Algebraic Structures II (MAE724)
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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. Books and other resources, not provided by Eudoxus: