Probability, a dynamic and crucial field in mathematics, influences various sciences such as quantum mechanics, statistics, genetics, epidemiology, economics, engineering, and computer science. This beginner-friendly course builds essential concepts from the ground up, focusing on intuitive understanding, rigorous proofs, and practical applications. Topics include combinatorial analysis, probability axioms, independence, conditional probability, distributions, functions of random variables, laws of large numbers, and central limit theorems. We also explore diverse applications to highlight the relevance of probabilistic concepts.
MATH 2400 or APPM 2350, along with MATH 2130/3130 or MATH 2135/3135, or instructor permission, is required.
A First Course in Probability by Sheldon Ross (10th Edition).
This course will follow a flipped classroom model, where students study core concepts before class, enabling deeper exploration and application during in-person sessions. Active engagement in small mathematics groups is central to this approach, reflecting research-backed best practices for effective learning. A meta-analysis of 225 studies demonstrates the benefits of active learning, with significant improvements in outcomes across science, engineering, and mathematics disciplines (see https://www.pnas.org/content/111/23/8410). Additional research on undergraduate STEM courses highlights the effectiveness of collaborative, small-group learning environments. This innovative pedagogical approach, successfully implemented over recent years, continues to deliver encouraging results.