Instructor: David A. Meyer
Email: dmeyer "at" math "dot" ucsd "dot" edu
Office hours (Fall Quarter): AP&M 7256, W 11:00am-12:50pm, or by appointment
Lectures:
Section A00: AP&M 2402 MWF 9:00am- 9:50am
Section B00: AP&M 2402 MWF 10:00am-10:50am
TA: Madhura Som
Email: masom "at" eng "dot" ucsd "dot" edu
Office hours (Fall Quarter): AP&M 5760, Th 6:00pm-7:00pm, or by appointment
Recitations:
Section A01: AP&M 2402 Th 4:00pm- 4:50pm
Section B01: AP&M B412 Th 8:00pm- 8:50pm
This course is a focused introduction to mathematical modelling. In 2017 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.
| Oct 23, 2017 |
Application deadline for National Science Foundation Research Fellowship |
| Oct 20, 2017 |
Murray and Adylin Rosenblatt Endowed Lecture in Applied Mathematics David Donoho Estimation of large covariance matrices in light of the spiked covariance model Robinson Auditorium, 4:15pm-5:15pm |
| Oct 20, 2017 |
Murray and Adylin Rosenblatt Endowed Lecture in Applied Mathematics Tamar Schlick Adventures in folding RNA and DNA: from graph theory to multiscale computations Robinson Auditorium, 3:00pm-4:00pm |
| 2017-18 |
UCSD Society of Undergraduate Mathematics Students |
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Sep 29, 2017 DM lecture |
administrative details overview/motivation simple population growth model HWK (for W Sep 28). 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. |
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Oct 2, 2017 DM lecture |
world population data (pre)historical world population world population since 1800 improved population growth model general principles of modeling improv modeling Section A00: The #1 Reason Bernie Sanders' Medicare-for-All Single-Payer Plan Is A Singularly Bad Idea Section B00: Origins of Sun's swirling spicules discovered Trump sent 18 tweets on Puerto Rico on Saturday. And made things a whole lot worse |
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Oct 4, 2017 DM lecture |
improv modeling Section A00: The Zika Virus Grew Deadlier With a Small Mutation, Study Suggests Shifting school start times could contribute $83 billion to US economy within a decade Is North Korea preparing its missles for action? Weapons moved amid threat to 'Reduce America into a sea of flames' Unlike Apple's Earlier Launches, No Long Lines for the iPhone 8 Uber's Self-Driving Cars Promised Pittsburgh A Revolution. But For Whom? The Senate Is About to Approve Commercial Sale of Self-Driving Cars (But Not Trucks) What happens if you turn off the traffic lights? Hurricane Maria could be a $95 billion storm for Puerto Rico Hurricane Harvey: How Many Billions of Dollars in Damage Will Historic Storm Cost? Hurricane Andrew damage cost $26.5 billion in 1992. How much will Irma cost us? Box Office Surge Ends as 3 Films Vie for Top Spot Elon Musk suggests using rockets for high-speed world travel Trump's whiplash weekend heightens questions over leadership Top Schools May Be Too Far Away From Community Colleges Robots: Is your job at risk? New York's Subway Delays Could Cost City $389 Million a Year Weapons cache found at Las Vegas shooter's home Southern Prisons Have a Cellphone Smuggling Problem These countries have the fewest toilets per person Fukushima Nuclear Disaster: Radioactive Water May Have Been Leaking from Reactors for Months On a collision course with game theory Multiple Weapons Found in Las Vegas Gunman's Hotel Room Las Vegas Shooting: 59 Killed and More Than 500 Hurt Near Mandalay Bay Target's move to $15 an hour 'blows up' this myth about raising minimum wage Obesity Was Rising as Ghana Embraced Fast Food. Then Came KFC. Tesla's Model 3 has a very bad September: Production falls far short Apple's most expensive iPhone is the device most people want Section B00: Chevron's CEO is leaving as oil industry faces uncertain future Irma Was Bad News For Iguanas, Good News For Mosquitoes Air France superjumbo engine failure forces emergency landing in Canada Heidi Montag and Spencer Pratt Welcome Son Gunner Stone The opportunity in Tom Price's resignation Political Polling Is A Flawed Science That Leads To Fatally