MATH 441 Projects, Fall 2018

Requirements
  • Projects must use a model(s) involving linear programming, integer programming, convex programming, quadratic programming.
  • Projects involve original software written only by the group members.
  • Projects must test the software with "toy data" (simple data with predictable solutions) as a correctness check.
  • Projects must compute at least 5 variants of a similar optimization problem and compare the results.
  • Projects must be written in LaTeX (overleaf.com is one easy way to write group projects in LaTeX);
  • Projects must indicate what each group member contributed to the project.
    • Research Projects Research projects can be done in groups of 3-4 students; depending on enrolment and demand, smaller group sizes may be possible.
    Projects generally model something in the real world and involving linear programming (e.g., simplex method for solving LP's, branch and bound method for solving integer LP's, etc.). Most projects involve some data, real or (partially) synthetic; finding the real data or generating realistic synthetic data can be a significant part of the problem.
    For project ideas, you can look at my list of project ideas and the applications we covered in last year's Math 441 course. I may cover some new applications this year.
    Please tell me your project idea before you present your proposal; you are encouraged to consult me during the term whenever you have questions or difficulties arise.
    Originality and Difficulty Part of the grade for projects (under the "Modeling terminology and content" row of the Writing Rubric) regards the originality and difficulty of the project.
    Tell Me Something We Don't Already Know Ideal research projects should tell me something that we don't already know.
    For example, say that you are working with data that tries to schedule UBC exams to minimize the number of student exam conflicts (or hardships).

    Here are some things we know:
  • The longer the alloted exam period, the fewer the number of conflicts and hardships in an optimal schedule.
  • If the number of exam time slots times the number of chairs in the univeristy is less than the sum of the number of students in each course, there will be at least one conflict.

    • Here are some things we don't know:
  • Fix a set of classes, of students, and of class lists (of which students are taking which classes). As the alloted exam period shrinks, does the number of conflicts increase gradually, or is there a sharp threshold? (I'm guessing that there is a pretty sharp threshold.)
  • Say that UBC takes certain large classes with many sections, and requires each section to have its own exam; now different sections of the same class can be scheduled at different times. Does this policy change significantly affect the number of exam conflicts?

    • Can you draw some useful principles based on your results?
    Final Report The final report should be a PDF file, written in LaTeX, of roughly 3-7 pages (i.e., 600-1400 words), excluding references and appendices. You will have to be concise and focused!
    You may put additional material in appendices to the paper, but this should be used only for data/tables/figures/software, not for exposition on the project.
    You should print out your report, as well as submit the report plus your software online. I should be able to test your software and duplicate your experiments.
    The same Writing Rubric will be used to grade your progress reports and final reports, with different weightings to the rows; for the final report, "Modeling terminology and content" given a weight of 5, and all other rows each given a weight of 1.
    Progress Report The progress report should be roughly 3-5 pages (i.e. 600-1000 words).
    Here is sample progress report from last year and its LaTeX source (which I have given a .txt extension).
    Here is a Writing Rubric as a guide to the grading of projects. The progress reports will be graded on your overview, motivation, specific questions, and models (which correspond to Sections 1 and 2 of the above sample).
    Presentations Each member of your group must present some material/slides, and must be prepared to answer questions on this material. Your group needs to email a PDF file of your slides by 7am on the day of your presentation (it's OK to make small corrections to the slides and to send me a revised set of slides later in the day, after your talk). Here is a guide to the grading of presentations.

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