


Motivation: Some students are taking this course because they have situations that they want to model. Typically, such students are PhD students in graduate programs outside the mathematics department. This course provides them with modeling examples, tools, and guidance. Other students are taking the course to fulfill an undergraduate mathematics major, often for the purpose of becoming secondary teachers. Such students may not come to the class with immediate ideas for a modeling project but should recognize the value of the teamwork and modeling experience as providing simulated realworld job training or providing exposure to the very modeling and team work concepts that they will be expected to teach their own students.
Software: In class demonstration of code will be presented, usually in Maple but only because Maple is the language that has been used for this class for years. You may use any language you want but for any language you choose to use, including Maple, you must (1) specify the language and (2) attach your code to your work.
Cheating Policy: Some components of this course, such as the projects, are collaborative and, short of plagiarism, are not subject to cheating allegations. To some extent the homework and to the maximum extent the exams should be your own individual effort, cheating will be taken seriously, and cheating on an exam will earn you an F in the course. Cheating on the homework will earn you a 0 for that homework for the first offence and an F in the course if it happens a second time. Plagiarism on a project will be handled on a casebycase basis and the sanctions imposed will be based on the extent of the plagiarism and the extent to which multiple team members participated in the plagiarism.
Religious Holiday Policy: If you will miss class, especially a class during which there will be an exam or other required work, for a religious holiday, you must inform me during the first two weeks of the semester.
Tentative Syllabus  

Date  Topics  Work Due 
Monday, September 1  Labor Day   
Wednesday, September 3  Course overview, model building, types of models: axiomatic, simulation, mathematical   
Friday, September 5  Axiomatic models: Kepler's laws for planetary motion, the value of simplicity, model prediction   
Monday, September 8  Axiomatic models: Voting Theory  Selfevaluation for use in assigning teams 
Wednesday, September 10  Axiomatic models: Voting Theory   
Friday, September 12  Axiomatic models: Voting Theory   
Monday, September 15  Simulation models, team assignments, first miniproject  Homework 1  2.3: 6, 7, 20, 21 
Wednesday, September 17  Simulation models: Generating discrete random values   
Friday, September 19  Simulation models: Discrete event simulation and flow charting. The text of the MAPLE code used in class is provided through the following links: Three Point Shots  Method 1 Three Point Shots  Method 2   
Monday, September 22  Simulation models: Writing code in MAPLE  Homework 2  4.1: 13 (provide a flow chart), 14 
Wednesday, September 24  Simulation models: Writing code in MAPLE (Example 4.7 code)   
Friday, September 26  Simulation models: Gambler's ruin (code)   
Monday, September 29  Simulation models: Population Growth (code)   
Wednesday, October 1  Simulation models: Stock Market (code)  Miniproject 1 due 
Friday, October 3  Simulation models: Betting Strategies in Roulette (code)   
Monday, October 6  Mathematical models: Newton's explanation of Kepler's laws 
Homework 3  4.2: 9 (provide your code); 4.3: 4 (provide a flow chart and your code) Class's collective solution for 4.3.4 
Wednesday, October 8  Mathematical models: Mendel's peas   
Friday, October 10  Mathematical models: Discrete population growth  Practice Exam 1 
Monday, October 13  Mathematical models: Discrete population growth, Maple code for cobwebbing   
Wednesday, October 15  Mathematical models: Stratified population models   
Friday, October 17  Mathematical Models: Stratified population models Some miscellaneous Maple code for use in analyzing stratified populations  Homework 4  2.1: 2, 6, 13; 2.2: 6 
Monday, October 20  Mathematical Models: Stratified population models Lande's Spotted Owl Demographic Model paper   
Wednesday, October 22  Review for Exam 1  Miniproject 2 due 
Friday, October 24  Exam 1   
Monday, October 27  Mathematical modeling: Markov chains  Take Home Part of Exam 1 due 
Wednesday, October 29  Basic properties of Markov chains   
Friday, October 31  Classification of states and Markov chains   
Monday, November 3  Mathematical analysis of regular Markov Chains  Homework 5  2.5: 6, 7; 3.2: 14 
Wednesday, November 5  Mathematical analysis of regular Markov Chains  Capstone Project Topic Description due 
Friday, November 7  Mathematical analysis of regular Markov Chains   
Monday, November 10  Mathematical analysis of absorbing Markov Chains  Homework 6  3.3: 1, 6, 11 
Wednesday, November 12  Mathematical analysis of absorbing Markov Chains  Practice Exam 2 
Friday, November 14  Mathematical analysis of absorbing Markov Chains   
Monday, November 17  Markov Chain examples  Homework 7  3.4: 1, 11 
Wednesday, November 19  Review  Capstone Project Outline, Task List and Assignment, and Timetable due 
Friday, November 21  Exam 2   
Monday, November 24  Help with projects  Take Home Part of Exam 2 due 
Wednesday, November 26  Thanksgiving Break   
Friday, November 28  Thanksgiving Break   
Monday, December 1  Mathematics of use for your specific projects   
Wednesday, December 3  Mathematics of use for your specific projects  Capstone Project Progress Report Due 
Friday, December 5  Mathematics of use for your specific projects   
Monday, December 8  Project Presentations   
Wednesday, December 10  Project Presentations   
Friday, December 12  Project Presentations   
Written Project Reports Due  Monday, December 15, noon  
Final  Friday, December 19, 12:302:30 pm  Project Presentations 