Galois Theory

Course Information
TitleΘΕΩΡΙΑ GALOIS / Galois Theory
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
Course ID40000303

Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 100
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specializationWinter-5.5

Class Information
Academic Year2020 – 2021
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Class ID
Type of the Course
  • Scientific Area
Course Category
Knowledge Deepening / Consolidation
Mode of Delivery
  • Face to face
Digital Course Content
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
Required Courses
  • 0106 Algebraic Structures I
  • Ν0107 Algebraic Structures II
General Prerequisites
The students who wish to enroll in this course must demonstrate knoweledge of the material covered in the courses Algebraic Structures I and II.
Learning Outcomes
Upon successful completion of the course students will i. will determine whether an extesnsion is simple ii. will determine the degree and the minimal polynomial of an extension iii. will construct the Galois group of an extension and determine its subgroups iv. will determine the intetermediate fields of an extension v. will recognize the correspondence between the subgroups of a Galois group and the intermediate fields of a normal extension vi. will apply the results of Galoi theory for the solvability of polynomials vii. will apply the results of Galoi theory on constructions by ruler and compass
General Competences
  • Apply knowledge in practice
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Make decisions
  • Work autonomously
  • Work in teams
  • Appreciate diversity and multiculturality
  • Respect natural environment
  • Demonstrate social, professional and ethical commitment and sensitivity to gender issues
  • Be critical and self-critical
  • Advance free, creative and causative thinking
Course Content (Syllabus)
Field extensions. Prime fields. Algebraic and Transcendental extensions. Classification of simple extensions. Constructions with ruler and compass. Algebraic closure of a field. Splitting fields. Normal and Separable extensions. Finite fields. Automorphisms of fields. Galois group and Galois extension. Fundamental Theorem of Galois Theory. Applications: solvability of algebraic equations - The fundamental theorem of Algebra - Roots of unity.
algebraic and Galois extensions, solvability, classical problems
Educational Material Types
  • Notes
Course Organization
Reading Assigment692.3
Written assigments280.9
Student Assessment
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative)
  • Written Assignment (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
Course Bibliography (Eudoxus)
1. Εισαγωγή στην Άλγεβρα, J. Fraleigh, ISBN: 978-960-7309-71-6, Πανεπιστημιακές Εκδόσεις Κρήτης 2. Άλγεβρα, Δ. Μ. Πουλάκης, ISBN 978-960-456-388-3, Εκδόσεις ΖΗΤΗ, Θεσσαλονίκη, 2015 3. Θεωρία Galois, J. Rotman, ISBN: 9607901126, ΔΙΑΔΡΟΜΕΣ
Additional bibliography for study
Θεωρία Galois, Θ. Θεοχάρη-Αποστολίδη, Χ. Χαραλάμπους, ISBN: 978-960-603-208-0, [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, ID Ευδόξου: 320037
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