INQ 241: Mathematical Reasoning--Mathematics of Democracy Western Perspective Roland Minton (Math/Computer Science/Physics) Overarching Goals 1. Students will be able to analyze the roles of math in elections throughout American history, contrasting potential outcomes from a variety of voting methods and judging which methods best promote the principles of democracy. 2. Students will be able to analyze quantitative information about different decision- making processes, identify underlying assumptions and evaluate ramifications of alternative processes. Skills Goals Writing: Students will be able to articulate the underlying assumptions in a variety of decision-making processes; construct arguments, both formal and informal, supporting a position on the benefits and flaws in a voting method or decision-making process. Quantitative reasoning: Students will be able to formulate questions about a decision- making situation in the language of mathematics, and identify and use appropriate mathematical techniques to derive relevant information to evaluate the situation. Broad Content Topics Assignments 1. Apportionment Introduction/motivation Informal writing Methods Clicker votes History Excel project/paper (below) Outcomes and paradoxes Census 2. Elections Introduction Clicker votes Methods Feedback lectures History Gerrymandering debate Outcomes and paradoxes Gerrymandering Mathematical research 3. Weighted voting Introduction/motivation Clicker votes Methods of measuring Informal writing power NY state case study/paper Outcomes and paradoxes 4. Google ranking Markov chains Feedback lectures Page rank Jigsaw on case studies Specific pages, abuses 5. Who’s Hot Introduction Student Questions Examples: Amazon, Informal writing Netflix, Kroger,…. Paper: is this democracy? Specific Assignment Background: Work with Excel spreadsheet to apportion Congress using a variety of methods, with a column showing the effect on (e.g.) the 2000 Presidential election Readings detailing constitutional constraints on apportionment, past controversies about apportionment and current controversies. Assignment: Write a “closing argument” for a court case challenging the legality of our current system. You may argue either for or against the current system. Assume that the jurors are intelligent but do not know the material or examples from our background work. Also, assume that the opposing lawyer will object (and the judge will sustain) to distortions of facts or misstatements. Start your argument by explaining why apportionment is important (use examples) and then indicate why your position is “better” in terms of historical and/or mathematical criteria. INQ 241: Mathematical Reasoning--Exploring Mathematical Connections Rebecca Wills (Math/Computer Science/Physics) Overarching Goal Students will be able to apply their knowledge of graph theory to formulate and solve a variety of practical connectivity problems. Ancillary Skills Goals Students will be able to classify problems and identify appropriate approaches to model problems. Students will be able to implement algorithms. Content Topics (1/2 to 2/3 of course content) Euler circuit problems (Traversability problems) Traveling salesman problems Minimum spanning trees Social networks Web search engine rankings (Google’s PageRank algorithm) Classroom Activity—variation of Gallery Walk (Speed Dating: “Date” a problem for 10 minutes) Content topic: Google’s PageRank Algorithm Number of problems: 4 (2 copies of each) Number of groups: 8 (groups of 3) Distribute 4 problems related to Google’s page rank algorithm to the groups. Each team spends 10 minutes examining each problem and writing or modifying solutions. After each group reviews 4 problems in a “speed date” setting, their original problems along with the modified solutions are returned to them. For the remainder of class, each group provides/presents modified solutions to the class. INQ 241: Mathematical Reasoning--Mathematics in American Government Bryan Snare (Math/Computer Science/Physics) I want my students to be able to… 1) support and criticize the use and misuse of mathematics as it applies to elections. 2) propose a solution to a complex scheduling issue and justify it as optimal. 3) take the mathematics they have learned and apply it to situations not covered in class. Broad Content Sequence of Topics Assignments/Activities Topics house.gov: Research and write House of about the role of the House of Representatives-role Representatives in our that it plays government Electoral College Apportionment History/present Find an interesting topic talked apportionment about Apportionment methods Paradoxes produced Follow your topic Weighted voting What will it take for your topic (electoral college) to pass? Voting Theory Voting methods Fairness criteria Arrow’s impossibility Favorite voting method? Swap and critique. Euler circuits, trash pick- up Find optimal paths for campus walks Management Science Hamilton Circuits-TSP Trees and Networks (lighting Alaska) Detailed Assignments: 1) Apportionment/weighted voting: What if we would have used a different apportionment method in the 2000 election. A different winner? Does mathematics affect/play a role in our lives? 2) Voting Methods: a. Pick a voting method that you believe to be the best and defend it with a two page paper. b. Swap papers with somebody and write a one page paper raising problems in their arguments. c. Swap back and make corrections to strengthen argument. 3) Find the most efficient way to light up Alaska.??? INQ 241: Mathematical Reasoning—How to Run the World Efficiently Karin Saoub (Math/Computer Science/Physics) Goals At the end of the course, students will be able to: Understand the use of various types of graphs in modeling real world situations Understand the challenges behind efficiency and evaluate strategies for finding optimal solutions Compare scheduling techniques and algorithms Apply the correct algorithm/technique to a real world problem, determine an optimal solution, and defend their choices. Draft of Course Plan Broad Content Sequence of Topics Ideas for Assignments/activities Topics and Concepts within Each Broad Content Topic Efficient Euler Tours 1. Find an Euler Tour for a town/city service Routes (garbage removal, mail delivery, snow removal). Hamiltonian 2. Find Hamiltonian Circuit for on/off campus Circuits delivery (flowers/packages/services). Spanning Trees 3. Find shortest route between 4/5 cities given airplane/train routes. Bipartite Resource 1. Assign tasks to employees, teachers to Graphs Allocation courses, etc. Coloring 2. Stable Marriage examples Stable Marriage Interval Coloring 1. Using FF algorithm for coloring Graphs Resource 2. Assigning meeting to rooms based on time Allocation restrictions. 3. DSA example with computer or train seats. Dynamic Storage Final Project Students will find a real world problem that applies to one of the three topics above. They will determine what an optimal solution entails and apply the correct algorithm/technique. These findings will be presented in a final report, as well as a defense of their choices and solution.