Galois Theory

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: 1
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specialization845.5

Class Information
Academic Year2015 – 2016
Class PeriodSpring
Faculty Instructors
Class ID
600004783
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)
  • English (Instruction, Examination)
Prerequisites
Required Courses
  • 0102 Introduction to Algebra
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
The students will acquire a deeper knowledge of the evolution of Algebra, they wil know how to solve algebraic equations, they will know the construction and structure of finite fields and they will be see applications of Algebra to other branches of mathematics.
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
Lectures
Tutorial
Total
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
Last Update
09-11-2015