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Regular version of the site
2018/2019

Introduction to Galois Theory

Type: Optional course (faculty)
When: 1, 2 module
Language: English

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. This course is optional. Pre-requisites : Basic algebra: groups, rings, linear algebra over a field.
Learning Objectives

Learning Objectives

  • Introduce the subject area to the students, and to offer them an opportunity to prepare and give a talk
Expected Learning Outcomes

Expected Learning Outcomes

  • Improve their presentation skills and prepare for participation in research projects in the subject area
  • Can solve tasks in Galois Theory
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 Cumulative Grade
  • non-blocking Final exam
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.4 * Cumulative Grade + 0.6 * Final exam
Bibliography

Bibliography

Recommended Core Bibliography

  • Ash, R. B. (2007). Basic Abstract Algebra : For Graduate Students and Advanced Undergraduates. Mineola, N.Y.: Dover Publications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1152113

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