Mathematical Modelling I

Instructor: David A. MEYER

Email: dmeyer "at" math "dot" ucsd "dot" edu

Office hours (Fall Quarter): M 11:00am-11:50am, AP&M 7218; or by appointment

Lectures:

Section A00: AP&M B412 MWF 10:00am-10:50am

Section B00: AP&M B412 MWF 9:00am- 9:50am

TA: Linbo LIU

Email: linbo "at" ucsd "dot" edu

Office hours (Fall Quarter): M 2:00pm-5:00pm and Th 2:00pm-3:00pm, AP&M 5412, or by appointment

Recitations:

Section A01: AP&M B412 Th 4:00pm- 4:50pm

Section B01: AP&M 5402 Th 1:00pm- 1:50pm

This course is a focused introduction to mathematical modelling. In 2019 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). It may be online at
SlideShare.

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 [3,4]. In any case, please do not send me Word documents; convert them to pdf first.

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 |

Nov 20, 2019 | Application deadline for Halıcıoğlu Data Science Institute Undergraduate Scholarship |

Nov 5, 2019 |
Math Department Undergraduate Colloquium David A. Meyer "Quantum data science?" AP&M, room B402A, 1:00pm-1:50pm |

Oct 23, 2019 |
Application deadline for Hertz Foundation Graduate Fellowship |

Oct 3, 2019 |
Institute for Practical Ethics Colloquium Anna Lauren Hoffmann "Beyond Fairness: Justice, Discourse, and Violence in a Datafied World" SSB, room 107, 4:00pm-5:30pm |

Oct 2, 2019 |
Microeconomic Theory Seminar Hiroki Nishimura "Preference structures" Sequoyah Hall, room 244, 2:00pm-3:20pm |

Sep 27, 2019 DM lecture |
administrative details overview/motivation HWK (for M Sep 30). Read Bender, Chap. 1. What is modeling? 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. |

Sep 30, 2019 DM lecture |
discussion of possible systems for mathematical modeling Section A00: Trump is hurting the market (Alex RUBER) Mathematical model offers new strategies for urban burglary prevention (Kyle SUNG) Uber is trying everything to make bikes and scooters a profitable business (Xinyue HE} The older the doctor, the higher the patient mortality rate (Enhao MA) Hate Speech and Hate Crime (Nicole CHEN) Section B00: The official U.S. poverty rate is based on a hopeles\ sly out-of-date metric (Kevin CHAN) Baidu Top (Yue SUN) Average Mauna Loa CO _{2} (Jiarui OU)Majority of Americans and Democrats approve of Trump impeachment inquiry (Meghedi ZARGARIAN) |

Oct 2, 2019 DM lecture |
continuing discussion of possible systems for mathematical modeling Section A00: Math models of flu transmission rates show dramatic savings with universal vaccine (Elisa LAU) Donald Trump's long history of racism, from the 1970s to 2019 (Zack JAFEK) How Kilauea's lava fed a massive phytoplankton bloom (Dylan VAN VALKENBERG) Estimating earthquake casualties and damage cost (Megan TANG) Italy, France agree on 'automatic' distribution of migrants (Honghao ZHA) McDonald's Is Becoming a Tech Company With Its Latest Purchase (Wayne NGUYEN) Just A Handful Of Nuts May Help Keep Us From Packing On The Pounds As We Age (Chris CHENG) The US has its first gas station that is fully electric (Emanuela BEALE) Pixel perfect: These modeling agencies don't hire real people (Sami WAHEED) Section B00: Attacking Contributions: Markov Models for Football (Taeho YUM) African swine fever (SooBin PARK) Amazon is purchasing 100,000 Rivian electric vans (Emily REXRODE) Black Scholes Model (Weiyuan XU) Men's NCAA Basketball Tournament Bracket History (Yunkai CHEN) The Art of Creating (Good) Music: Mixing & Mastering (Chuanchuan LIU) Air pollution modeling (Rundong ZHONG) California fire insurance (Siqi LIU) Weather prediction (A Young KIM) 'Historic' winter storm dumps 3 feet of snow, smashes records in West (Evan CHANG) Typhoon (Taekyeong LEE) Wealth tax (Rachel LEE) fantasy football (Jasmin ZHANG) Blended Facial Expressions towards Facial Expression Modeling (Yingkun WANG) |

