Instructor: David A. MEYER
Email: dmeyer "at" math "dot" ucsd "dot" edu
Office hours (Fall Quarter): AP&M 7218, Th 1:00am-1:50pm, or by appointment
Lectures: AP&M B402A MWF 11:00am-11:50am
TA: Bingni GUO
Email: b8guo "at" ucsd "dot" edu
Office hours (Fall Quarter): AP&M 6442 Tu 2:00pm-4:00pm
Recitations: AP&M 2402 Tu 1:00pm-1:50pm
This course is a focused introduction to mathematical modelling. In 2018 I plan to discuss mathematical models drawn from a wide range of topics, but mostly outside the familiar contexts of the physical sciences and engineering. (For inspiration see [1,2].) I do, however, plan to 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), 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.
| Feb 1, 2019 |
Application deadline for Perimeter Scholars International Masters Program |
| Jan 31, 2019 |
Application deadline for Mathematical and Theoretical Biology Institute Summer Program |
| Jan 7, 2019 |
Application deadline for Perimeter Institute's Undergraduate Theoretical Physics Summer Program |
| Nov 8, 2018 |
Psychology Colloquium Clinton Davis-Stober on preference relations/decision making Mandler Hall, room 3545, 11:00am-12:30pm |
| Oct 11, 2018 |
Fall Career Fair (including data science jobs at companies like Acumen) Price Center, 10:00am-2:30pm |
| Oct 10, 2018 |
Science and Technology Career Fair RIMAC, 9:30am-3:30pm |
| Oct 8, 2018 |
AI Seminar Mengting Wan Exploring structures behind heterogeneous human activities in recommender systems CSE 4140, 12:00pm-12:50pm |
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Sep 28, 2018 DM lecture |
administrative details overview/motivation simple population growth model example of UC undergraduate enrollment [plot] first order linear ODE HWK (for M Oct 1). Read Bender, Chap. 1. What is modeling? HWK (for Tu Oct 2). Bender, Chap. 1., Prob. 8 |
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Oct 1, 2018 DM lecture |
model for the stoop of a peregrine falcon PBS NATURE, "Raptor Force - The Peregrine's Stoop" [video] BBC, "Peregrine Falcon Sky Dive - Inside the Perfect Predator" [video] drag [4] diagram of peregrine foveal plane [5] geometrical model plotting the spiral |
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Oct 3, 2018 DM lecture |
beyond a spiral comparison with data [6] BBC, "Flying with the fastest birds on the planet: Peregrine Falcon & Goshawk" [video] "Dora's BackCam - Peregrine taking a Duck" [video] pursuit models [7,8] HWK (for F Oct 5). Find something in the news or elsewhere that suggests a question about a system that could be informed by making a mathematical model; email me link (if there is one) and be prepared to discuss in class. |
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Oct 5, 2018 DM lecture |
improv modeling An Analysis of the Basketball Endgame: When to Foul When Trailing and Leading [John Lam] Let the hacking begin UCSD shuttle service [Yvonne Li] I spent 53 minutes in Amazon Go and saw the future of retail [Weining Xu] A Geometric Model for On-line Social Networks [Evan Krause] New Two-Hour Limit Placed on La Jolla Scenic Parking to Remove Students [Jenny Pi] UCSD Unveils New Technologically-Advanced Osler Parking Structure McDonald's should pay its workers $15 an hour, Bernie Sanders says [Nathan Castillo] |
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Oct 8, 2018 DM lecture |
improv modeling What Happens When a Spinning Basketball is Thrown Off a Dam! [Xiaohang Mao] Marriage and divorce: patterns by gender, race, and educational attainment [Mayla Chen] Can Insurance Help Californians Recover from Natural Disasters? [Yimin Yang] The Stockholm Sleepy Brain Study: Effects of Sleep Deprivation on Cognitive and Emotional Processing in Young and Old [Jenny Hamer] Reaction times in a sleep deprivation study Need for Sleep: the Impact of a Night of Sleep Deprivation on Novice Developers' Performance Dear Elon Musk: Sleep Matters, But Not For The Reason You Think How much sleep do you need? More than you're getting Teacher Evaluation: An Issue Overview [Marina Torras] Teachers Deserve More Information on Evaluation Systems The Effect of Teacher Coaching on Instruction and Achievement: A Meta-Analysis of the Causal Evidence How the mushroom dream of a long-haired hippie could help save the world's bees [Mariana Meirelles] Introducing the TWS SwingSeat model [John Lam] Have Starbucks' limited time offers lost their appeal? [Crystal Wang] We Wanted Workers [Zixuan Feng] Center for Immigration Studies Latent Dirirchlet Allocation [Nick Roberts] Aggregate demand/aggregate supply [Jiajie Luo] The dynamics of audience applause [Cathleen Uy] Forecasting Player Behavioral Data and Simulating in-Game Events [Brian Nguyen] |
