Knots and Seifert surfaces

Abstract

[en] Since the beginning of the degree that I think that everyone should have the oportunity to know mathematics as they are and not as they are presented (or were presented) at a high school level. In my opinion, the answer to the question "why do we do this?" that a student asks, shouldn’t be "because is useful", it should be "because it’s interesting" or "because we are curious". To study mathematics (in every level) should be like solving an enormous puzzle. It should be a playful experience and satisfactory (which doesn’t mean effortless nor without dedication). It is this idea that brought me to choose knot theory as the main focus of my project. I wanted a theme that generated me curiosity and that it could be attractive to other people with less mathematical background, in order to spread what mathematics are to me. It is because of this that i have dedicated quite some time to explain the intuitive idea behind every proof and definition, and it is because of this that the great majority of proofs and definitions are paired up with an image (created by me). In regards to the technical part of the project I have had as main objectives: to introduce myself to knot theory, to comprehend the idea of genus of a knot and know the propeties we could derive to study knots.