Mathematical Modeling in Biology, M375, Fall 2002
Class meetings: Tuesday and Thursday, Tu-Th 11-12:30 , RLM
Office: RLM 9.114
Office Hours: TBA
TA: Helena Ristov
Office Hours: Tu-Th 2-3
Purpose: There are several purposes
to this class. The main one is to learn how to relate mathematical
structures to real-world (especially biological) systems. This is
a 2-step process. Most real-world systems are horribly complicated,
and we must make simplifying assumptions to reduce everything to the study
of a few essential variables, described by a few essential equations, with
parameters that can be determined experimentally. That's the first
step, and requires a fair level of scientific sophistication. However,
it does not require a lot of mathematical sophistication.
The second step is to solve these equations, either by hand or by computer,
and interpret the results to obtain useful information about the underlying
The equations we will be concentrating on are differential
equations, and a secondary goal of this course is to learn how to analyze
differential equations. Compared to a course like M427K, we will
be spending little time on how to solve differential equations,
and lots of time on why, and on how to interpret the results.
The prerequisites are calculus (M408D or equivalent) and
a willingness to think mathematically about the real world. Taking M427K,
either beforehand or concurrently, is useful but not essential.
Textbook: Modeling Differential Equations in Biology,
by Clifford Taubes. We will cover roughly chapters 1-17.
Computers: Computers make "step 2" remarkably
easy in many cases, and it would be criminal not to learn how to take advantage
of that. Accounts on the math department computer system will
be given out, and roughly half the homework will be computer based.
Attendance: Attendance and participation is
mandatory. This is a small seminar-style class, and reading the book
alone is no substitute for learning from, and contributing to, class discussions.
If you must miss a class, please tell the professor or the TA in advance.
Homework: There will be weekly homework. Every
other week, the homework will consist of computer exercises.
Collaboration: Science is not a solitary endeavor!
We encourage collaboration for everything but the midterm and final exams.
In fact, collaboration is required for the computer segments. As
Dr. Uhlenbeck remarked when teaching this class: "One person versus a computer
is unfair competition (the computer wins)".
Exams: There will be one midterm during the week of
Term projects: Each student (or rather, team of students)
is expected to do a minor project and a major project. The minor
project is presented to the class in late October, the major project at
the end of the term. The major project is typically, but not necessarily,
an extension of the minor project.
Grading: All students who do the work can expect
at least a B. Assuming all work is done reasonably, your grade
will be based on the top five of the following eight items:
1) Class participation and regular homework
2) Computer exercises
3) Minor project
5,6) Major project (counts twice)
7,8) Final exam (counts twice). If your scores from
the first six items are good enough for you, you are welcome to skip the
Disabilities: The University of Texas at Austin provides
upon request appropriate academic accommodations for qualified students
with disabilities. For more information, contact the Office of the Dean
of Students at 471-6259, 471-4641 TTY