|Course Dates||Length||Meeting Times||Status||Format||Instructor(s)||CRN|
|July 12, 2021 - July 28, 20217/12 - 7/28||2 Weeks||Online||Open||Online||Anna Grim||11767|
Although the concept of infinity has been pondered since the time of the ancient Greeks, this idea was very controversial up until the mid 1900s. The beginning of the 20th century marks the beginning of some understanding of the infinite, but the next fifty years was filled with controversy, paradox, and eventual acceptance of the infinite. This course will explore both the mathematics and the rich history behind this controversial topic. As we dig into the mathematics, we'll discover that accepting the notion of infinity is met by a number of paradoxes such as a logical conundrum called the 100 Rooms Problem.
This course is designed for students who love puzzles, problem solving, and are curious about higher level mathematics. The primary goal of this course is to learn how to solve the 100 Rooms Problem, which only requires three mathematical tools: equivalence classes, sequences, and the axiom of choice. In the first few days of the course, we will develop these tools and solve small problems with them. A secondary goal of this course is to emphasize that the 100 Rooms Problem fits into a broader context of mathematics, which includes rich historical roots and other mathematical paradoxes. To meet this goal, some additional topics in this course include sizes of infinity, Banach-Tarski Paradox, red/blue hat problems, Hilbert Hotel Paradox, the biggest number in math, and logical puzzles.
This course will introduce students to higher level math in an engaging and interesting manner and help students develop abstract thinking and problem solving skills. This will be unlike a traditional high school math class where the focus is on calculations. Students should walk away from the course more interested in math and with a broader understanding and fresh perspective on the kinds of problems they can solve with it. Moreover, that mathematics is a very active field and there are many open problems that these students could solve someday.
Prerequisites: There are no pre-requisites other than a curious mind.