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Department
of Mathematics
Mathematics 36. Mathematical and
Computational Methods
for the Life Sciences
Fall 2007
Course Outline
T=
ime
and Place: =
MWF
10:00 am - 10:50 am
Millikan 207
Instructor: =
&=
nbsp; Dr.
Adolfo J. Rumbos
Office:<=
span
style=3D'mso-spacerun:yes'> =
Andre=
w 259.
Phone / e-mail: =
ext. 18713 /
Office Hours: =
&=
nbsp; MWF
9:15 am-9:50 am; Tu 9:15 am-10:50 am, 2:30 pm-3:30 pm
or by appointment
Text:<=
span
style=3D'mso-tab-count:3'> &=
nbsp; &nbs=
p; Mathematical
Models in Biology by E. S. A=
llman
and J. A. Rhodes
Prerequisites:<=
span
style=3D'mso-spacerun:yes'> Passing
score in Math 32 placement exam.
=
The main goal of this course is the
exploration of mathematical topics that have relevance in the study of
biological systems. The topic=
s will
range from difference and differential equations to probability and stochas=
tic
processes. The mathematics is
motivated by biological questions and developed in that context. Emphasis will be placed on the pro=
cess
of mathematical modeling; this consists of (1) translation of questions in
Biology into mathematical formalism (variables, parameters, functions,
equations, etc.); (2) formulation of mathematical problems (e.g., Can a giv=
en
equation or system of equations be solved? What are the properties of the
solutions?); (3) analysis of the mathematical problem; and (4) translation =
back
into the Biological situation.
Another important aspect of the course will be computation and data
analysis; this provides a link between the mathematical models and the actu=
al
biological systems under consideration.
=
The
specific topics to be covered are listed in the attached Tentative Schedule of Lectures and Examinations.
Grades will be based on the homewo=
rk, two
50-minute examinations, plus a comprehensive final examination. The grades will be computed as fol=
lows:
=
homework
&=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; 20%
=
Two
50-minute exams &nbs=
p; &=
nbsp; &=
nbsp; 50%
=
final
examination &n=
bsp;  =
; &n=
bsp;  =
; 30%
Time: =
Monday,
December 17
9:00 am
Place: Millikan
207
Math 36<=
span
style=3D'mso-spacerun:yes'> &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; &nb=
sp; =
&nb=
sp; &=
nbsp; Fall 2007
Tentative Schedule of Lecture=
s and
Examinations
Date &=
nbsp; &nbs=
p; Topic
W Sep.<=
span
style=3D'mso-spacerun:yes'> 5 A
problem from microbial genetics: bacterial resistance
F &=
nbsp; Sep. 7&n=
bsp; Modeling
bacterial growth: discrete approach
M &n=
bsp; Sep. 10&=
nbsp; Logistic
difference equation
W Sep. 12&=
nbsp; Numerical
analysis of the logistic equation: Introduction to MATLAB
F &=
nbsp; Sep. 14 Qualitative anal=
ysis
of the logistic difference equation: cobweb analysis
M &n=
bsp; Sep. 17 Equilib=
rium
points and stability
W Sep. 19 Princip=
le
of linearized stability
F &=
nbsp; Sep. 21 Oscilla=
tions
and chaos
M &n=
bsp; Sep. 24 Modeling
bacterial growth: continuous approach
W Sep. 26 Exponen=
tial
growth
F &=
nbsp; Sep. 28 Logistic
growth
M &n=
bsp; Oct. 1 Existence
and uniqueness of solutions
W Oct. 3 Global
existence and long-term bahavior
F &=
nbsp; Oct.
5 Qualitati=
ve
analysis: equilibrium points, stability and linearized stability
M &n=
bsp; Oct. 8 &=
nbsp; Linear
first order models
W Oct. 10 Solving
the logistic equation
F &=
nbsp; Oct. 12 Problems
and examples: One-compartment models
M &n= bsp; Oct. 15 Review<= o:p>
W Oct. 17 Exam
1
F &=
nbsp; Oct. 19 Random
variables and distributions
M &n=
bsp; Oct. 22 Fall
recess: No Classes
W Oct. 24 Probabi=
lity
distributions in genetics
F &=
nbsp; Oct. 26 Probability
distributions in genetics (continued)
M &n=
bsp; Oct. 29 Probabi=
listic
models
W Oct. 31 Probabi=
listic
models (continued)
F &=
nbsp; Nov. 2 Pr=
oblems
and examples
M &n=
bsp; Nov. 5 Mo=
deling
bacterial mutations
W Nov. 7 Ra=
ndom
Processes
F &=
nbsp; Nov. 9 The
Poisson process
M &n=
bsp; Nov. 12=
The
Poisson process (continued)
W Nov. 14&=
nbsp; Goodness
of fit
F &=
nbsp; Nov. 16=
Goodness
of fit (continued)
M &n=
bsp; Nov. 19=
Modeling
the development of resistance
W Nov. 21=
Modeling
the development of resistance (continued)
F &=
nbsp; Nov. 23=
Thanksgivi=
ng
recess
M &n=
bsp; Nov. 26=
The
Luria-Delbrück experiment: average number of resistant bacteria
W Nov. 28=
The
Luria-Delbrück distribution
F &=
nbsp; Nov. 30=
The
Luria-Delbrück distribution: Goodness of fit
M &n=
bsp; Dec. 3 Pro=
blems
and examples.
W Dec. 5 Rev=
iew
F &=
nbsp; Dec. 7 E=
xam 2
M &n= bsp; Dec. 10= Review<= o:p>
W Dec. 12= Review<= o:p>
M =
Dec. 17=
Final
Examination