Mathematical models describe a variety of real-world situations, providing unique information and insight. Systems that can benefit from modeling range from daily occurrences (e.g. optimizing campus parking) to highly complex interactions (e.g. predicting weather) to currently theoretical scenarios (e.g. computing the best vaccination or treatment strategy in case of bioterrorist attack).
Mathematical modeling is a mathematical tool for solving real world problems. In this course, students study a problem-solving process. They learn how to identify a problem, construct or select appropriate models, figure out what data needs to be collected, test the validity of a model, calculate solutions and implement the model. Emphasis lies on model construction in order to promote student creativity and demonstrate the link between theoretical mathematics and real world applications.
Throughout this semester, we study a variety of modeling types. Topics include proportionality models, fitting models to data, creating simulations, dimensional analysis, probabilistic modeling, optimization, and both discrete and continuous models. For day-to-day details, see the calendar pages of our class website.
Additionally, students work in small groups on a semester-long modeling project. Early-semester activities include discussions of possible project ideas, a workshop on technical writing, project proposals, and brief presentations in class. Later activities include individual group meetings, peer-reviewed rough drafts, and longer final presentations to the class.
Course Objectives
Mathematical Modeling is an area of applied mathematics that uses mathematical tools for exploring and studying "real world" problems. The overall objective of this course is to provide an introduction to the process of mathematical modeling while giving students an opportunity to
- develop and construct appropriate models for various problem situations,
- analyze given models to uncover underlying assumptions, and
- investigate particular problems to find out what has already been done toward developing solutions.
Through work on assigned projects, students increase their fluency in technical reading and writing, and develop skills in mathematical problem solving. Students learn to
- use the modeling process to translate problem situations to mathematical expressions,
- use a variety of mathematical resources and tools to study problem situations, and
- use appropriate technology to assist in the problem-solving process.
Beyond the content of individual courses, the major in mathematics is designed to prepare students for the 21st century by helping students to become problem solvers, effective communicators, users of appropriate technology, and team players. In this course, students will be engaged in a variety of activities which will help them to move toward achieving these goals.
Textbooks:
- Jahandideh M. T. (2011) An Introduction to Mathematical Modelling.
- A First Course in Mathematical Modeling, by Giordano, Fox, Horton and Weir. 4th Edition.