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Oct 10, 2018 DM lecture |
hazards of regression models motivating example [9] some data from Amazon linear models for these data, with R2 > 0.9 [code] why these models are misleading |
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Oct 12, 2018 DM lecture |
a mathematical model of voting formalization of voting desiderata for voting rules Arrow's Theorem [10] HWK (for M Oct 15). Read Varian [12], Gray [13] and Goldin [14]. Begin thinking about the system you want to model for your project. |
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Oct 15, 2018 DM lecture |
proof of Arrow's Theorem [11] discussion sample project proposal HWK (for M Oct 22). Draft 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. |
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Oct 16, 2018 BG section |
LaTeX tutorial [notes] |
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Oct 17, 2018 DM lecture |
network models undirected graphs and adjacency matrices counting paths by raising an adjacency matrix to a power structural balance models [15,16] signed network data frequencies of different triads un/balanced triads an "energy" function for signed graphs |
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Oct 19, 2018 DM lecture |
digression on agent-based models (ABM) making predator prey models spatial reintroduction of wolves in Yellowstone [17,18] prediction with structural balance models probabilistic models expectation values entropy Boltzmann distribution |
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Oct 22, 2018 DM lecture |
as maximum entropy distribution with fixed mean energy review of Lagrange multipliers for constrained optimization [code] derivation of Boltzmann distribution HWK (for W Oct 24). Read Bender, Appendix A: Some Probabilistic Background, and Chap. 4: Basic Optimization. Extra Credit (for Tu Oct 30). Which gives more information about a set of real numbers, e.g., a set of test scores, the average or the median? Formulate this question precisely and explain your answer. |
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Oct 24, 2018 DM lecture |
computing the probabilities for an unknown sign review of Bayes' Rule how to estimate β from multiple sample graphs |
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Oct 26, 2018 DM lecture |
from a single signed graph derivation of Maximum Likelihood Estimator dynamics for structural balance models a discrete time Markov process as an example of Monte Carlo simulation HWK (for M Oct 29). Read Bender, Chap. 3: Graphical Methods.. |
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Oct 29, 2018 DM lecture |
Cournot's model of duopoly [19] Bertrand's observation of instability [20] Hotelling's model of spatial competition [21] |
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Oct 31, 2018 DM lecture |
Smithies' introduction of elastic demand [22] HWK (for W Nov 7). Prepare 1 minute "elevator pitch" on your project to present in class. |
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Nov 2, 2018 DM lecture |
solving Smithies' extension of Hotelling's model numerically mathematics and metaphors application of spatial models to voting |
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Nov 5, 2018 DM lecture |
more on spatial voting models HWK (for M Nov 12). Interim progress report describe your model in detail (don't need to include results) where you are relative to proposed timeline revised timeline |
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Nov 7, 2018 |
students' elevator pitches |
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Nov 12, 2018 |
No lecture; Veterans' Day (also Armistice Day) holiday. |
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Nov 16, 2018 DM lecture |
HWK (for weeks 9, 10 & 11). 12+3 minute presentation describe system & state question [~4 minutes] describe model, but don't go into too many details [~5 minutes] explain results & answer to question [~2 minutes] how could model be improved/extended? [~1 minute] I recommend a slide presentation for efficiency. |
