Galois Theory
| Title | ΘΕΩΡΙΑ GALOIS / Galois Theory |
| Code | 0134 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Coordinator | Chrysostomos Psaroudakis |
| Common | No |
| Status | Active |
| Course ID | 40000303 |
Programme of Study: Merikīs Foítīsīs (2014-sīmera)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 1
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | 7 | 4 | 5.5 |
| Academic Year | 2013 – 2014 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Class ID | 40049389
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/40049389
- 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)
- English (Instruction, Examination)
Prerequisites
Required Courses
- 0102 Introduction to Algebra
- 0131 Group Theory
- 0106 Algebraic Structures I
- 0107 Algebraic Structures II
Learning Outcomes
With the successful fullfilled of the course the students have a deep knowledge of the evolution of Algebra, they know to solve algebraic equations, they know the structure and constructure of finite fields and they are introduced to the 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
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 42 | ✓ | ✓ | ✓ | |
| Tutorial | 13 | ||||
| Total | 55 |
Student Assessment
Description
The valuation of the students is the result of their performance in the solutions of the exercises in the class, the two written progress examinations and the final written examinations.
The rules of the valuation are given through the lectures.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative)
- Written Assignment (Formative, Summative)
- Written Exam with Problem Solving (Formative)
Bibliography
Course Bibliography (Eudoxus)
J. Rotman, Θεωρία Galois
J. Fraleigh, Εισαγωγή στην Άλγεβρα
Additional bibliography for study
Θ. Θεοχάρη-Αποστολίδη και Χ. Χαραλάμπους, Θεωρία Galois, Ηλεκτρονικό βιβλίο.
Last Update
05-09-2013
