MATH 111A (Fall Quarter 2019). 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

Course description

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.

Related events

 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

Syllabus (homework in green)

 [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] LaTeX for Beginners Workbook (2011). [5] J. Marshall and R. A. Plumb, Atmospher, Ocean, and Climate Dynamics: An Introductory Text (Burlington, MA: Elsevier Academic Press 2008). [6] E. Berman, J. H. Felter, J. N. Shapiro and E. Troland, "Modest, secure, and informed: successful development in conflict zones", American Economic Review 103 (2013) 512—517. [7] H. R. Varian, "How to build an economic model in your spare time", The American Economist 41 (1997) 3—10. [8] N. Gray, "Abstract science", The Huffington Post (2012). [9] A. Bleicher interview with R. Goldin, "Why math is the best way to make sense of the world", Quanta magazine (2017). [10] A. Cournot, Recherches sur les principes mathématiques de la théorie des richesses (Paris: Hachette 1838) Chap. VII. [11] J. Bertrand, "Théorie des richesses", Journal des Savants (1883) 499—508. [12] H. Hotelling, "Stability in competition", The Economic Journal 39 (1929) 41—57. [13] A. Smithies, "Optimum location in spatial competition", Journal of Political Economy 49 (1941) 423—439.

Titles of projects from previous years

• A Quantum Lattice Gas Model for the d+1 Dimensional Dirac Equation
• Modeling the Point Spread in the NFL
• Nuclear Fallout Dispersion of the Windscale Disaster, 1957
• Modeling the Expected Time at a Traffic Light
• Seasonal Distributions of the Pacific White-Sided Dolphin
• Software and Hardware Failure Model: Markov Chain Analysis
• Variability of Starting vs. Ending Positions of Indy 500 Races 1911-2007
• Strategic Positioning in a Parking Lot: A Location Game
• The Reality of the Gender Wage Gap
• Using GARCH for Risk Management Forecasting
• Quantitative Comparison of Prokaryotic and Eukaryotic Transcription
• Applying Dijkstra's Algorithm with Variable Weights
• A Gradient-Based Approach to the Problem of Rainfall Flow as Applied to the Surface of the UCSD Campus
• Inventory Model
• Kobe the Savior or Kobe the Cancer
• The Effects of Spatial Decisions on Housing Demand: A "San Diego" Simulation
• Luck vs. Skill Poker Model
• Police Activity: What is the Probability of Encountering a Police Vehicle?
• Deal or No Deal
• AIDS in America: A Mathematical Model
• School of Fish Simulation
• Crude Oil Supply and Demand: Forecast by Season
• Signaling and the Southwest Effect
• Barter Economy Model
• Simulation of Submarine Control System
• Equity Index Tracking with Realistic Constraints via Particle Swarm Optimization
• Modeling Crystal Structure in Curved Space
• Taking a Penalty Kick: May the Odds Be Ever in Your Favor
• Arrow-Debreu Economy with Floating Gift Cards