College of the Holy Cross
Mathematical Modeling
Course Description

Catalog Description

Mathematics 303 -- Mathematical Models - Alternate years (traditionally in the spring, but we're trying it as a fall course in 2006)

Introduction to the role of mathematics as a modeling tool, including the construction, interpretation and application of mathematical models. Applications will be chosen to illustrate various modeling paradigms such as deterministic, probabilistic, discrete and continuous modeling and may include population dynamics, bio-medical applications, stock market analysis, and network and traffic flows.

Prerequisite: Mathematics 242 and 244.
Breadth area: Applied Mathematics.
One unit.

Course Objectives

The overall goal of this course is to provide a thorough introduction to the entire modeling process. The theme that links our models together will be environmental issues, such as water and air pollution, global warming, and estimating oil reserves on the planet. You will have the opportunity to learn and practice the following:

Creative and Empirical Model Construction Given a real-world scenario, you will learn to identify a problem, make assumptions and collect data, propose a model, test the assumptions, refine the model as necessary, fit the model to data if appropriate, and analyze the underlying mathematical structure of the model in order to appraise the sensitivity of hte conclusions in relation to the assumptions. You will learn to generalize the construction to related scenarios.

Model Analysis Given a model, you will learn to work backward to uncover the implicit underlying assumptions, assess critically how well those assumptions reflect the real-world sceanrio at hand, and estimate the sensitivity of the conclusions when the assumptions are not precisely met.

Data Analysis You will have a real world opportunity to conduct a survey, and then enter and analyze the data using Excel.

Model Research You will learn to investigate an area of interest to gain knowledge, understanding and an ability to use what already has been created or discovered. Model research provides for determining the state of the art in a subject area.

Capstone Component

The faculty in the Department of Mathematics & Computer Science are considering implementing a capstone course for all majors. In such a course, students would use mathematical material from several of their other courses and would be expected to make a final oral presentation. Mathematical Models has been recognized as a course with the potential to serve as a capstone course, although it has not yet been formally designated as a capstone. Each project will end with a formal presentation to the non-profit organization that benefits from the project.

Community-Based Learning Component

The course is designated as a Community-Based Learning (CBL) course. You can learn more about the College's program by visiting the website for the Donelan Office of Community Based Learning, which states "Community-based learning provides opportunities for faculty and students to combine experiential learning in the Worcester community." Each student will participate in a project that will provide you with the chance to use your quantitative skills to assist a local agency with a real-world problem. Typically, students spend about 20 hours over the course of the semester off-campus. In this class, we may partner with the Mass Audubon Broad Meadow Brook Conservation Center and Wildlife Sanctuary, a local ecology museum called the EcoTarium, or the Regional Environmental Council of Central MA. The class will have field trips and class visitors in order to learn about the range of possible projects, and then each student will select a project that matches their interests and skills. Typically, three or four students will work together on a project, although how this work is structured is flexible and is worked out between the professor, the students, and the local agency.

Instructor Personal-Bias Statement

I am an applied mathematician. My doctorate degree is in Engineering Sciences and Applied Mathematics from Northwestern University (1992).
Applied mathematics explores the interdependence of mathematics and the sciences. In attempting to solve problems, applied mathematicians, engineers and scientists use a variety of approaches and techniques. While mathematics permits us to clarify and understand the physical aspects of a problem, so can physical insights assist us in finding the appropriate mathematical line of approach. You will find that my approach as an applied mathematician will influence this course -- my examples will be based in the real world as much as possible. I am particularly interested in helping you to develop effective problem solving techniques.

Instructor Pet-Peeve Statement

Clear communication is really important to me. Please speak up, both during class and outside of class. An engaged group of students is just so much more rewarding for everyone involved. Attendance is also really important to me. Please make the effort to come to class. If you contact me ahead of time, then I will help provide you with the information that you missed. Otherwise, it is your responsibility to get notes from one of your peers and to make sure that you understand the material that you missed. While we're on the topic of pet peeves, please turn off your cell phone and leave your gum out of the classroom. Thanks.