MATH 111B (Spring quarter 2004).
Introduction to Mathematical Modelling

Instructor: David A. Meyer
Office hours (Spring quarter): AP&M 7256, T 12:30-1:30 and F 1:00-2:00, or by appointment
Lecture: HSS 1106A, MWF 12:00-12:50

Course description

This course is a focused introduction to mathematical modelling. In 2004 I plan to concentrate on two topics: (1) the use of power laws to model distributions such as city sizes and Internet node connectivities, and (2) the use of diffusion to model the evolution of scalar quantities, like temperature, on fixed structures. Along the way I will introduce basic ideas in probability and statistics (random walks, normal distributions, hypothesis testing), graph theory (traditional and recent random graph models), analysis (the Laplacian and its spectrum), and geometry (Voronoi cells, Hausdorff dimension).

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. In the Spring quarter class hours will often involve discussions or brief presentations by students.

I intend this course to be interesting for and accessible to quantitatively oriented social science majors as well as physical science, engineering and mathematics majors. To that end, many of the phenomena modelled will be drawn from geography, economics, political science and communications.

The prerequisites are the lower-division math sequence through differential equations (21D) or linear algebra (20F), or consent of the instructor. Please contact me if you are interested but unsure if your mathematics background will suffice. It is not necessary to have taken 111A in the Winter quarter to enroll this quarter.

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

Related events

13-14 apr 04 U. S. Census Bureau at the UCSD Spring Job Fair
7 apr 04
Valentino Dardanoni 		The measurement of mobility: a class of distance indicies
7 apr 04
Raissa D'Souza 		Networks, power-laws, and self-organization

Syllabus (homework in green)

29 mar 04
no lecture today, sorry
31 mar 04
re-introduction [notes1]
wealth distribution in China
read course notes from 111A; ask questions on friday
collect Forbes 400 data for years preceeding 2003; compute least-squares fit to log-log plot of wealth vs. rank; email me results before monday's class
2 apr 04
overview [notes2 (contact me for hardcopy)]
city sizes
networks
5 apr 04
Forbes 400 wealth distribution
review of models of wealth distribution
7 apr 04
David Shrekenhamer: California road network
10 may 04
Ising model for ferromagnetism
definition
Glauber dynamics [Mathematica code]

References (on reserve at S&E library)

[1] R. J. Larsen and M. L. Marx, An Introduction to Mathematical Statistics and Its Applications (Upper Saddle River, NJ: Prentice Hall 2001).
[2] T. M. Porter, The Rise of Statistical Thinking, 1820-1900 (Princeton, NJ: Princeton University Press 1986).
[3] G. K. Zipf, National Unity and Disunity: The Nation as a Bio-social Organism (Bloomington, IN: The Principia Press 1941).
[4] G. K. Zipf, Human Behaviour and the Principle of Least Effort (Cambridge, MA: Addison-Wesley 1949).
[5] M. Fujita, P. Krugman and A. J. Venables, The Spatial Economy: Cities, Regions, and International Trade (Cambridge, MA: MIT Press 1999).
[6] P. Krugman, The Self-organizing Economy (Cambridge, MA: Blackwell 1996).
[7] F. R. K. Chung, Spectral Graph Theory, Regional Conference Series in Mathematics no. 92 (Providence, RI: AMS 1997).
Last modified: 11 may 04.