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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 | ||