Algebraic Structures II (MAE724): Διαφορά μεταξύ των αναθεωρήσεων
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(Νέα σελίδα με '=== General === {| class="wikitable" |- ! School | School of Science |- ! Academic Unit | Department of Mathematics |- ! Level of Studies | Undergraduate |- ! Course Code | MAE823 |- ! Semester | 8 |- ! Course Title | Algebraic Structures II |- ! Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 6) |- ! Course Type | Special Background |- ! Prerequisite Courses | - |- ! Language of Instruction and Examinations | Greek |- ! Is the Cour...') |
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Γραμμή 79: | Γραμμή 79: | ||
* The Fundamental Theorem of Galois Theory | * The Fundamental Theorem of Galois Theory | ||
* Discriminants | * Discriminants | ||
* Polynomials of degree | * Polynomials of degree less 4 and Galois Groups | ||
* Ruler and Compass constructions | * Ruler and Compass constructions | ||
=== Teaching and Learning Methods - Evaluation === | === Teaching and Learning Methods - Evaluation === | ||
{| class="wikitable" | {| class="wikitable" |
Αναθεώρηση της 19:54, 29 Ιουνίου 2022
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE823 |
Semester |
8 |
Course Title |
Algebraic Structures II |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | https://sites.google.com/site/apostolosthomamath/teaching |
Learning Outcomes
Learning outcomes |
The students will acquire with the successful completion of the course
|
---|---|
General Competences |
The course aim is for the student to acquire the ability in analysis and synthesis of knowledge in Field Theory and produces free, creative and inductive thinking. |
Syllabus
- Rings
- Integral Domains, Fields, Homomorphisms and Ideals
- Quotient Rings
- Polynomial Rings over fields
- Prime and Maximal Ideals
- Irreducible Polynomials
- The classical methods of solving polynomial equations
- Splitting fields
- The Galois Group
- Roots of unity
- Solvability by Radicals
- Independence of characters
- Galois extensions
- The Fundamental Theorem of Galois Theory
- Discriminants
- Polynomials of degree less 4 and Galois Groups
- Ruler and Compass constructions
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
- S. Andreadakis: "Galois Theory", (Greek), Symmetria Publishing Company, (1999).
- M. Holz: "Repetition in Algebra", Greek Edition, Symmetria Publishing Company, (2015).
- J. Rotman: "Galois Theory", Greek edition, Leader Books, (2000).
- Th. Theochari-Apostolidou and C. M. A. Charalambous: "Galois Theory", (Greek), Kallipos Publishing (2015).