Flawed Reporting Volkswagen's diesel scandal costs hit $30 billion Two Women Killed in Knife Attack at Marseille Train Station This hurricane season has been brutal but it's not over yet. What's coming next? By the numbers: More than half of Puerto Rico still without drinking water 15-year-old boy in San Juan raising funds for solar lamps Tax Reform Is there a relationship between recent team performance and in-stadium attendance? Analyzing the Relationship Between Team Success and MLB Attendance With GARCH Effects Multiple Weapons Found in Las Vegas Gunman's Hotel Room Antoine Griezmann 'keen on' January transfer to Man United despite signing improved Atletico Madrid deal Why the US has the most mass shootings |
|
Oct 5, 2017 MS section |
introduction to LaTeX Template Proposal main.tex citations.bib |
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Oct 6, 2017 DM lecture |
improv modeling Section A00: 2014 San Antonio Spurs vs. 2015 Golden State Warriors - Team Comparisons 2016 San Antonio Spurs vs. 2016 Golden State Warriors - Team Comparisons San Antonio Spurs/Golden State Warriors Game 4 Analysis Analysis: Would the U.S. benefit from a merit-based immigration system? Find Out If President Trump Would Let You Immigrate to America Section B00: Ronaldo, Neymar, Messi nominees for FIFA prize for 3rd year Analysis: Would the U.S. benefit from a merit-based immigration system? Find Out If President Trump Would Let You Immigrate to America |
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Oct 9, 2017 DM lecture |
combining rankings definition of relation definition of (strict) total order definition of (strict) partial order definition of (strict) weak order illustration of Hasse diagrams definition of intersection of relations proof that the intersection of partial orders is a partial order example that intersection of total orders need not be weak order descriptive statistics for graduation admissions data |
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Oct 11, 2017 DM lecture |
combining rankings for graduate admissions data HWK (for F Oct 13). Read Bender, Chap. 4. Basic optimization |
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Oct 12, 2017 MS section |
more LaTeX notes |
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Oct 13, 2017 DM lecture |
correcting for possible bias in graduate admissions data finding a best fit by optimization HWK (for F Oct 20). Read Varian's article on how to build a model [4]. Read Gray's article on how to write an abstract [5]. Read interview with Goldin on why math is the best way to make sense of the world [6]. 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, 2017 DM lecture |
Do online dating sites/apps affect intermarriage rates in the US? MIT Technology Review: First Evidence That Online Dating Is Changing the Nature of Society G. M. Livingston and A. Brown, Intermarriage in the U.S. 50 Years After Loving v. Virginia, Pew Research Center (18 May 2017). demography of the US simplistic ODE models [code] |
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Oct 18, 2017 DM lecture |
J. Ortega and P. Hergovich, The Strength of Absent Ties: Social Integration via Online Dating, arXiv:1709.10478 [physics.soc-ph] (2017). graph representing connections matching allowed only if all pairs k-connected in graph feature space of agents as Rd preferences as distance functions on feature space definition of stable matching; proof of existence and uniqueness |
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Oct 19, 2017 MS section |
questions and answers about student project proposals |
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Oct 20, 2017 DM lecture |
putting the pieces together into a simulation social statistics results [code] discussion of results; non-edge-monotonicity of statistics |
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Oct 23, 2017 DM lecture |
