First-Year Writing Seminar (101-8-1)

Topic

Concepts of Mathematical Infinity

Instructors

Lance Rips
847/491-5190
314 Swift Hall

Meeting Info

Swift Hall 231: Tues, Thurs 2:00PM - 3:20PM

Overview of class

Infinity is a central property of most number systems. The natural numbers, integers, rationals, reals, and complex numbers all include an infinite number of elements. People's concepts of these systems would be confused if they failed to grasp the fact that there is no end to these numbers. However, most people have great difficulty understanding infinite sets like these. Are there more positive integers than positive even integers? Are there more rational numbers than natural numbers? Are there more real numbers than rational numbers? You might be surprised at the correct answers to some of these questions. To set the stage, we'll look (informally) at some of the math background on infinity, as developed by Georg Cantor and others in the 19th Century. Then we'll examine some reasons why thinking and reasoning about infinity is so difficult. We'll read some cognitive psychology experiments that address how children first learn about the infinity of the positive integers, how they learn about infinite divisibility, and how older students (NU undergrads) think about number systems in general.

Registration Requirements

Enrollment Requirements: Reserved for Freshmen and Sophomores

Evaluation Method

Written Homework Assignments, Class participation, Final Paper

Class Materials (Required)

Cheng, E. (2017). Beyond Infinity. Basic Books. ISBN-13: 978-1541644137

Class Materials (Suggested)

Huemer, M. (2016). Approaching Infinity. Palgrave Macmillan.
Rayo, A. (2019). On the Brink of Paradox. MIT Press.
Stillwell, J. (2010). Roads to Infinity. A K Peters.

Class Attributes

WCAS Writing Seminar
Attendance at 1st class mandatory

Enrollment Requirements

Enrollment Requirements: Weinberg First Year Seminars are only available to first-year students.