Algebraic Structures II (MAE724)
Undergraduate Courses Outlines - Department of Mathematics
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) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
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 than 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
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Additionally:
- M. Holz: "Repetition in Algebra", Greek Edition, Symmetria Publishing Company, (2015).
- Th. Theochari-Apostolidou and C. M. A. Charalambous: "Galois Theory", (Greek), Kallipos Publishing (2015).