TFAE stands for “the following are equivalent.” This statement is fairly common in mathematical theorems. Why, you may ask? Well, there is a lot of power in being able to do something multiple ways. It gives us options to find one that can best fit our mathematical needs. A very familiar example of equivalency would be the Fundamental Theorem of Calculus, it tells us we can either evaluate the integral or anti-differentiate. A less familiar example is Euclid’s propositions 5 and TFAE: A brief history of the Axiom of Choice Rebecca Miller 04/22/2017

TFAE stands for “the following are equivalent.” This statement is fairly common in mathematical theorems. Why, you may ask? Well, there is a lot of power in being able to do something multiple ways. It gives us options to find one that can best fit our mathematical needs. A very familiar example of equivalency would be the Fundamental Theorem of Calculus, it tells us we can either evaluate the integral or anti-differentiate. A less familiar example is Euclid’s propositions 5 and

For my undergraduate thesis my focus was in knot theory, a subset of topology and a newer subject in mathematics. These are not the knots we think of in our daily life. The knots I studied had no ends and no thickness. Knots as we know them in everyday life have been around since before the Greeks. The book of Kells is decorated with intricate knot work. Sailors have used them on their ships. The Incas even used them to keep track of their accounting. The Incan civilization started in modern day Knots by Number, Quipu Lauren Miller 10/11/2016

For my undergraduate thesis my focus was in knot theory, a subset of topology and a newer subject in mathematics. These are not the knots we think of in our daily life. The knots I studied had no ends and no thickness. Knots as we know them in everyday life have been around since before the Greeks. The book of Kells is decorated with intricate knot work. Sailors have used them on their ships. The Incas even used them to keep track of their accounting. The Incan civilization started in modern day