# Properties of Cyclotomic Polynomials

In this post we study cyclotomic polynomials in field theory and deduce some baisc properties of it. We will also use it to solve some problems in field theory.

Read moreIn this post we study cyclotomic polynomials in field theory and deduce some baisc properties of it. We will also use it to solve some problems in field theory.

Read moreWe study the height of polynomials and derive some important tools.

Read moreIn this episode we focus on the rational field. What can we know about the Galois group of an irreducible polynomial with prime degree? There is a method by counting the number of nonreal roots. From this, we obtain an algorithm to compute the Galois group.

Read moreWe study the Galois group of a cubic polynomial over a field with characteristic not equal to 2 and 3.

Read moreWe try to prove the fundamental theorem of algebra, that the complex field is algebraically closed, using as little analysis as possible. In other words, the following proof will be *almost* algebraic.

Read moreIn this post, we study the concept of character, what it is about in abstract harmonic analysis and how to use it Galois theory.

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