Mathematics

• Topological Data Analysis Handouts

  Moon Duchin, Tom Needham, and Thomas Weighill

  31 October 2019

  handouts higher-ed tda vrdi

  Materials from the breakout sessions on Topological Data Analysis at VRDI, 2019.

• Optimization Handouts

  Austin Buchanan, Sarah Cannon, Zachary Schutzman, and Justin Solomon

  31 October 2019

  handouts higher-ed optimization vrdi

  Handouts from the breakout sessions on Optimization at VRDI, 2019.

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  Networks Handouts

  Daryl DeFord

  31 October 2019

  handouts higher-ed networks vrdi

  What’s the difference between graphs and networks? How do can we use networks to model systems, and what questions does this help us answer? How can we use networks to think about census data and redistricting? This post contain a series of two-hour lesson plans on metrics and measures, null models, clustering, and network dynamics, in the context of applications to redistricting. No prior exposure to network theory is required, although some exposure to graph theory is assumed.

• The History of Voting in the USA

  Nikki Kennedy

  31 October 2019

  course-resources lesson-plans syllabus

  Course resources for Nikki Kennedy’s History of Voting in the USA course. These resources contain a syllabus, slides, and example student work. as well as a list of ideas of secondary mathematics topics with redistricting applications.

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  Discrete Mathematics

  Diana Davis

  31 October 2019

  course-resources syllabus lesson-plans higher-ed

  The post contains course resources for Diana Davis’s Discrete Mathematics class. This course is a problem-based curriculum for a semester-long discrete math course, with topics including graph theory, map coloring, apportionment, voting methods, random walks, and gerrymandering.
  Course resources include a syllabus, course map, book, and guide to creating/teaching a problem-centered curriculum.

• Mathematics of Social Choice

  Moon Duchin

  20 September 2019

  course-resources syllabus higher-ed handouts slides

  This post contains course resources from Moon Duchin’s Mathematics of Social Choice class, which focuses on the mathematical theory of voting, but also brings in topics from history, political science, civil rights, political philosophy, sociology, and psychology to provide context for, and explain limitations of, the mathematical approach.
  Course resources include a syllabus, handouts on partisan metrics and apportionment, an activity on IRV in Burlington, sample homework problems, etc.

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  Outlier Analysis and Gerrymandering

  Michelle Jones, Parker Rule, Gabe Schoenbach, Hamidreza Validi, and VRDI

  20 September 2019

  mcmc high-school

  This interactive web-based activity introduces metrics for defining and detecting gerrymandering. It provides background on gerrymandering and methods to study it, focusing on outlier analysis. Students will learn both about the principles of outlier analysis and how it was applied in recent Supreme Court cases pertaining to partisan gerrymandering in North Carolina. The activity conclude with a guided exploration of a Districtr module to understand the current North Carolina Congressional plan.

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  Redistricting Gridlandia

  Zachary Schutzman and MGGG

  01 September 2018

  statistics mcmc combinatorics networks high-school

  These interactive web-based activities introduce students to mathematical approaches in understanding electoral redistricting. Through a series of examples on small grids, students will learn about how the space of possible districting plans can be represented mathematically and how quickly the number of possible valid plans grows. Students will also learn how outlier analysis can be used to detect gerrymandering, by exploring how adjusting the voter distribution affects the space of outcomes and by building plans and comparing their properties to the distribution of other plans. The activity concludes with introducing Markov chain Monte Carlo sampling as a method for drawing conclusions about the space of plans when there are too many to list. This activity might be applicable to a statistics course, or any class that touches on combinatorics or graphs/networks.