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Nov 19, 2018 DM lecture |
HWK (due Friday, Dec 7). Final project report Introduction: describe system & explain question and why it is interesting Describe model: what is being included/excluded; how do different pieces fit together; derive model/eqiuations [somewhere in the Introduction or Description, explain previous relevant models & why yours is different] Describe data: what are they? from where do they come? how reliable are they? Analyze model: explain math/computations; give results Conclusion: what is the answer to the question, from results? discuss answer; How might model be extended/improved? References: standard bibliographical format; citations in text; not wikipedia Approximately 10 pages; pdf, not Word.. You can include data/code as separate files, or links. Not a diary ("First I did this, then this, ..."); it should read like a scientific paper. Write sentences, paragraphs, sections, in the best English you know; not bullet points like on a slide presentation. |
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Nov 21, 2018 |
No lecture. |
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Nov 23, 2018 |
No lecture; Thanksgiving holiday. |
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Nov 28, 2018 DM lecture |
proof of convergence of continued fractions observation that the golden ratio is the "most irrational" number implications for parastichy the silver, bronze and plastic numbers definition of Pisot-Vijayaraghavan numbers mathematics and metaphors application of spatial models to voting |
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Nov 30, 2018 lecture |
Student project presentations. Jenny HAMER and Nick ROBERTS, "Kumaraswamy-beta variational autoencoder" |
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Dec 3, 2018 lecture |
Student project presentations. Mariana MEIRELLES and Marina TORRAS, "Pattern generation simulator" |
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Dec 4, 2018 recitation |
AP&M 2402. Student project presentations. Chengyou JU, "Applications of graph theory in the real world" Vasu IDDAMSETTY, "Protein homology: A graph-based approach" |
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Dec 5, 2018 lecture |
Student project presentations. John LAM, "Light pollution mapping" Jiajie LUO, "How to make decisions" Brian NGUYEN, "Football field goal" |
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Dec 6, 2018 extra lecture |
HSS 2321, 6:00pm-6:50pm, then CSB 004, 7:00pm-10:00pm. Student project presentations. Erin WARNER, "Military arsenal: A consequence of alliances" Zixuan FENG, "The model of a teapot" Haoran ZHANG, "Blood alcohol concentration and safe drive" Yvonne LI, "Random graph models of social media networks" Yosira HERNANDEZ, "Success among college students with generational differences" Wenyuan LIU, "How to avoid getting wet in the rain" Vivian SHI, "Amazon and Costco proposed acquisition" Ye Ji JEOUNG, "Modeling attention on Instagram" Evan KRAUSE, "Erg scores to on-the-water times as a function of weight in relation to surface area" Tianho REN, "Probability of bus delay" Lisbeth LOPEZ-HERNANDEZ, "Role of socio-economic status in education" Bingjie ZI, "Do last hits and denies play a significant role for DOTA2 carry players?" Jiayi SHEN, "How to get a high rating score in APP store" Yue JIANG, "Predict winning team in League of Legends game" |
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Dec 7, 2018 lecture |
Student project presentations. Cathleen UY, "Lost in Translation: An American Sign Language classifier" Samantha NGAN, "How to win friends and influence people: Stardew Valley" Lanxiang LI, "Hurricane Florence" |
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Dec 11, 2018 Final exam |
AP&M B402A, 11:30am-2:29pm. Student project presentations. Xiaohang MAO, "Exchange rate fluctuation" Chuqi LIU, "Hair loss model" Nathan CASTILLO, "Optimization with queueing" Jerry DONG, "Understanding the systematic risk of financial market - game theory and market graph" Ping CHEN, "Venture capital's investment model" Iris WANG, "Predator-prey interaction with migration" Sijia GUO, "Circular fire propagation: How many firefighters should be assigned to wildfire task?" Weining XU, "Networks between rhizosphere and non-rhizosphere soils" Ziyi ZHANG, "The evaluation of the redesign projects of student dormitory" Bingqi TU, "Racing line in an auto-racing game" |