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.