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: 41
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2018 – 2019 |
| Class Period | Spring |
| Instructors from Other Categories |
|
| Weekly Hours | 3 |
| Class ID | 600121466
|
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/1/600121466
- 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 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
| 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. Θεοχάρη-Αποστολίδη και Χ. Χαραλάμπους, Θεωρία Galois, Kallipos
Last Update
24-04-2019
