# 20511 Field Extensions and Galois Theory 1

**Credits**: 4 advanced credits in Mathematics

**Prerequisites**: Students must fulfill all **English** requirements and take **bibliographic instruction** in the Library.

Required: Linear Algebra I, Algebraic Structures, Infinitesimal Calculus I, and having accumulated at least 36 credits in Mathematics

**Authors**: Abraham Ginzburg, Israel Friedman

Galois Theory is known for its internal beauty as well as its extensive applicability in Mathematics. It has been used to solve numerous interesting basic problems.

**Topics**: Field extensions; Field extensions as linear spaces; Simple algebraic extensions; Algebraic and transcendental numbers; Ruler and compass constructions; Splitting fields of polynomials; The fundamental theorem of algebra; Normal extensions; Automorphisms of fields; Separability; Symmetric polynomials; The fundamental theorem of Galois Theory; Equation solvability by radicals; Regular polygon constructions.

1A short non-credit seminar may be added to this course. See note under Mathematics seminars.