Real Analysis

3 Credits · Level: Undergraduate

This course explores the "why" and "how" of calculus. This is not a course about calculations (you do not need any background in math to take this course). Rather, this is a course about concepts. The core idea that underlies it all is the idea of a space, full of points bunched together into neighborhoods. What precisely does it mean for one point to be "near" another point? And what if you stretch the space? In this course, we begin by studying the basic spatial properties of an infinitely dense line of points (the so-called "real number line"). Then we generalize what we learn to two, three, and more dimensions. Finally, we leave behind fixed spaces and study much more general (and stretchy) spaces, i.e., spaces of any shape. The ideas about "spaces of points" that we cover in this course form the conceptual bedrock that underlies modern data analysis, statistics, physics, and much more.