3 (due 02/20)  - Data file. Description of the data
Homework 4 (due 03/01) - Data file 1(.dat) Data file 1 (.xls). Description of the data 1.
                                        Data file 2 (.dat) Data file 2 (.xls). Description of the data 2
Homework 5 (due 03/08)
Homework 6 (due 03/22)
Homework 7 (due 04/03)
Homework 8 (due 04/11)
Exam: There will be a two-hour exam for this course covering the topics discussed in class.
Assessment:  Your final grade will be computed based on the follwing scheme.
                        15 % Homeworks
                        50 % Project
                        25 % Exam

                        10 % Quizzes / Oral Presentation
  If you have any suggestions, please fell free to bring them up!

Introduction to some Maple commands
The motion of a spring in Maple
Systems of Differential Equations in Maple - exact solutions, plots, eigenvectors and eigenvalues
Euler's Method for DEs and for systems
Nonlinear Systems of Differential Equations