Math-M 447 Mathematical Models and Applications I

Section: 11100
Class Day and Times: MWF 10:10-11:00
Class Location: SE 240
Text: Mathematical Modeling and Computer Simulation by Maki and Thompson
WEB Page:
Instructor: Elizabeth Housworth
Office and Office Hours: 371 Rawles Hall, 12-1 Tuesdays, 1-2 Thursdays, 2-3 Sundays and by appointment
Important dates: Last day for automatic withdrawals is Wednesday, October 29. The final exam for our section of Math 447 is 12:30-2:30 on Friday, December 19. We will use that time for final project reports.

Grading Procedure and class policies: You will have regular homework to ensure that you understand the basic mathematics behind the models we discuss in class. You may discuss the homework with other students and with me but the work you turn in should be your own and not a copy of the work of anyone else. No homework will be accepted late. However, if you know you will have to miss class, you can turn in your homework early. There will be 7 homework assignments out of which your best 5 will determine your homework grade. If you fail to turn in an assignment on time, it will count as one of your dropped assignments.

You are required to attend class, participate in class, and participate in your team work for your projects. Participation and attendance make up 10% of your grade for this class.

You will have a Capstone Project in which you choose your own modeling problem, form a model, explore the model, write a summary report, and present your topic and results to the other students in the class. You will work in teams of three to four students. I will assign the teams based on a form you will submit about your own preferences, your own strengths, and your own weaknesses. Your team will have 2 mini-projects to complete together before your final project is due which will give your team experience about how to work well together. Everyone should contribute to the team effort and everyone will fill out an evaluation form in which you describe your own contribution and the contribution of the other members of your team. These evaluations along with my own observations will allow me to assign individual grades for the project.

You will have two exams on which you will demonstrate your individual competency in the mathematics and modeling techniques taught in this course. These exams will have an in-class and a take-home component. All of the work on the exams must be your own - no outside help is allowed. Any cheating will be taken seriously, and, if I determine you have cheated, you will be assigned an F in the course.

Homeworks    50
Attendance and Participation    50
Mini-project 1    25
Mini-project 2    25
Exam 1  100
Exam 2  100
Capstone Project  150
Total  500

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 real-world 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 case-by-case 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 Self-evaluation 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) Mini-project 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 Mini-project 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, 12:30-2:30 pm -- Project Presentations