Oct 3, 2019 LL section |
LaTeX [template] |

Oct 4, 2019 DM lecture |
greenhouse effect [5] solar flux at Earth physics of atmospheric heating Stefan-Boltzmann law |

Oct 7, 2019 DM lecture |
simple model for Earth surface and atmosphere solving the model for temperatures PGA golf description of the game data HWK. Read Bender, Appendix A: Some Probabilistic Background. |

Oct 9, 2019 DM lecture |
exploratory data analysis basic statistics: mean, variance, covariance, correlation statistical model fitting the statistical model R as measure of fit [6]^{2}[code] [driving accuracy data] [driving distance data] [putting accuracy data] [winnings data] |

Oct 10, 2019 LL section |
MATLAB [tutorial] [script] |

Oct 11, 2019 DM lecture |
towards a mathematical model expectation value power law distributions a revised statistical model comparison of R as measure of goodness^{2}[code] HWK (for M Oct 14). Read Bender, Chap. 3. Graphical Methods, Chap 4. Basic Optimization. Read Varian [7], Gray [8] and Goldin [9]. Begin thinking about the system you want to model for your project. Please plan to discuss your ideas with professor or TA next week. |

Oct 14, 2019 DM lecture |
sample project proposal Cournot's model of duopoly [10] HWK (for M Oct 21). 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. |

Oct 16, 2019 DM lecture |
Cournot's model of duopoly [10] Bertrand's observation of instability [11] |

Oct 18, 2019 DM lecture |
Hotelling's model of spatial competition [12] |

Oct 21, 2019 DM lecture |
mathematical modeling as metaphor [slides] Smithies' introduction of elastic demand [13] |

Oct 23, 2019 DM lecture |
numerical solution of Hotelling-Smithies model [code] application of Hotelling-Smithies as a spatial voting model survey data from Morning Consult |

Oct 25, 2019 DM lecture |
If candidates are located at A < B < C < D < ..., then exactly AB, BA, BC, CB, CD, DC, ... are
posisble (1st,2nd) choices inconsistency with Democratic primary data combinatorial optimization within Hotelling-Smithies model [code] Extra Credit (turn in at section on Th Oct 30). Can 4 candidates be located in R^{2} so that each ordered pair is possible (1st,2nd) choices for some voter?Prove your answer. |

Oct 28, 2019 DM lecture |
continuous and differentiable loss functions gradient descent and Monte Carlo methods for optimization numerical optimization of loss function [code] HWK (due F Nov 1). Prepare 1 minute "elevator pitch" on your project to present in class Friday. See, for examples, UC San Diego Jacobs School of Engineering blog. |

Nov 1, 2019 |
student elevator pitches |

Nov 4, 2019 DM lecture |
quality measures graduate applications data discussion of possible models |

Nov 6, 2019 DM lecture |
exploratory data analysis Model 0 unbiased estimate of variance standard error |

Nov 8, 2019 DM lecture |
using χ distribution to estimate standard errors Model 1A low rank approximation HWK (due W Nov 13). Progress report describe your model in detail (don't need to include results) where you are relative to proposed timeline revised timeline |

Nov 11, 2019 |
No lecture; Veterans' Day (also Armistice Day) holiday. |

Nov 13, 2019 DM lecture |
definition of partially ordered set (poset) examples intersection of partial orders singular value decomposition matrix approximation theorem |

Nov 15, 2019 DM lecture |
Model 1A: rank 1 approximation of sparse data matrix alternating minimization comparison of ordering with Model 0 Model 1B: additive approximation of sparse data matrix comparison of ordering with Model 0 and Model 1A |

Nov 18, 2019 DM lecture |
Model 2 comparison with Models 0, 1A, and 1B leave 1 out cross-validation comparison of models HWK (due Week 9, 10, or 11). Project presentation 13+2 minute oral presentation of your project computer slides recommended; email to me beforehand |

Nov 20, 2019 DM lecture |
number of human ancestors recurrence relation analogy with differential equation solution how many generations ago must model fail? number of bee ancestors bee biology recurrence relation Fibonacci numbers "almost geometric" sequence solution: "Binet's formula" |

Nov 22, 2019 DM lecture |
phyllotaxis etymology flowers with Fibonacci numbers of petals succulent with angles 2π/φ between leaves proof of irrationality of φ continued fractions for 67/29, for φ, for √2 convergents "φ is the most irrational number" growth model simulations HWK (due Friday, Dec 6). 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/equations [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. |