improving the model of J. Ortega and P. Hergovich? should edges be added independently of group membership? M. J. Rosenfeld and R. J. Thomas, Searching for a mate: The rise of the internet as a social intermediary, American Sociological Review 77 (2012) 523-547. how match search works at OK Cupid match questions model in which intergroup edges only added if distance less than threshold value [code] correlation between group and features? what does network of connections really look like? |
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Oct 25, 2017 DM lecture |
models for random graphs [notes] the Erdős-Rényi model [7] is really the Gilbert model [8] de Solla Price's model of preferential attachment [9] limiting solution |
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Nov 15, 2017 DM lecture |
What would happen to sea level if Greenland's ice sheet melted? [slides, part 1] |
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Nov 20, 2017 DM lecture |
What would happen to sea level if Greenland's ice sheet melted? [slides, part 2] |
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Nov 22, 2017 |
No lecture |
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Nov 24, 2017 |
No lecture |
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Nov 27, 2017 DM lecture |
What would happen to sea level if Greenland's ice sheet melted? |
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Nov 29, 2017 presentations |
Section A Chunmei Chen, Prison Education Reform as a Solution for Mass Incarceration Woong Suh, Happy Forecast: Weather, Events, and Cities Elizabeth Yee, San Diego's Hepatitis A Outbreak Section B Huawen Liang, American Economy under Merit-Based System Jiahao Ren |
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Nov 30, 2017 presentations |
Section A: AP&M 2402 4:00pm-4:50pm Yuxuan Liu, How to Find a Parking Spot at Rush Hour Cynthia Nguyen, Effects of Changes in Housing and Population Density Section B: AP&M B412 8:00pm-8:50pm |
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Dec 1, 2017 presentations |
Section A Megan Chang Jason Chung, San Andreas Fault Line Estimator Fangyu Yu, Population and Air Pollution Section B Shengkai Xu, Estimation of Hair Growth Waner Xu, Optimal Betting Strategies in Poker Game |
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Dec 4, 2017 |
No lecture |
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Dec 6, 2017 presentations |
Section A Fang Lin Jue Wang Wenxi Zhao (Fanfeng Liu) Section B Yunzhu Fei Weixiang Liao Ian Toperczer |
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Dec 6, 2017 presentations |
HSS 1128A, 6:00pm-9:00pm Section A Tian Fu Yanying Wang Fei Yang Mingming Zheng Section B Haoyun Cui Mairead Lavery Fanfeng Liu Jiaci Zhang |
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Dec 7, 2017 presentations |
Section A: AP&M 2402 4:00pm-4:50pm Jonathan Domingo Xinning Han Nevin Nguyen (Yan Wu) Section B: AP&M B412 8:00pm-8:50pm Joonsook Hong Waleed Razaq Yutong Zhang |
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Dec 8, 2017 presentations |
Section A Eldwin Li Michael McCumber Scott Nguyen Section B Avanika Gupta Molly Poole Gabby Rivas |
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Dec 8, 2017 presentations |
HSS 1128A, 6:00pm-9:00pm Section A Jk Wen Yan Wu Moyan Zhou Section B Teng Gao Nicola Hillis Yuzhou Hu Jessica Lee Edison Liu Ying Zhang Jiayuan Zhu |
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Dec 13, 2017 presentations |
8:00am-11:00am Section A (Fang Lin) Vivian Truong Shu Wang Weiqi Xu Jiayu Zhang Section B Ksenia Bukshtynova Kevin Chen Anand Das Kai Seng Leong Shiyao Li |
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Dec 15, 2017 presentations |
8:00am-11:00am Section A David Franco Koon Hor Itai Khen Section B Jack Chan Joseph Gilby Harmaneet Gill Chia-Chieh Kao Kelly Richmond Jiazheng Song |
| [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). |
| [7] | P. Erdős and A. Rényi, "On the evolution of random graphs", A Matematikai Kutató Intézet Kōzlemémyei V (1960) 17-61. |
| [8] | E. N. Gilbert, "Random graphs", The Annals of Mathematical Statistics 30 (1959) 1141-1144. |
| [9] | D. de Solla Price, "A general theory of bibliometric and other cumulative advantage processes", Journal of the American Society for Information Science 27 (1976) 292-306. |
