Introduction to Galois Theory
- The seminar is intended to introduce the subject area to the students, and to offer them the opportunity to work through many concrete examples and applications.
- Review of polynomial rings and more general principal ideal domains.
- Extensions of fields, algebraic and transcendental
- Splitting fields of polynomials and Galois groups.
- The fundamental theorem of Galois theory
- Computing Galois groups
- Midterm exam
- Final examThe exam will be written and closely based on the example problem sheets from the seminar.
- Instructor Luís Finotti, Textbook D. Dummit, R. Foote, & Abstract Algebra. (n.d.). Math 551: Modern Algebra I – Fall 2007. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.1CEBE666
- Emil Artin. (2007). Algebra with Galois Theory. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1495050