Nov 25, 2019 presentations |
Section A (10:00am) Annsley RUBINO, Video games: Does history repeat itself? Raul ANAYA VENEGAS, Triple jump optimization Section B (9:00am) Albert CHIU*, A game-theoretic model of protest participation Emily REXRODE, Combinatorial optimization of wireless networks Guanxin LI*, Beam bridge weight limit |

Nov 27, 2019 |
No lecture. |

Nov 29, 2019 |
No lecture; Thanksgiving (A Native American View) holiday. |

Dec 2, 2019 presentations |
Section A (10:00am) Ronan SULLIVAN, Laser ice drill Alex RUBER, Modeling the perfect free kick Chris CHENG, Maximizing MPG Section B (9:00am) Weiyuan XU, Copula model and its analysis Jiarui OU, Buy the anime DVD/BD or not? A decision model Jingwei YU, Who is the overpaid player in NBA? |

Dec 4, 2019 presentations |
Section A (10:00am) Zheng QU and Zihan WU, Economically efficient earthquake alert system Xinyue HE, DOTA 2 analysis Section B (9:00am) Mianlin HU, Starbucks: eco-hypocrite? Yujia XIE, Model for SARS Spreading in Beijing |

Dec 5, 2019 presentations |
Section A (4:00pm) Nicole CHEN Jasmin ZHANG*, Kevin Durant's value to the Warriors Enhao MA, The reality of job descrimination Section B (1:00pm) Annie TAN, Mahjong decision model Rachel LEE, Temperature influence on methylmercury concentration in marine organisms |

Dec 5, 2019 presentations |
HSS 1305 (6:00pm-10:00pm) Shinho JUNG, Electricity efficient model Zijing WANG, Mathematical model for rowing competition results Joseph HWANG, Fantasy Basketball: rookie prediction model Jiaxin LI, Umbrella optimization Elisa LAU, Melting Antarctica and rising sea levels Pujiang HUANG, Pai Gow poker: how to split Yining YUAN, Modeling intrinsic value of a stock Tianyi ZHANG, Solar tree optimization in San Diego Kyle SUNG, Predicting the next NBA MVP Yiwen LI, Topic modeling |

Dec 6, 2019 presentations |
Section A (10:00am) Sami WAHEED, Modeling the perfect angle to shoot three-pointers Cody EMRICK, Monarch butterfly population Section B (9:00am) Siqi LIU, Mathematical model of relationship between daily routine and health Meghedi ZARGARIAN, Predicting changes in price in high frequency trading Yingkun WANG, Earthquake explosion triggers earthquake |

Dec 11, 2019 presentations |
Section B Final (AP&M B412, 8:00am-11:00am) Chuanchuan LIU, When a new infectious disease attacks Rundong ZHONG, Find cheapest cost using graph theory Mingqian (Megan) TANG, How data affects the overall rating of King of Glory professional players Kevin CHAN, Epidemic modeling Taeho YUM, Homerun optimization for batters Jiawen ZHU, Mathematical modelling for determining whether sleep duration affects health Joshua JUSAY, Combinatorial optimization of owning an electric vehicle Huiyi QI, A guide to sourdough starter Nick WONG, A dynamic and stochastic model for Lambda phage and Escherichia coli: An insight into coevolution and resistanceElizabeth TANG, How to bowl a perfect strike |

Dec 13, 2019 presentations |
Section A Final (AP&M B412, 8:00am-11:00am) Vicky VO, Getting a last minute campsite in Yosemite during peak season A Young KIM, Car race strategy Zack JAFEK, Modeling testing accommodations needs for students with disabilities Evan CHANG, Ranking a roller coaster Samantha OROZCO, Life-cycle costs of infrastructure Kevin VILDOSOLA, Student refractory period Donghao XUE, Analysis of the maximum profit of producing glasses Jennifer SANDOVAL, JPEG image compression Yunkai CHEN, Baby's weight prediction Shirley ZHANG, Boba vs. tea consumption Yifan WU, Solving the free rider problem in a company with the Multiplayer Boxed Pigs game model Yenia GRADA, What is the weather today?: A San Diego weather prediction mathematical model Wayne NGUYEN, Ranking the Super Smash Bros. Ultimate characters Justin PERALTA, Mastering music? - A mathematical model Emanuela BEALE, A mathematical approach to quantifying gerrymandering Taekyeong LEE and Soobin PARK, The demand for taco: How many tacos will one eat at the taco shop? |

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Last modified: 12 December 2019.