Math 87, Duchin
Part I: Model Blitz
Method
Calculus-style optimization Sensitivity analysis Optimization w/ constraints Root finding
Finite differences
Linear programming
Integer programming Max flow
Min cut
Matchings
Finite state automata
Monte Carlo methods
Markov chains
MCMC optimization
Poisson processes
Linear least squares
Principal component analysis
Description
Critical pts as potential extrema. Set derivs to zero.
Back-substitution or Lagrange multipliers. Newton’s method and alternatives
Taylor approximations for derivatives
Linear objective, convex feasible region.
Simplex algorithm, dual LP, complem. slackness. Fair division.
Branch-and-bound.
Network and capacities set up LP. Dual to max flow.
Add source/terminus, use max flow. Stable matchings.
Nodes and transitions.
Randomize and evaluate repeatedly.
Random walk on graphs.
Metropolis–Hastings.
Fix λ “ pn, simulate.
Minimize residual with normal equations. Dimension reduction by fitting line, plane, etc.
Spring 2020
Examples from class
Clean oil spill. Manufacture 2 products.
Blood testing. Diet problem.
Israel/Palestine negotiation. Mixed integer example. Soviet rail network.
Boston T system.
Alaska district pairings. Medical residency match. Population growth. Buffon’s needle. Approximate integrals. Stock market steady state. Autocomplete, PageRank. Code-breaking.
Bus arrival predictions. Line fit, curve fit.
IQ, personality, music.
TUFTS UNIVERSITY DEPARTMENT OF MATHEMATICS Final Assignment, with Project Pitch
Your task: choose four methods learned in class and write one paragraph each about a problem you could approach with this method. Be creative!
(The methods you choose for this part should be different from the one(s) featured in your project pitch.)
Part II: Project Pitch
The aim of the project pitch is to communicate a clear question, modeling approach, and an ap- propriate formulation of the key aspects of the problem you are studying. Your model should include the gathering of appropriate data. You should discuss how you expect that a solution (from the model) will lead you to an answer (to the motivating question).
Your proposal should be 2-3 page PDF using a font size of 10 points and one-inch margins on all sides. The pitch should include the following:
• Full statement of the problem to be investigated. This includes any constraints you may have to consider, and your choice of parameters.
• Clear statement of why this problem is interesting to you and others.
• Justification for modeling approach. Discussion of potential interpretations of outputs.
• Brief literature review. (Cite a few references that you used to get a deeper understanding than the introduction in lectures. Don’t use only Wikipedia.)
• Concise description of data collection strategy or sourcing and computational methods.
• Clearplansforplausibilitychecks,sensitivityanalysis,andwaysofassessingmodelsuccess.
References can be cited throughout, but should be listed in a separate section at the end.
You should then prepare exactly 2 slides for the final presentation of your pitch. You will have 3 minutes to present it in the block for our final exam slot on Monday May 4 from 3:30-5:30pm Eastern.
Due Dates
Draft due Thursday April 30 at 8pm
You’ll get feedback by Friday May 1
Final pitch and slides due Sunday May 3 at 8pm