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: UPS of School of Mathematics (2014-today)
Registered students: 32
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2019 – 2020 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600147668
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study 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 self-critical
- 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: 978-960-7309-71-6, Πανεπιστημιακές Εκδόσεις Κρήτης
2. Άλγεβρα, Δ. Μ. Πουλάκης, ISBN 978-960-456-388-3, Εκδόσεις ΖΗΤΗ, Θεσσαλονίκη, 2015
3. Θεωρία Galois, J. Rotman, ISBN: 9607901126, ΔΙΑΔΡΟΜΕΣ
Additional bibliography for study
Θεωρία Galois, Θ. Θεοχάρη-Αποστολίδη, Χ. Χαραλάμπους, ISBN: 978-960-603-208-0, [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, ID Ευδόξου: 320037
Last Update
15-03-2020
