Office: 421 Brink Hall
Office Hours: by appointment
Class Time: 2:30 MWF
Place: TLC 140
Exam 1:
Prerequisite: Math 310 (Ordinary Differential Equations), or
some other exposure to differential equations and consent of instructor.
Text: Fred Brauer and Carlos Castillo-Chavez, Mathematical
Models in Population Biology and Epidemiology,
Springer, 2nd ed.
This course combines ideas from two subjects: mathematics (mostly
differential equations) and biology. This is an exciting and very
active area, with contributions coming from both mathematicians and
biologists. We will primarily study qualitative
issues, such as modeling (deterministic) biological phenomena, stability of
solutions to differential equations, etc. This semester,
we will focus on models in ecology and population biology although the same
mathematics applies to models in physiology and molecular biology.
There is no biology prerequisite and you won't have to dissect any
frogs.
The course is suitable for students of mathematics, biology, ecology,
physics, and any of the other disciplines that use things like
differential equations (see topics below). We focus mostly on nonlinear
models; these are the ones that arise in real biological systems.
The book for the course is very
well written and is full of interesting biological models.
Homework is due at the beginning of class on the due date.
The "project" involves picking a
research article in mathematical biology,
working through it (with help from me or others), then telling me
about it. This basically means that you will teach me what's in the
paper during an informal chat in my office. Plan on a 10 minute
presentation and 5 minutes of questions.
A good source of references is your text; I can help
you find something appropriate. When you have picked
one or more possibilities, you must get the paper approved by me (to
be sure it has a reasonable amount of math and biology in it). Try to
get this done some time in March
so you have time to work through it.
Your "final discussion" with me should be before THE END OF
FINALS WEEK. I encourage you to get this done
earlier rather than later; the end of the semester is hectic, as you know.
One of the exciting things about this course is that it will
quickly prepare you to read a sizeable portion of the research literature.
Course Outline:
1. Continuous-Time Models and Ordinary Differential Equations
2. Spatial Models and Partial Differential Equations
Additional References:
Some Mathematical Biology Journals (You might need to be on campus
to access some of these online.)