Albion College Mathematics and Computer Science Colloquium

Title: Wheels: How to Divide by Zero
Speaker:Brian Wu, `14
Senior Mathematics Major
Albion College
Albion, Michigan
Abstract: As a young student, we initially learned that we could not take the square root of a negative number. Eventually, we learned about the set of complex numbers, which was invented in order to calculate all of the roots of any polynomial, including those involving square roots of negative numbers. Additionally, we learned that parallel lines never intersect. Upon looking at them from a new perspective, we learned that in projective geometry, parallel lines intersect at a point "at infinity." Currently, we are told that division by zero is a forbidden mathematical operation due to the lack of a multiplicative inverse. Alternately, there is no solution to the equation $0x = 1$. However, mathematicians recently defined $\perp$ and $\infty$, consistent with previous mathematics, representing the two cases that arise when attempting to divide by zero. These two new elements are placed into a field, yielding a special structure called a wheel. However, division by zero is not entirely without consequences. This talk will review the familiar algebraic structures, including rings and fields, and then proceed onto wheels and how incorporating these two new elements change the properties of polynomials.
Location: Palenske 227
Time: 3:30 PM

author  = "{Brian Wu, `14}",
title   = "{Wheels: How to Divide by Zero}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month   = "{1 May}",
year    = "{2014}"