FALL 2023 CORE-UA 107, Quantitative Reasoning:Problems, Statistics, & Decision Making
Prof. Majmudar [Syllabus]
This course examines the role in mathematics in making "correct" decisions. Special attention is devoted to quantifying the notions of "correct," "fair," and "best" and using these ideas to establish optimal decisions and algorithms to problems of incomplete information and uncertain outcomes. The mathematical tools used include a selection of topics in statistics, probability, game theory, division strategies, and optimization.
FALL 2023 CORE-UA 110, Quantitative Reasoning: Great Ideas in Mathematics
Prof. Espinosa [Syllabus]
This one semester course serves as an introduction to great ideas in mathematics. During the course we will examine a variety of topics chosen from the following broad categories. 1) A survey of pure mathematics: What do mathematicians do and what questions inspire them? 2) Great works: What are some of the historically big ideas in the field? Who were the mathematicians that came up with them? 3) Mathematics as a reflection of the world we live in: How does our understanding of the natural world affect mathematics (and vice versa!). 4) Computations, proof, and mathematical reasoning: Quantitative skills are crucial for dealing with the sheer amount of information available in modern society. 5) Mathematics as a liberal art: Historically, some of the greatest mathematicians have also been poets, artists, and philosophers. How is mathematics a natural result of humanity's interest in the nature of truth, beauty, and understanding? Why is math a liberal art?
FALL 2023 CORE-UA 111, Quantitative Reasoning: From Data to Discovery
Prof. Oveys
Today's technology enables us to collect massive amounts of data, such as images of distant planets, the ups and downs of the economy, and the patterns of our tweets and online behavior. How do we use data to discover new insights about our world? This course introduces ideas and techniques in modern data analysis, including statistical inference, machine learning models, and computer programming. The course is hands-on and data-centric; students will analyze a variety of datasets, including those from the internet and New York City. By the end of the course, students will be able to (1) apply quantitative thinking to data sets; (2) critically evaluate the conclusions of data analyses; and (3) use computing tools to explore, analyze, and visualize data. Throughout the course, we will also examine issues such as data privacy and ethics.