Text: A first course in mathematical modeling.Giordano, Weir and Fox.

Meeting times: MWF 11, EE-205.

Contact: Professor Kirby, Weber 134, kirby@math.colostate.edu

Office Hours: NEW Tuesday 12:30-1:30; Wednesday 10-11; Thursday 9:30-10:30

Prerequisite: M160;   Co-Requisite: M161
 

This is a recently introduced undergraduate course in mathematical modeling of interest to both majors and non-majors alike.   Emphasizing breadth of topics and the modeling process as opposed to turn-the-crank solution recipes,  students work together in groups of three or four to create mathematical models for a wide range of phenomena from the economics of major league baseball.  For students interesting in continuing their study of mathematics this course counts towards the new concentration in computational mathematics.  Also, we plan to field a team in the 2002 mathematical modeling competition.  For more information please contact Professor Kirby, Department of Mathematics, kirby@math.colostate.edu.

• Topics Outline
• What Group Am I In?
• Homework Assignments
• How are the grades are calculated?
• Lecture Schedule
• Modeling Competition (interested students should contact me)
• MATLAB CODE (shuffling bugged fixed in blackjack.m on Friday, November  16)
• Last Year's Final Examination

•      Graphs of Functions as Models
•      The Modeling Process
•      Modeling with Discrete Dynamical Systems
•      Modeling Using Proportionality
•      Model Fitting
•      Experimental Modeling
•      Simulation Modeling
•      Continuous Optimization Models
•      Linear Programming
•      Modeling with Differential Equations
•      Probabilistic Modeling
•      Dimensional Analysis and Similitude

Need to check your group?

The group projects count for half of your grade and therefore play a fundamental role in the class.  Every two weeks each group will hand in a single type-written project.  Although you are working in a group for these assignments, each student is responsible to see that every part of the assignment is turned in.  Indeed, each student should be able to reproduce any of the contents of a given project.  Thus, the purpose of the group is to assist in learning and not to divide the homework assignment into parts to lessen your workload.  View each project as your project as the single grade for the project will be your grade.  Note: If any part of a group assignment is missing for whatever reason (without medical excuse or circumstances related to a sanctioned CSU event) then a grade of zero will be awarded for that component of the assignment.

• Group Project Number 1.
• Group Project Number 2.
• Group Project Number 3. Page 117 Problems 4.4 #3, #4, page 119-120 Projects #3, #4.
• Groupt Project Number 4.
• Group Project Number 5.   This assignment consists of two Monte Carlo simulations.  Please submit your code with your completed projects and carefully comment.
• Problem 1. After reading the rules of the game of black jack in the text create a computer program to implement a monte-carlo simulation of this card game.  Assume the dealer uses two decks of cards.  Compare the results of ignoring the dealers showing card with exploiting knowledge of the dealer's showing card when deciding when to stop getting new cards.  Experiment with your code and compare strategies. Also, experiment with the player's stragety for deciding whether to select an ace as a one or eleven.  Can you improve your strategy?  (You may use the matlab code below to get you started).
• Problem 2.  problem 7.4  number 1.  Use Table 7.11 in your daily demand submodel.   In this problem experiment with values of Q (quantity delivered) and T (delivery interval) using the analytical results as your starting point.
• Problem 3. problem 7.4 number 2.
• Problem 4. Construct a Monte Carlo simulation of a baseball game.  Assume each team has the same batting average but that you may assign individual batting averages as you like and adjust the order of the batters. Use this simulation to determine a batting order strategy.  Hint: consider simplifying assumptions to make the model more simulation more manageable.  This project is due November 16.
• FINAL PROJECT:  8.4 #3, #5.  9.1#2.  13.1 #7, #8. 13.2 #9 Due Wednesday Dec. 5.  Graded homework will be discussed on Friday Dec 7, the last day of classes.  You may hand in this assignment individually or in groups.

•      Group Projects 50%
•      Exams/Quizzes 30%
•      Final in class Exam 20%

Group Projects
These will be due every two weeks.  Each project will require 2-3 group meetings
outside of class; it is recommended that you schedule these in advance.  All group
reports must be typed.  LaTeX is recommended but other mathematical typesetting
packages are acceptable.

Exams
On Fridays when group reports are NOT due there will be an in class quiz.  These
quizzes will cover elementary material from lecture.  If you are following what is
going on in lecture,  they should not be difficult.  If you are not following the
lectures or group discussions come see me.

Final Exam
There will be a final in class exam.

A list of topics covered in lecture and associated reading will be logged here.

• blackjack.m
• my_card_value.m
• dealer_card_value.m
• baseball.m