Course Description

Students will apply mathematical and statistical methods to address societal problems, make personal choices, and reason critically about the world. Students will address questions like: How can quantitative methods be used to determine authorship? How can we tell if gerrymandering or election fraud have occurred? What fraction of the population needs to be vaccinated to prevent a measles outbreak?

The course has three target audiences:

• students from nonscience majors who wish to satisfy the Quantitative Reasoning focus of the General Education curriculum;
• students who wish to have additional preparation before taking the quantitative courses required of science majors; and
• students interested in learning how to apply quantitative reasoning to their world.

Course Goals

Students will learn to apply mathematical concepts in authentic contexts, developing tools for reasoning with data, logic, and quantitative methods.

Some of the kinds of questions we will address are:

• What is the role of mathematics in organizing and interpreting measurements of our world?
• How can mathematical models and quantitative analysis be used to summarize or synthesize data into knowledge and predictions?
• What methodology can we apply to validate or reject mathematical models or to express our degree of confidence in them?

Student Learning Outcomes

• Summarize, interpret, and present quantitative data in mathematical forms, such as graphs, diagrams, tables, or mathematical text.
• Develop or compute representations of data using mathematical forms or equations as models and use statistical methods to assess their validity.
• Make and evaluate important assumptions in the estimation, modeling, and analysis of data, and recognize the limitations of the results.
• Apply mathematical concepts, data, procedures, and solutions to make judgments and draw conclusions.
• Synthesize and present quantitative data to others to explain findings or to provide quantitative evidence in support of a position.

Course Notes

Introduction

S0.0 Course Logistics

S0.1 Graphs Tell a Story

S0.2 Misleading Graphs

S0.3 Gapminder

Elections and Voting

S1.1 Gerrymandering Introduction

S1.2 Gerrymandering and Efficiency Gap

S1.3 Gerrymandering and Efficiency Gap Applied to NC and MD

S1.4 Gerrymandering and Compactness Part 1

S1.5 Gerrymandering and Compactness Part 2

S1.6 Gerrymandering and Compactness Applied to NC and MD

S1.7 Sampling and Bias

S1.8 Margin of Error

Finance

S2.1 Expected Value

S2.2 Vision Plans

S2.3 Dental Plans

S2.4 Health Plans

S2.5 Compound Interest

S2.6 Loans

S2.7 Law School

S2.8 Baseball and Retirement

Health and Risk

S3.1 SIR Disease Model

S3.2 SIR Model Parameters

S3.3 SIR Model and Vaccination

S3.4 Exponential Growth

S3.5 Covid and Curve Fitting

S3.6 Covid and Logistic Curves

S3.7 Sensitivity and Specificity

S3.8 HIV Vaccine Clinical Trials

Digital Humanities

S4.1 Stylometry and Distributions

S4.2 Stylometry and Chi Squared

Spreadsheets and Data Files

The spreadsheets and data files used in the pilot version this course (Spring 2020) are available here. For updated spreadsheets and data files, please email greenl@email.unc.edu.

For Instructors

Instructors: if you would like additional teaching materials, including instructional notes, solutions to in class exercises, homework problems and solutions, and source latex files, please email greenl@email.unc.edu.

Credits

These course materials were developed by Linda Green, Jeff McLean, Viji Sathy, and Todd Vision at UNC