MATH 111A (Fall quarter 2007).
Introduction to Mathematical Modelling

Instructor: David A. Meyer
Office hours (Fall quarter): AP&M 7256, M 1:00pm-2:00pm, Th 2:00pm-3:00pm, or by appointment
Lecture: Warren Lecture Hall 2114, MWF 11:00am-11:50am

TA: Jon Grice
Office hours (Fall quarter): AP&M 5768, W 12:00pm-1:00pm, Th 7:00pm-8:00pm, or by appointment
Section: AP&M 2301, Th 8:00pm-8:50pm

Course description

This course is a focused introduction to mathematical modelling. In 2007 I plan to discuss mathematical models for epidemics, chemical reactions, political organizations, magnets, economic mobility, and geographical distributions of species. The relevant mathematical methods include: (systems of) ordinary differential equations, graphs/networks, probability, partial differential equations, eigenvalues/eigenvectors, permutations, and dimension theory.

The goals of this course are: (1) to explain what it means to construct a mathematical model of some real-world phenomenon, (2) to introduce some of the mathematical ideas that are used in many such models, (3) to apply these methods to analyze one or more real problems, and (4) to understand how new mathematical ideas are motivated by such modelling.

The prerequisites are the lower-division math sequence through differential equations (20D) or linear algebra (20F), or consent of the instructor. Please contact me if you are interested but unsure if your mathematics background will suffice.

The (recommended) textbook is E. A. Bender, An Introduction to Mathematical Modeling (Mineola, NY: Dover 2000).

I expect interest and enthusiasm from the students in this class. 30% of the grade is class participation, which includes occasional homework assignments, often for class discussion. 70% of the grade is based upon a mathematical modelling project for which each student writes a proposal (15%), writes a preliminary report (10%), gives a final presentation (20%), and writes a final report (25%).

Related events

1 dec 07 Putnam exam
contact Jeff Rabin for information about practice sessions
15 oct 07 NSA Director's Summer Program applications due

Syllabus (homework in green)

28 sep 07
DM lecture
administrative details
what is a mathematical model?
population growth
read Bender, chap. 1
do problems 7 (for discussion in lecture) and 8 (to hand in at section on 4 oct 07)
1 oct 07
DM lecture
evaluating the ODE population growth model
comparison with data
asymptotic behavior
macroscopic vs. microscopic models
a probabilistic microscopic model for population growth
simulation [Mathematica code]
read introductory notes on probability
read Bender, Appendix A1-A3
3 oct 07
DM lecture
comparison with the ODE population growth model
probabilistic predictions
5 oct 07
DM lecture
wealth distribution
Forbes 400
Pareto distribution
mobility
look at news (scientific news is ok) and identify a system for which one might be able construct a mathematical model
what question would you like the model to answer?
what features/variables should the model include?
what features/variables should be taken to be exogenous?
what kind of mathematics would the model use?
be prepared to discuss in class on monday 7 oct 07
8 oct 07
DM lecture
discussion of homework assigned 5 oct 07
9 oct 07
JG section
review of probability; see reading assigned 1 oct 07
10 oct 07
DM lecture
wealth mobility
rank and cumulative probability distribution
log-log linearity of the Pareto distribution
permutations
write project proposal to hand in on wednesday 17 oct 07
Describe the system for which you propose to construct a mathematical model.
What question will the model answer? Why is that important/interesting?
What features/variables will the model include? What features/variables may be relevant but will be exogenous to your model? What kind of mathematics will you use?
If you intend to use real data, describe them and explain how you will get them.
Give an approximate timeline for accomplishing the various pieces of your project. If you will be working with someone else, explain how the work will be allocated and coordinated.
22 oct 07
No lecture today. UCSD closed due to fires.
24 oct 07
No lecture today. UCSD closed due to fires.
26 oct 07
No lecture today. UCSD closed due to fires.
Suggested reading:
O. H. Pilkey and L. Pilkey-Jarvis, "Why mathematical models just don't add up".
C. Wunsch, "Misuse of models".
W. Kolata, "A useless case".
9 nov 07
DM lecture
fitting the SIR model to the 1995 Kikwit Ebola outbreak
12 nov 07
No lecture today. Veteran's Day..
14 nov 07
DM lecture
epidemic models without the mass action assumption
SIR model on a semi-infinite chain
solving the SI model on a semi-infinite chain
a discrete time SI model on a semi-infinite chain
Last modified: 14 nov 07.