Προβολή πηγαίου κώδικα για τη σελίδα Rings, Modules and Applications (MAE628)

[[Undergraduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]

=== General ===
{| class="wikitable"
|-
! School
|
School of Science
|-
! Academic Unit
|
Department of Mathematics
|-
! Level of Studies
|
Undergraduate
|-
! Course Code
|
MAE628
|-
! Semester
|
6
|-
! Course Title
|
Rings, Modules and Applications
|-
! 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)
| See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina.
|}

=== Learning Outcomes ===
{| class="wikitable"
|-
! 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 ===
{| class="wikitable"
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! Delivery
|
Classroom (face-to-face)
|-
! Use of Information and Communications Technology
| -
|-
! Teaching Methods
|
{| class="wikitable"
! Activity
! Semester Workload
|-
| Lectures (13X3)
| 39
|-
| Working independently
| 78
|-
| Exercises-Homeworks
| 33
|-
| Course total 
| 150
|}
|-
! Student Performance Evaluation
|
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. 
|}
=== Attached Bibliography ===

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See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

{{MAE628-Biblio}}