Description: |
Galois theory is one of the most spectacular mathematical theories. It brings together several branches of mathematics and creates a powerful machine for the study of some historical problems, such as solubility of polynomial equations by radicals, and duplication of a cube by ruler and compass. The most famous application of Galois theory is the proof that the general quintic equation with rational coefficients cannot be solved by radicals. The main theorem of Galois theory, the fundamental Galois correspondence, is one of the most beautiful theorems in all of mathematics.
The course begins by discussing the problem of solutions of polynomial equations, and goes on to cover field extensions, algebraic and transcendental numbers, Galois groups, the Galois correspondence, etc. It may include applications to finite fields and to the fundamental theorem of algebra.
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