Course Information
TitleΘΕΩΡΙΑ GALOIS / Galois Theory
Code0134
FacultySciences
SchoolMathematics
Cycle / Level1st / Undergraduate
Teaching PeriodSpring
CommonNo
StatusActive
Course ID40000303

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

Registered students: 0
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specialization845.5

Class Information
Academic Year2019 – 2020
Class PeriodSpring
Faculty Instructors
Weekly Hours3
Class ID
600147668
Type of the Course
  • Scientific Area
Course Category
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
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 self-critical
  • 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
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures652.2
Reading Assigment692.3
Written assigments280.9
Exams30.1
Total1655.5
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. Θεοχάρη-Αποστολίδη και Χ. Χαραλάμπους, Θεωρία Galois, Kallipos
Last Update
24-04-2019