Title  ΘΕΩΡΙΑ GALOIS / Galois Theory 
Code  0134 
Faculty  Sciences 
School  Mathematics 
Cycle / Level  1st / Undergraduate 
Teaching Period  Spring 
Common  No 
Status  Active 
Course ID  40000303 
Programme of Study: UPS of School of Mathematics (2014today)
Registered students: 0
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Elective Courses belonging to the selected specialization  8  4  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
Specific Foundation / Core
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
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. perform computations on polynomial rings such as division and finding the greatest common divisorθ
ii. compute the irreducibility of a polynomial
iii. will determine whether an extesnsion is simple
iv. will determine the degree and the minimal polynomial of an extension
v. will construct the Galois group of an extension and determine its subgroups
vi. will determine the intetermediate fields of an extension
vii. will recognize the correspondence between the subgroups of a Galois group and the intermediate fields of a normal extension
viii. will apply the results of Galoi theory for the solvability of polynomials
ix. 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)
Construction of fields. Algebraic extensions  Classical Greek problems:
constructions with ruler and compass. Galois extensions  Applications: solvability of
algebraic equations  The fundamental theorem of Algebra  Roots of unity  Finite fields.
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
The students will be evaluated based on their performance of two mideterms of a final examination.
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)
J. Rotman, Θεωρία Galois
J. Fraleigh, Εισαγωγή στην Άλγεβρα
Δ. Πουλάκης, Άλγεβρα
Σ. Ανδρεαδάκης,
Additional bibliography for study
Θ. ΘεοχάρηΑποστολίδη και Χ. Χαραλάμπους, Θεωρία Galois, Kallipos
Last Update
24042019