Cluster 2: Reasoning About Luck: Probability, Statistics, and Their Uses in Science


Instructors: Professors Franklin Dollar and Albert Siryaporn, UC Irvine, Department of Physics and Astronomy

Prerequisites: Algebra II or Integrated Math II

Course Description:
Thinking logically about probability is crucial to many aspects of science and impacts our lives in many different ways. From the trivial (deciding whether to carry an umbrella on a given day based on the weather forecast), to the profound (understanding complex issues such as the global energy crisis), a deep understanding of probability and statistics is critical to assess a range of problems. In this cluster, students will be taught how to reason about luck in both quantitative and qualitative ways by exploring the foundations of probability through a variety of interactive games, classroom discussions, and hands-on programming sessions. Guest lecturers will illustrate how probability is a foundational tool across all of science from astrophysics to biology. Students will learn how to assess the validity of scientific studies and think crucially about the scientific method. Students will learn how to analyze and visualize large datasets using a variety of methods, including an introduction to ideas from machine learning and “Big Data” and will make extensive use of the Python programming language and its capabilities for numerical and data analysis via hands-on tutorials and demonstrations.

Students will form groups of 4-5 and will use probability and/or statistics to solve a unique problem: for instance, analyzing polling data from different sources or determining whether a vaccine is working to protect people from infection. Projects in previous years include studying the distribution of galaxies, estimating the mass of the Higgs boson, designing the fairest scoring rules for a Rubik’s cube tournament using statistical simulations of player abilities, and an analyses of weather data to study “extreme” events using extreme value statistics. Skills developed during the course, such as programming and analyzing data in Python, will form an integral part of these projects.