Jim Belk University of Glasgow

Mathematical Modeling

I developed an upper-level mathematical modeling course for Bard College which I taught in the fall of 2016. This page contains information about this course.

Summary

The course focused on modeling with ordinary differential equations and difference equations, and we explored applications to growth of organisms and allometric laws, population dynamics, HIV modeling, and climate modeling. The only prerequisite was Bard's Linear Algebra and Ordinary Differential Equations course, and most of the students in the class were sophomore, junior, or seniors majoring in mathematics, science, or economics.

The textbook for the course was Topics in Mathematical Modeling by K. K. Tung

Homework Assignments

Here are the weekly homework assignments for the course, which were worth 40% of the course grade. These assignments are a mixture of problem-solving and computer analysis in Excel, SageMath, or Mathematica. Students were encouraged to work together on the homework but were required to write up their own solutions individually.

Takehome Exams

There were two takehome exams for the course, both of which were worth 25% of the grade.

Syllabus

Here was the syllabus for the course.

Textbook Information

The textbook is Topics in Mathematical Modeling by K. K. Tung. You will need a copy of the textbook for reading and homework problems, though you do not need to bring it to class. The textbook is available online via JSTOR: The above link only works from on campus. From off campus, you will need to use the following link and sign in with your bard acount: I'm not completely sure that the textbook will be available online for the entire semester, so if you have your own computer I recommend downloading all of the PDF's.

If you want a paper copy, there are currently new copies selling on Amazon.com starting at $41, and used copies starting at $30.

Course Policies

Course Description

What is a mathematical model? And how can it be used to help solve real world problems? This course will provide students with a solid foundation in modeling and simulation, advancing understanding of how to apply mathematical concepts and theory. Though we will discuss many different kinds of mathematical models, the focus of this course will be on modeling with ordinary differential equations.

Prerequisites

The only prerequisite is Math 213 (Linear Algebra with ODE's), though some prior experience with computer programming would be helpful.

Homework

There will be a weekly homework assignment, usually due on Fridays. Homework will involve constructing and analyzing mathematical models, often with the aid of Mathematica. All homework assignments should be written in either LaTeX or Mathematica and submitted to me by e-mail.

Final Project

There will be a final project on a topic of your choice. I am happy to allow group projects, though each member of a group must contribute as much effort as a student working individually. A typical project for a pair of students consists of a 10 15 minute class presentation discussing either an original mathematical model or a model that you found in a published paper or book, together with a writeup covering the model in more detail. More information on the final project will be given in the second half of the semester.

Exams and Grading

The grade will be based on the homework, the final project, a takehome midterm, and a takehome final exam:

Homework 40%
Takehome Midterm 25%
Takehome Final 25%
Final Project 10%

Project Information

Part of the requirements for this class include a final project. Here is some basic information about the project:

Project Topics

Your choice of topic may involve constructing your own mathematical model of a given situation, describing a well-known model from science or economics, or describing a class of models including at least one specific example. Here are some ideas to get you started: