Surprises at Infinity
Our intuitions about sets, numbers, shapes, and logic all break down in the realm of the infinite. Seemingly paradoxical facts about infinity are the subject of this course. We will discuss what infinity is, how it has been viewed through history, why some infinities are bigger than others and how a finite shape can have an infinite perimeter. This will very likely be quite different from any mathematics course you have ever taken. Surprises at Infinity focuses on ideas and reasoning rather than algebraic manipulation, though some algebraic work will be required to clarify big ideas. The class will be a mixture of lecture and discussion, based on selected readings. You can expect essay tests, frequent homework, and writing assignments. No prerequisite. Typically offered every other year.