SIGNATURE WORK
CONFERENCE & EXHIBITION 2022

Abstract algebra exists as an important branch of mathematics, and Galois theory as one of the main theorems helps lay a foundation for its development. This project mainly focuses on the mathematical relationship between group theory and Galois theory, which owns unique development history, valuable content, and diverse applications of Galois theory. As a theory that covers number theory, group theory, and field theory, Galois theory itself has unparalleled mathematical value. As the basis of many progressive ideas, it extends the concepts of the Galois field and the Galois group. At the same time, the development history and the life experience of mathematician Galois are excellent and exciting. Based on the literature of Galois theory researchers, I introduced the research history of Galois theory and Galois’s legendary experience in the intro. Then, the basic mathematical concepts and logic of Galois theory itself were put forward in the theoretical elaboration part, which paved the way for later proofs. Furthermore, I took both transcendental number and ruler & compass construction as the applications of the theorematic basis. It is worth mentioning that the research significance of this project was mainly reflected in the connection between Galois theory and group theory, together with applications of transcendental number and ruler and compass construction based on historical research and theoretical systems.