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Regular version of the site
Master 2021/2022

Introduction to Galois Theory

Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Type: Elective course (Mathematics and Mathematical Physics)
Area of studies: Mathematics
When: 2 year, 1, 2 module
Mode of studies: distance learning
Open to: students of one campus
Instructors: Nikita S. Markaryan
Master’s programme: Mathematics and Mathematical Physics
Language: English
ECTS credits: 5
Contact hours: 30

Course Syllabus

Abstract

Galois theory is the study of roots of polynomials and their symmetries in terms of Galois groups. As the algebraic counterpart of the fundamental group of topology, the Galois group is an essential object in algebraic geometry and number theory.
Learning Objectives

Learning Objectives

  • 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.
Expected Learning Outcomes

Expected Learning Outcomes

  • Successful participants will develop facility in applying ideas
Course Contents

Course Contents

  • 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
  • Applications
Assessment Elements

Assessment Elements

  • non-blocking Midterm exam
  • non-blocking Final exam
    The exam will be written and closely based on the example problem sheets from the seminar.
  • non-blocking Midterm exam
  • non-blocking Final exam
    The exam will be written and closely based on the example problem sheets from the seminar.
Interim Assessment

Interim Assessment

  • 2021/2022 2nd module
    40% midterm; 60% final. Final mark: round percent/10 to nearest integer
Bibliography

Bibliography

Recommended Core Bibliography

  • 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

Recommended Additional Bibliography

  • 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