SPRING 2017 CORE-UA 101, Quantitative Reasoning: Math Patterns in Nature
Examines the role of mathematics as the language of science through case studies selected from the natural sciences and economics. Topics include the scale of things in the natural world; the art of making estimates; cross-cultural views of knowledge about the natural world; growth laws, including the growth of money and the concept of "constant dollars"; radioactivity and its role in unraveling the history of the earth and solar system; the notion of randomness and basic ideas from statistics; scaling laws and why things are the size they are; the cosmic distance ladder; and the meaning of "infinity." This calculator-based course is designed to help you use mathematics with some confidence in applications.
SPRING 2017 CORE-UA 105, Quantitative Reasoning: Elementary Statistics
Introduction to statistics and probability appropriate for students who may require such for their chosen field of study. Actual survey and experimental data are analyzed. Topics include the description of data, elementary probability, random sampling, mean, variance, standard deviation, statistical tests, and estimation. For a less rigorous introduction to such topics, students are encouraged to register for another QR course.
SPRING 2017 CORE-UA 107, Quantitative Reasoning: Problems, Statistics, and Decision-Making
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.
SPRING 2017 CORE-UA 110, Quantitative Reasoning: Great Ideas in Mathematics
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?