Math 345, Introduction to Mathematical Biology, Fall 2006
Syllabus
| Instructor: Professor Junping
Shi |
| Office: Jones
Hall 122 |
| Office Hour: TRF 2-3pm or by appointment |
| Phone: 221-2030 |
| email: jxshix@wm.edu |
Course Description
This course introduces many mathematical models in biology. The
increasing
use of mathematics in biology is inevitable as biology becomes more
quantitative.
We use the mathematical tools like difference equations, differential
equations
to model various biological phenomena, and we also introduce the basic
analytical method based on calculus and algebra, qualitative analysis
based
on elementary geometry and computer aid numerical method to completely
analyze some basic models. These mathematical tools will be useful for
life sciences major students in any quantitative and qualitative
analysis
in the future. Biological applications include various population
growth
models (Malthus, Logstic, competion, predator-prey, cooperating),
epidemic
models, chemostat, HIV virus models, enzyme kinetics,
and others. The prerequisites of the course are Math 111 and 112
(Calculus
I and II). Math 211 (multivariable calculus) and 212 (linear algebra)
are
not needed, but we will learn some material on these subjects during
the
course. There is some overlap between this course and Math 302
(Differential
Equations), but this course emphasizes applications in biology while
Math
302 also includes applications to physics, chemistry and
eigeneering.
Course Webpage: http://www.math.wm.edu/~shij/math345/index.html
Meeting Times and places: Tuesday and Thursday,
9:30-10:50am, Jones Hall 306
Prerequisites: Math 111/131 and Math 112/132
Textbook: Essential
Mathematical Biology, By Nicholas F.
Britton,
Springer-Verlag,
London, (2003). We will cover roughly Chapters 1--4 and some other
material not in textbook.
References: some material of the course will from these
books,
you don't have to buy these books.
- Mathematical Biology, Vol. 1: An Introduction. By James
Dickson
Murray, Springer-Verlag, New York, (2002).
- Mathematical Biology, Vol. 2: Spatial Models and
Biomedical
Applications.
By James Dickson Murray, Springer-Verlag, New York, (2002).
- Mathematical Models in Biology. By Leah
Edelstein-Keshet,
McGraw-Hill,
Boston, (1988). SIAM, (2005).
- Elements of Mathematical Ecology. By Mark Kot,
Cambridge
University
Press, (2001).
-
Modeling Differential
Equations in Biology By Clifford
Henry Taubes, Prentice
Hall (2000).
- Growth and Diffusion Phenomena: Mathematical Frameworks
and
Applications.
By Robert Banks, Springer-Verlag, New York, (1993).
- Life's Other Secret: The New Mathematics of the Living World.
By
Ian Stewart, Wiley, John & Sons, Inc., (1999).
- Complex Population Dynamics :
A Theoretical/Empirical Synthesis,by Peter Turchin, Princeton
University Press, (2003).
-
Mathematics in Population
Biology, by
Horst R. Thieme, Princeton University Press, (2003).
-
An Introduction to Mathematical
Biology by
Linda J.S. Allen, Prentice Hall (2006).
Computer and Calculators: Computer demonstrations will be
given
in classes sometime, and software Maple and Matlab will be used in some
homework assignments and possibly
in your semester project. Maple/Matlab are available on all
university
network computers, please visit webpage http://www.wm.edu/IT/labs/
for lab information. Graphing calculator is not necessary for this
course, though a simple
scientific calculator may be useful for some numerical
calculations.
Course Grade:
| Test #1 |
15% |
| Test #2 |
15% |
| Homework |
30% |
| Project |
40% |
| Total |
100% |
|
|
| Percentage |
Letter grade |
| 90-100 |
A |
| 80-90 |
B |
| 70-80 |
C |
| 60-70 |
D |
| below 60 |
F |
|
|
Tests and Final Exam: We will have two take-home tests during
the semester, and there is no in-class final exam. Each test accounts
for 15% of the grade.
Homework: Homework will be assigned (the list
is available from course webpage) and will be collected and graded.
Homework accounts for 30% of the semester grade.
Project: A semester long project is to choose one of
your
favorite topics as an application of techniques learned from
this course. Your work should include mathematical modeling, analytic
computation,
qualitative analysis and numerical computations. The final product is a
report to be submitted in December 12th (Tuesday) 9am. Your
report should record all
your
works, including possible graphic illustrations. You can choose the
topic of your project, or you can choose
one from a list of possible topics provided by the instructor on the
course
webpage. In any case, you need to talk with me about your biological
interest before Septmeber 29th,
and you should submit a title and a 200 word abstract
by email to the instructor by October 23rd. In the final two
weeks, you will do a 10-minute presentation of your project in class.
The project accounts for 40% of the grade (presentation 10%, and report
30%)