Special Topics in Algebra (MAE723)
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- Undergraduate Courses Outlines
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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 (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 principal aim of the course is to introduce the students to the main ideas and methods of Commutative Algebra. |
|---|---|
| General Competences |
The course promotes inductive and creative thinking and aims to provide the student with the theoretical background and skills of commutative rings. |
Syllabus
- Polynomial Rings
- Hilbert's Basis Theorem
- Localization
- Integral dependence
- Hilbert Series
- Dimension
- Groebner Bases
- Hilbert's Nullstellensatz Theorem
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:
- J.Beachy, Introductory Lectures on Rings and Modules, LMS, Cambridge University Press, (1999).
- D.Dummit, R.M.Foote, Abstract Algebra, 3 edition, Prentice Hall, (2003).
- N.Jacobson, Basic Algebra I & II, W. H. Freeman and Company, (1985 & 1989).
- S.Lang, Algebra, Graduate Texts in Mathematics, Springer (2002).
- L.Rowen, Ring Theory, Academic Press, 2 edition (1991).
- Μαλιάκας. Ταλέλλη, Πρότυπα πάνω από Περιοχές Κυρίων Ιδεωδών και Εφαρμογές, Εκδ. Σοφία (2009).
- Α. Μπεληγιάννης, Μια Εισαγωγή στη Βασική Άλγεβρα, Εκδ. Κάλλιπος (2015).