@deilann
Bouncing back on the subject, I took Artin's #GaloisTheory with me to #Benasque and I think on page 25 there is a complete discussion. As you said any #algebraicNumber, defined as a root of a real polynomial, can be seen as a root of a unique polynomial of lowest degree which is irreducible, i.e. not divisible by any other poly omial with coefficients in the base field.

The coefficient of the highest power needs to be 1, one should divide the contending polynomials by each other and evaluate at the shared root showing that, having the same degree, they have 0 polynomial ring division remainder so must be the same.

I'm reading Artin's #GaloisTheory and I'm wondering if the #math exposition of the #matrix #determinant relying on homogeneity properties is related to the #BrunnMinkowski #inequality

I will check my handwritten notes when I'll be in Poland end of July but I remember that homogeneity played a role there.

This rambling is related to my struggle to understand the #BrascampLieb and #rearrangementInequality. Any hints much appreciated 🥹😅🙈😊

#maths #GaloisTheory #OU - Donald Rumsfeld said "There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know." I thought what a pratt. I am currently doing a course on Galois Theory & now realise that this is all about getting from what don't know I don't know to where I can say these are things that I know that I don't know

Hey everyone!

My name is Jesse, and I am an undergraduate student of #Mathematics and #ComputerScience. I really enjoy #Algebra the most out of the #math disciplines I've studied. I mainly self-taught myself a good portion of topics from a first year semester of #AbstractAlgebra (#Groups, #Rings, #Fields, and some basics of #GaloisTheory ), I plan to take a #RingTheory course next semester, and I am also trying to learn #UniversalAlgebra currently on the side. Glad to be here!

#introduction