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Regular version of the site
Bachelor 2019/2020

## Introduction to Galois Theory

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Type: Elective course (Mathematics)
Area of studies: Mathematics
When: 3 year, 3, 4 module
Mode of studies: distance learning
Language: English
ECTS credits: 5

### 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

• 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

• Successful participants will develop facility in applying ideas

#### 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

• Midterm exam
• Final exam
The exam will be written and closely based on the example problem sheets from the seminar.

#### Interim Assessment

• Interim assessment (4 module)
0.7 * Final exam + 0.3 * Midterm exam

#### 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