Have you ever wondered what $$\sqrt{-1}$$ really is? Mathematicians call this number imaginary, but is it even a number at all? In this course, we'll explore imaginary numbers and how they arise from arithmetic operations. We'll trace the development of different number systems as we try to gain intuition about how imaginary numbers work.

Have you ever thought about how trains turn? Train wheels are usually connected by a fixed axle, so the wheels on both sides of the train rotate at the same rate. However, when rounding a corner, the outside wheel must travel a longer distance than the inside wheel, which is a paradoxical result. In this class, we aim to answer this paradox and other interesting physics puzzles. Students will work independently or in groups to try to solve these paradoxes. The instructor will provide hints along the way and discuss solutions at the end of class.

Have you ever wondered what $$\sqrt{-1}$$ really is? Mathematicians call this number imaginary, but is it even a number at all? In this course, we'll explore imaginary numbers and how they arise from arithmetic operations. We'll trace the development of different number systems as we try to gain intuition about how imaginary numbers work.

Have you ever wondered what $$\sqrt{-1}$$ really is? Mathematicians call this number imaginary, but is it even a number at all? In this course, we'll explore imaginary numbers and how they arise from arithmetic operations. We'll trace the history of numbers and learn about the development of different number systems as we try to gain intuition about how imaginary numbers work. Along the way, we'll discuss some of their applications to physics, electrical engineering, and computer science.