MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01CA99DD.63BC2FE0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01CA99DD.63BC2FE0 Content-Location: file:///C:/1EF21713/Math36Spring2010Syllabus.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
Department
of Mathematics
Mathematics 36. Mathematical and
Computational Methods
for the Life Sciences
Spring 2010
Course Outline
Time and
Place: =
MWF
11:00 am - 11:50 am
Millikan 213
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
9:00 am-9:50 am 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
Course Website: &nb=
sp; http://pages.po=
mona.edu/~ajr04747/
Prerequisites:<=
span
style=3D'mso-spacerun:yes'> Math
31 (Calculus II) or 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, three
50-minute examinations, plus a comprehensive final examination. The grades will be computed as fol=
lows:
=
homework
&=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; 20%
=
Three
50-minute exams &=
nbsp; 50%
=
final
examination &n=
bsp;  =
; &n=
bsp;  =
; 30%
Time: =
Tuesday,
May 11 9:00
am &nbs=
p; Place:
Millikan 213
Math 36<=
span
style=3D'mso-tab-count:10'> =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
Spring
2010
Tentative Schedule of Topics and
Examinations
Date &=
nbsp; &nbs=
p; Topic
W Jan 20 =
span>A
problem from microbial genetics: bacterial resistance
F &=
nbsp; Jan 22 =
span>Modeling
bacterial growth: discrete approach
M &n=
bsp; Jan 25 =
span>Logistic
difference equation
W Jan 27 =
span>Numerical
analysis of the logistic equation: Introduction to MATLAB
F &=
nbsp; Jan 29 =
span>Qualitative
analysis of the logistic difference equation: cobweb analysis
M &n=
bsp; Feb 1 Equilibrium
points and stability
W Feb 3 Principle
of linearized stability
F &=
nbsp; Feb 5 Oscillations
and chaos
M &n=
bsp; Feb 8 Modeling
bacterial growth: continuous approach
W Feb 10=
E=
xponential
growth
F &=
nbsp; Feb 12=
L=
ogistic
growth: Qualitative Analysis
M &n=
bsp; Feb 15=
E=
xistence,
uniqueness and long term behavior of solutions
W Feb 17=
R=
eview
F &=
nbsp; Feb 19=
<=
b>Exam
1
M &n=
bsp; Feb 22=
<=
/span>Examples:
Linear first order
models
W Feb 24=
P=
rinciple
of linearized stability
F &=
nbsp; Feb 26=
Q=
ualitative
analysis: equilibrium points, stability and linearized stability
M =
Mar 1 &=
nbsp; Solving the logistic equation
W &nb=
sp; Mar 3 &=
nbsp; Solving the logistic equation (continu=
ed)
F &nb=
sp; Mar 5 &nbs=
p; Random variables and distributions
M =
Mar 8  =
; Probability
distributions in genetics
W Mar
10  =
; Probability
distributions in genetics (continued) =
F &=
nbsp; Mar
12  =
; Probabilistic
models
M &n=
bsp; Mar 15=
Spring Recess
W Mar 17=
Spring Recess
F &=
nbsp; Mar 19=
Spring Recess
M &n=
bsp; Mar 22=
Probabilistic
models (continued)
W Mar 24=
R=
andom
Processes
F &=
nbsp; Mar 26=
Cesar Chavez Day (observed)
M &n=
bsp; Mar 29=
T=
he
Poisson process
W Mar 31=
R=
eview
F &=
nbsp; Apr 2 Exam
2
M &n=
bsp; Apr 5 The
Poisson process (continued)
W Apr 7 Goodness
of fit
F &=
nbsp; Apr 9 Goodness
of fit (continued)
Math 36<=
span
style=3D'mso-tab-count:10'> =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
Spring
2010
Date &=
nbsp; &nbs=
p; Topic
M &n=
bsp; Apr 12 M=
odeling
the development of resistance
W Apr 14 M=
odeling
the development of resistance (continued)
F &=
nbsp; Apr 16 M=
odeling
the development of resistance (continued)
M &n=
bsp; Apr 19 T=
he
Luria-Delbrück experiment: average number of resistant bacteria
W Apr 21 T=
he
Luria-Delbrück distribution
F =
Apr 23 <=
/span>The Luria-Delbrück distribution:
Goodness of fit
M &n=
bsp; Apr 26 P=
roblems
and examples
W Apr 28 R=
eview
F &=
nbsp; Apr 30 <=
b>Exam
3
M &n=
bsp; May 3 Revi=
ew
W May 5 Revi=
ew
Tu May 11=
Final Examination