Title  ΘΕΩΡΙΑ GALOIS / Galois Theory 
Code  0134 
Faculty  Sciences 
School  Mathematics 
Cycle / Level  1st / Undergraduate 
Teaching Period  Winter 
Common  No 
Status  Active 
Course ID  40000303 
Programme of Study: UPS of School of Mathematics (2014today)
Registered students: 32
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Elective Courses belonging to the selected specialization  Winter    5.5 
Academic Year  2019 – 2020 
Class Period  Spring 
Faculty Instructors 

Weekly Hours  3 
Class ID  600147668

Type of the Course
 Scientific Area
Course Category
Knowledge Deepening / Consolidation
Mode of Delivery
 Face to face
Digital Course Content
 eStudy Guide https://qa.auth.gr/en/class/1/600147668
 At the Website of the School: math.auth.gr
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
 Greek (Instruction, Examination)
Prerequisites
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 selfcritical
 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.
Keywords
algebraic and Galois extensions, solvability, classical problems
Educational Material Types
 Notes
Course Organization
Activities  Workload  ECTS  Individual  Teamwork  Erasmus 

Lectures  65  2.2  ✓  ✓  
Reading Assigment  69  2.3  ✓  
Written assigments  28  0.9  
Exams  3  0.1  ✓  
Total  165  5.5 
Student Assessment
Description
Student Assessment methods
 Written Exam with Short Answer Questions (Formative)
 Written Assignment (Formative, Summative)
 Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
1. Εισαγωγή στην Άλγεβρα, J. Fraleigh, ISBN: 9789607309716, Πανεπιστημιακές Εκδόσεις Κρήτης
2. Άλγεβρα, Δ. Μ. Πουλάκης, ISBN 9789604563883, Εκδόσεις ΖΗΤΗ, Θεσσαλονίκη, 2015
3. Θεωρία Galois, J. Rotman, ISBN: 9607901126, ΔΙΑΔΡΟΜΕΣ
Additional bibliography for study
Θεωρία Galois, Θ. ΘεοχάρηΑποστολίδη, Χ. Χαραλάμπους, ISBN: 9789606032080, [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, ID Ευδόξου: 320037
Last Update
15032020