MATH 111B (Winter Quarter 2020).
Mathematical Modelling II

Instructor: David A. MEYER
Email: dmeyer "at" math "dot" ucsd "dot" edu
Office hours (Winter Quarter): AP&M 7256 M 11:00am-12:50pm, or by appointment
Lectures: AP&M 2402 MWF 10:00am-10:50am

TA: Linbo LIU
Email: linbo "at" ucsd "dot" edu
Office hours (Winter Quarter): AP&M 5412, MW 2:00pm-3:00pm, or by appointment
Recitations: AP&M B412 Tu 8:00am-8:50am

Course description

This is a second course in mathematical modelling. In 2020 I plan to focus on mathematical models drawn from a range of topics coordinated with students' projects, which are often outside the more familiarly mathematical sciences. (For inspiration see [1,2].) I may also, however, discuss some models of weather and of climate change. The relevant mathematical methods will 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) and linear algebra (18 or 31A), and a first course in mathematical modeling (111A), or consent of the instructor. Please contact me if you are interested but unsure if your mathematics background will suffice.

The 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%). Some titles of projects from previous years are listed below.

I recommend, but do not require, that you prepare your written materials using some dialect of TeX [3]. In any case, please do not send me Word documents; convert them to pdf first.

Related events

Apr 10 Application deadline for Air Force Research Lab Summer of Topological Data Analysis Intern.
Mar 9 Application deadline for UC San Diego Physical Sciences Undergraduate Summer Research Award.
Feb 22, 2020 Final application deadline for USC Security and Political Economy Lab NSF Research Experience for Undergraduates
Feb 19 MATLAB seminars, "Data Analysis and Visualization with MATLAB for Beginners", 10:00am-12:00nn, Geisel Library, Classroom 2,
"What's New in MATLAB?", 1:00pm-3:00pm, Geisel Library, Classroom 2.
Feb 17, 2020 Application deadline for University of Washington Data Science for Social Good Summer Program.
Feb 6 Alex Hening, "Stochastic persistence and extinction",
11:00am-11:50am, AP&M 6402.
Jan 31, 2020 Application deadline for Mathematical and Theoretical Biology Institute Summer Program
Jan 6, 2020 Application deadline for Perimeter Institute Theoretical Physics Summer Program

Syllabus (homework in green)

Jan 6, 2020
DM lecture
administrative details
         models, metaphors & imagination [slides]
discussion of project ideas
HWK (for W Jan 8).
         (Re)read Bender, Chap. 1. What is modeling?; Varian [4]; Gray [5]; Goldin [6]

Jan 8, 2020
DM lecture
Albert CHIU, Game theoretic model of protest participation
Jan 8, 2020
DM lecture
Nick WONG, Models for Lambda phage and Escherichia coli
HWK (for F Jan 17).
         Project proposal:
                 Describe the system for which you propose to construct a mathematical model.
                 What question will the model answer? Why is that important/interesting?
                 Has anything relevant been done to model this system previously? Give references.
                 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.
         Should be 2-4 pages. Please submit a pdf file electronically, ideally from a TeX [3] document.
Jan 13, 2020
DM lecture
Meghedi ZARGARIAN, High frequency algorithms
Jan 15, 2020
DM lecture
Emily REXRODE, Markov chain model for bull/bear markets
Jan 17, 2020
DM lecture

Suggested reading

[1] I. Asimov, The Foundation Trilogy (New York: Gnome Press 1951).
[2] P. R. Krugman, "Introduction to The Foundation Trilogy" (Folio Society 2012).
[3] D. E. Knuth, The TeXbook, Computers and Typesetting, Volume A (Reading, Massachusetts: Addison-Wesley 1984).
[4] H. R. Varian, "How to build an economic model in your spare time", The American Economist 41 (1997) 3—10.
[5] N. Gray, "Abstract science", The Huffington Post (2012).
[6] A. Bleicher interview with R. Goldin, "Why math is the best way to make sense of the world", Quanta magazine (2017).

Titles of projects from previous years

Last modified: 13 February 2020.