Instructor: David A. Meyer
Office hours (Fall Quarter): AP&M 7256, W 10:00am-11:00am, or by appointment
Lecture: Warren Lecture Hall 2112, MWF 9:00am-9:50am
Email: dmeyer "at" math "dot" ucsd "dot" edu
TA: Gautam Wilkins
Office hours (Fall Quarter): AP&M 5712, W 11:00am-1:00pm, or by appointment
Section: Warren Lecture Hall 2112, M 7:00pm-7:50pm
Email: gwilkins "at" math "dot" ucsd "dot" edu
This course is a focused introduction to mathematical modelling. In 2013 I plan to discuss mathematical models drawn from a wide range of topics (but mostly outside the familiar contexts of the physical science and engineering) including biology, economics, political science, and culture. (For inspiration see [1,2].) 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) and linear algebra (20F or 31A), 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 at the bottom of the page.
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.
| 1 Mar 14 |
Application deadline for undergraduate summer program in mathematical and theoretical biology at Arizona State University. |
| 15 Dec 13/15 Jan 14 |
Application deadline for graduate studies at the University of Waterloo Institute for Quantum Computing. |
| 1 Nov 13 |
Submission deadline for Hertz Foundation Graduate Fellowships. |
| 16 Oct 13 |
"Math and the Body and the Mind" Arthur C. Clarke Center for Human Imagination Colloquium, Atkinson Auditorium, 5:30-7:30pm |
| 10 Oct 13 |
Meg Urry (Yale), "The growth of supermassive black holes and galaxies over cosmic time" Physics Colloquium, BSB Garren Auditorium, 4:00pm |
| 9 Oct 13 |
Meg Urry (Yale), "Why so few? The dearth of women in physics and astronomy" Astrophysics Seminar, SERF 383, 4:00pm See also Eileen Pollack, "Why are there still so few women in science?", New York Times Magazine (3 October 2013). |
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27 Sep 13 DM lecture |
administrative details overview/motivation population growth model HWK (for M 30 Sep 13). Read Bender, chap. 1. Find something in the news or elsewhere that suggests a system that could be modeled (or not); email me link (if there is one) and be prepared to discuss in class. Solve y' = (M - y)y; turn in written solution in section. |
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30 Sep 13 discussion |
discussion of news items or other sources suggesting mathematical models (or not) Energy requirements for hot-air balloons Rise and fall of slang words/expressions Admission of freshmen and transfer students to UCSD Optimizing study schedules Economic benefits of TV/movie production: "Breaking up with 'Breaking Bad' is hard for Albuquerque" |
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2 Oct 13 discussion |
overview of the process of constructing a mathematical model continued discussion of news items or other sources suggesting mathematical models (or not) "In fragmented forests, rapid mammal extinctions" Unemployment rate Optimizing dining hall hours HWK. Read Bender, chap. 2 (for F 4 Oct). Solve problems 5, 7 (Bender, pages 33, 34); turn in written solution in section (M 7 Oct). |
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4 Oct 13 DM lecture |
scaling as a technique for mathematical modeling length, area, volume of similar shapes more then 3 dimensions surface to volume scaling with dimension human weight vs height example: basketball players who declare for the NBA draft does weight scale as the cube of height? [Mathematica notebook] images: Shawn Bradley, Shaquille O'Neal, LeBron James, Carmelo Anthony, Tim Hardaway, Jr., Isaiah Thomas |
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7 Oct 13 DM lecture |
least-squares fits: definition and computation [Mathematica notebook] Does a better fit mean a better model? distribution of residuals normal distributions [notes] distribution of adult heights HWK. Read Bender, appendix A. |
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9 Oct 13 DM lecture |
graphical methods for optimization indifference curves Pareto set in Edgeworth box optimization subject to budget constraint substitutes and complements demand sets HWK. Read Bender, chap. 4. Solve prob. 6 (Bender, page 90); turn in written solution in section (M 14 Oct). |
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11 Oct 12 discussion |
HWK. Read Varian's article on how to build a model [4]. Read Gray's article on how to write an abstract [5]. Look at some proposals/videos on Kickstarter, e.g., GoldieBlox. Draft project proposal (due by M 21 Oct 13): 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. Should be 2-4 pages. I prefer that you submit an electronic version, ideally a pdf file of a TeX [3] document. If you want to try making a video à la Kickstarter, I'll be pleased to watch it. |
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14 Oct 13 DM lecture |
towards a model for school choice in the San Diego Unified School District (SDUSD) motivation: 'excessed teachers' reassigned in week 6 of school year estimating neighborhood enrollment many factors binomial distribution expectation and variance of random variables HWK. Read Bender, chap. 5. |
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16 Oct 13 DM lecture |
school capacity utility as function of enrollment [notes] |
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18 Oct 13 |
No lecture; work on project proposal. (DM at Johns Hopkins University memorial for father) |
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23 Oct 13 DM lecture |
feedback on project proposals broad range of interesting topics content problems some need more details on math part of model if a regression model, include developement of functional form of dependence some need more discussion of existing models writing problems [6,7,8] punctuation: Latin phrases, commas, semicolons grammar: subject/verb agreement, moun/pronoun agreement ("their"), verb tenses style: "however", split verbs, repetition, parallel construction |
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25 Oct 13 |
No lecture; work on project.. (DM at UC diversity workshop) |
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1 Nov 13 DM lecture |
do polymath projects examplify benefits of diversity, or of collaboration? digression and mathematics cultural enrichment Prime Number Theorem Prime Pairs Conjecture Zhang's Bounded Gap Theorem [9] polymath 8 reduction of Zhang's bound [10] Hong and Page's search problem [11] simulations [Mathematica notebook] |
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25 Nov 13 presentations |
Chessa Filip |
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27 Nov 13 presentations |
Anthony Christina Clara |
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29 Nov 13 |
Thanksgiving vacation. |
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2 Dec 13 presentations |
Carlos Kunal Steven P. |
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2 Dec 13 section |
Francisco/Jennifer |
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4 Dec 13 presentations |
Björn Tylon |
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5 Dec 13 presentations |
Thursday evening 6pm until we finish, AP&M 6402; pizza Avani Grace Jack Jason Joshua B. Joshua S. Peihong Stephanie Ziyi/Fengyi |
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6 Dec 13 presentations |
Helen June Steven N. |