BMA/MA/ST 771: Biomathematics I, Fall 2010

Prof. S. R. Lubkin
SAS 4226, 5-1904
lubkin@eos.ncsu.edu, http://www4.ncsu.edu/~lubkin/
Office hours: MW 2-2:45 or by appointment

Class meets Mon and Wed 3-4:15 in Harrelson G100

Text: Mathematical Models in Biology, Leah Edelstein-Keshet. SIAM, 2005. If you find a used copy, you will be fine no matter what the edition, because this book has never been revised. For new copies, your cheapest option is to get the member discount from SIAM. Because NCSU has a student chapter of SIAM, membership is free! Do not monopolize the library copy.

Prerequisites: This course is suitable for grad students and undergrads, depending on your math background. You are expected to have passed multivariate calculus and linear algebra, and you should remember the material well enough to build on it. A course in differential equations is not required; BMA 771 is an introductory differential equations course. You should have, as your second text for BMA 771, a calculus and/or linear algebra book for reference, of your choosing. Keep it easily accessible.

Grades: 8-12 homework sets (60% total) and two exams (midterm 15%, final 25%). Not all homework problems will be graded, but all should be turned in. Exams must be an individual effort, but homeworks need not be. I encourage you to work with others on the homeworks, and will pass out a phone list to facilitate this. If you work with someone else, put both (all) names on the paper for a common grade. Not more than 3 to a paper, please. Some of the homeworks are intended to be done "by hand", but unless I say so specifically, you may use computer assistance, if you include the details in your writeup (e.g. "using Maple function 'eigenvals' to find the eigenvalues, we find lambda = 1, 2, and pi").

Important point about working with others: The point is to learn. If one person is doing the work and someone else is copying, then someone is not learning. If you begin every problem by asking your partner how to do it, you are not learning. If you try to solve it alone, and need some assistance along the way, that is learning. By the way, explaining things to others contributes very nicely to your own learning!

Goals: By the end of the course, you should be able to construct, interpret, analyze, understand, discuss, and critique linear and nonlinear ordinary differential and difference equations as models of biological systems, by various methods, and you should know something about the types of behavior that these models exhibit (equilibria, oscillations, bifurcations, etc.).

Another goal and a warning: Although assignments at the beginning will be quite structured, they will get more and more vague; you will have to figure out what is called for. This represents the transition from undergraduate-style to graduate-style work, in preparation for the "real world" and/or research. The vagueness will at first be uncomfortable, but soon it will be exciting, like much in life.

Help: Come to office hours, or send me e-mail. Ask each other. Ask other students.

Homework aesthetics:

• Please staple all homeworks.
• Every graph must be labeled. Always label all axes. Arrowheads have a very specific meaning indicating the direction of motion or of a vector or time. Arrows do not belong on axes or curves unless they are intended to indicate time or motion or vectors.
• If you are asked to make an argument, or "show that..." then you need to use enough words to make that argument. Mathematical symbols without context make no sense. Look at your textbook: it is mostly words with symbols used within the sentences. That is how your homework should be written.
• If you do calculations in Maple (for instance) and hand in the Maple session, the printout should be edited for clarity and conciseness just as you would edit your handwritten notes (only giving me your best work). It is easy to make graphs in Maple, but you should only show those graphs which illustrate your point. Delete graphs which do not contribute to your discussion. The same holds for any computer tool, e.g. Excel. Clean it up, but show what you did. Show what you did, but clean it up.

Courtesy

· Since this is a small class, try to let someone know if you will be late or absent so we don't hold up the beginning of class.

· If you're sick, get some rest at home. You can get the notes from someone.

Links

Logistic map applets:

http://www.enm.bris.ac.uk/staff/hinke/courses/Chaos/applets/iteration/Iteration.html

http://www.lboro.ac.uk/departments/ma/gallery/doubling/