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thefly
- 7
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I would like to study Galois theory by myself (I've already studied group theory). Can anyone suggest any good video lecture or pdf available on the web?
thank you in advance
thank you in advance
Galois theory is a branch of abstract algebra that studies the properties of field extensions, which are algebraic structures that extend the set of rational numbers. It provides a way to understand the solutions of polynomial equations and has important applications in number theory, cryptography, and physics.
Studying Galois theory is important because it allows us to understand the limitations of algebraic equations and find solutions to unsolvable equations. It also has applications in various fields such as cryptography, coding theory, and algebraic geometry.
The basic concepts of Galois theory include fields, field extensions, and automorphisms. Fields are algebraic structures that follow specific rules, and field extensions are created by adjoining elements to a field. Automorphisms are functions that preserve the structure of a field.
Galois theory is closely related to group theory because it studies the symmetries of equations and their solutions. The Galois group of a polynomial is a subgroup of the group of permutations of its roots, and it provides important information about the solvability of the equation.
There are many resources available for studying Galois theory, including textbooks, online courses, and lecture notes. Some recommended books include "Galois Theory" by Ian Stewart and "Field and Galois Theory" by Patrick Morandi. Online resources such as MIT OpenCourseWare and Khan Academy also offer free courses and videos on Galois theory.