Special Topics in Algebra (MAE723)
Undergraduate Courses Outlines - Department of Mathematics
General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAE723 |
| Semester |
7 |
| Course Title |
Special Topics in Algebra |
| Independent Teaching Activities |
Lectures, laboratory exercises (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) | - |
Learning Outcomes
| Learning outcomes |
The principal aim of the course is to introduce the students to the main tools and methods of the theory of modules and rings. At the end of the course we expect the student to have understood the definitions and basic theorems which are discussed in the course, to have understood how they are applied in discrete examples, to be able to apply the material in order to extract new elementary conclusions, and finally to perform some (no so obvious) calculations. |
|---|---|
| General Competences |
The contact of the undergraduate student with the ideas and concepts of the theory of modules and rings, (a) promotes the creative, analytical and deductive thinking and the ability to work independently, (b) improves his critical thinking and his ability to apply abstract knowledge in various field. |
Syllabus
- Elementary Ring Theory.
- Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.
- Module Theory.
- Modules over polynomial rings.
- Finitely generated and free modules.
- Modules over Principal Ideal Domains.
- Decomposition Theorems.
- Applications to Linear Algebra and Abelian groups.
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 Eudoxus. Additionally:
- Μ. Μαλιάκας - Ο. Ταλέλλη: «Πρότυπα πάνω σε Περιοχές Κυρίων Ιδεωδών και Εφαρμογές», Εκδόσεις Σοφία.
- Μ. Μαλιάκας: «Εισαγωγή στη Μεταθετική Άλγεβρα», Εκδόσεις Σοφία.
- N. Jacobson: “Basic Algebra I”, Dover Publications (1985).
- S. Lang: «Άλγεβρα», Εκδόσεις Πολιτεία (2010).