Fields and Galois theory

Course Code :1002WETKLG
Study domain:Mathematics
Academic year:2017-2018
Semester:1st semester
Sequentiality:-
Contact hours:60
Credits:6
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:English
Exam period:exam in the 1st semester
Lecturer(s)Boris Shoykhet

3. Course contents *

  • Rings of polynomials, the procedure of joining a root of a polynomial to the field.
  • Algebraic field extensions, normal extensions.
  • Definition and construction of an algebraic closure of a field.
  • Basis of Galois theory, Galois correspondence between subextensions and subgroups.
  • Cyclotomic field extensions.
  • Applications of Galois theory: solving of concrete polynomial equations, constructions with ruler and compass.
  • Proof of the Fundamental Theorem of Algebra.