Education Resources - Institute for Mathematics and Democracy

Materials for the AMS workshop on Mathematical Foundations of Democratic Processes

IMD partnered with the American Mathematical Society to deliver the first workshop in their Engaged Pedagogy series. Led by seven IMD affiliates, the workshop provided the tools and materials for those who are interested in bringing topics such as voting, apportionment, and gerrymandering into their classrooms. Materials include lecture notes, group activities, and ideas for research projects.

Math and Politics class at Wellesley College

Class notes and other materials from the Math and Politics class taught by Prof. Ismar Volić at Wellesley College. Topics include Electoral College, voting, apportionment, gerrymandering, power assessment, and much more.

Mathematics of Social Choice class at Oberlin College

Class notes and other materials from the Mathematics of Social Choice class taught by Prof. Kevin Woods at Oberlin College. This is an upper-level course whose topics include both political content (voting, apportionment, fair division) and economic content (auction theory, matching markets, strategizing).

Math of Voting class at St. Mary's College

Class materials from the Math of Voting class taught by Prof. Ranjan Rohatgi at St. Mary’s College. This is a course taught during the 3-week winter term at St. Mary’s. It gives an accelerated look at topics including voting methods, apportionment, and gerrymandering.

Voting Theory class at Wheaton College

Course materials (including homework assignments and a schedule of topics) from Tommy Ratliff’s Voting Theory course at Wheaton College. The course examines how different voting procedures can yield different outcomes, as well as the Gibbard-Satterthwaite theorem, Arrow’s impossibility theorem, measures of voting power, apportionment, and applications of consensus theory.

An Introduction to Voting Theory class at University of Pennsylvania

Lecture slides on An Introduction to Voting Theory taught by IMD affiliate Thomas Brazelton at University of Pennsylvania.

Optimized Democracy class at Harvard University

Class materials from the Optimized Democracy class taught by Prof. Ariel Procaccia at Harvard University. The course examines the mathematical underpinnings of democracy. The course aims to “provide students with a rigorous perspective on, and a technical toolbox for, the design of better democratic systems.” Topics include social choice, fair division, apportionment, sortition, liquid democracies, and weighted voting games.

Math and Politics teaching modules created by Wellesley College students

Teaching modules created by Wellesley College students on various math and politics topics. The modules contain lesson plans and exercises and can be used in middle school and high school classes.

Election math materials created by middle school teachers

Several middle school teachers used and modified IMD’s teaching materials on math behind elections in fall 2020, resulting in complete lesson plans on voter turnout, voting methods, Electoral College, and gerrymandering.

2020 Election Night IMD event materials

Lecture slides and a video from IMD’s 2020 election night event. Institute fellows and co-founder Prof. Stanley Chang delivered lectures on voting, apportionment, gerrymandering, and quantification of power.

Math in Democracy Desmos mini-unit

A mini-unit composed of Desmos activities for middle school math students created by Alison Strole. These activities serve as an introduction to the intersection of math and democracy. Topics covered include voting methods, efficiency gap, voter turnout, and the electoral college.

Math of Social Choice class at Tufts University

Lectures, worksheets, and other class materials from the Math of Social Choice course taught by Prof. Moon Duchin at Tufts University. Topics include include ranking, determining the strength of, and choosing participants in multicandidate and two-candidate elections, and apportioning votes and rewards to candidates.

Math and Politics lesson plans created by a Wellesley student

Lesson plans on Voting Methods, Gerrymandering, and Electoral College by IMD student, Guadalupe Portillo Deras.

Modeling Decision-Making class at University of Massachusetts

Notes from a class taught by Prof. Mark Wilson at University of Massachusetts covering models related to collective decision-making, including voting, apportionment, and many other topics.

Gerrymandering Class at Saint Mary's College of California

Syllabus and class materials from the class Math in Our Democracy: Detecting and Preventing Gerrymandering taught by Dr. Ellen Veomett at Saint Mary’s College of California. Topics include shape metrics, racial gerrymandering, GEO metrics, and much more. Dr. Ellen Veomett is now a professor at University of San Francisco.

AI for Redistricting class at University of San Francisco

The outline of an upcoming class on AI for redistricting taught by Dr. Ellen Veomett at University of San Francisco. Topics include graphs, metrics, Markov Chain, and more.