August 2026 semester 

MT 3174: Fields and Galois Theory

• Course contents: Fields and extensions, examples, algebraic extensions and algebraic elements, transcendental elements, existence of algebraic closure, separable extensions, normal extensions, automorphisms, solvable groups and solvability, main theorem of Galois theory, finite fields, Galois groups of finite fields, cyclotomic extensions, impossibility of solving polynomial equations of degree 5 or more by radicals. And other topics as time permits.

• Reference: Primary references

  • Artin, Michael. Algebra. 2nd ed., Pearson Prentice Hall, 2011.

  • Dummit, David S., and Richard M. Foote. Abstract Algebra. 3rd ed., Wiley India, 2003.

  • Stewart, Ian. Galois Theory. 3rd ed., Chapman & Hall/CRC, 2003.

• All updates will be posted on the Google Classroom page of the course.