Course Details
Textbooks
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Mathematical Modeling, Third Edition by Mark Meerschaert, 2007 Michigan State University, MI Find this text on Amazon |
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Introduction to Computational Science by Angela B. Shiflet and George W. Shiflet, 2006 Wofford College, SC Find this text on Amazon |
Overview
Mathematical modeling is the process of analyzing real-world problems through the lens of mathematics and then relating the solutions back to the real world. Topics to be covered include discrete-time simulations of dynamical systems, Markov chains and Monte Carlo simulation, cellular automata, diffusion, agent-based models, and linear programming.Disabilities
Centenary assures students with disabilities equal opportunity to reach the same level of achievement as other students. Strict confidentiality will be maintained on students with disabilities. Services for students with disabilities are available through the Counseling Center, located on the ground floor of Rotary Residence Hall, phone (318) 869-5424.Honor Code
All students are bound by the Honor System. The Honor System is applicable to all academic work. See the Centenary College Handbook for the complete Honor Code. All code you write and turn in for a grade is understood to be pledged. You may discuss topics with other students and tutors, but all code you write must be your own, and you must be able to explain to me how it works. In this course, it is a violation of the honor code to look at code from previous semesters or in other students' directories.Extensions
Extensions and rescheduling for labs, projects, exams and quizzes are only given when circumstances beyond your control (e.g. being sick, choir or sports travel) prevent you from completing a project on time. You must notify me either by email or phone of your circumstances well in advance of the due date. No extensions are given for requests made within three days of the due date.Quizzes and Participation
You are encouraged to attend class and participate in discussions every day. Sporadically throughout the semester, there will be short quizzes covering material from the previous class. These quizzes will serve as records of your attendance, and in total they will comprise 5% of your final grade. Active participation in class discussions will comprise another 5% of your final grade. This will be awarded for answering questions, asking questions, presenting material, etc.Extra Credit
Extra credit for this course can be earned by participating in the Centenary Math Problem of the Week (POTW). Each reasonable submission will be worth an additional 0.5% toward your final grade, CC me with your submission for credit. A maximum of 7% extra credit can be applied to your final grade.Syllabus
We will be using pieces from both textbooks and alternating between their approaches. We will also be using additional supplemental material such as relevant web-pages and background material for the lab assignments. Readings will be assigned before material will be covered in class. You are expected to review the material and come to class prepared. As readings are assigned, they will be posted here.- Jan 12 - Meerschaert Chapter 1, Shiflet Chapter 1
lecture notes - Jan 15 - Shiflet Chapter 3
growth.py, logistic.py
repeated.py, drugs.py
- March 19 - Markov Chains
Probability Textbook
Labs
Much of your experience with modeling in this course will be through semi-weekly labs, which will comprise 30% of your final grade. All labs are weighted equally within the Lab portion of your final grade.You may work with a partner on the lab assignments if you choose. Their name must be listed on any work you hand in as joint work.
- Lab 1: Oil Spill
- Lab 1a: Car Sales Profit
You may resubmit Lab 1 modeling the Car Sales Profit problem from the lecture notes above. Follow the same format as Lab 1, using the OilSpill Maple Worksheets as a template. Be sure to tweak a parameter and discuss the robustness of your model. - Lab 2: Growth and Decay
- Assigned: Jan 22th
- Due: Jan 27th
- Lab 3: Caffeination
- Assigned: Jan 27th
- Due: Feb 3rd
- Lab 4: Population - Competition
- Assigned: Feb 10th
- Due: Feb 12th
- Lab 6: Monte Carlo Simulation
- Assigned: March 12th
- Due: March 17th
- Lab 7: Markov Chains
- Assigned: March 24th
- Due: March 26th
Project
You will have one large project in this course. The purpose of this project is to improve your research, writing and communication skills as well as give you an opportunity to explore in-depth a particular area of modeling. You will analyze, model, and evaluate a real-world situation and and share this with the rest of the class through a paper and a presentation.
The details for this project will be posted as the semester progresses. One option for
a project topic is to work on the
Mathematical Contest in Modeling on February 5-9.
Exams
There will be two exams, each worth 20% of your final grade. They
will consist of modeling theory and practical situations.
- Exam 1: March 3rd
- Exam 2: May 6th 12-3 pm
Grading
Your final grade for this course will be based on the Labs, Projects, Quizzes, Exams and Participation described above.
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© Mark Goadrich, Centenary College of Louisiana