General
| School
|
School of Science
|
| Academic Unit
|
Department of Mathematics
|
| Level of Studies
|
Graduate
|
| Course Code
|
AΛ1
|
| Semester
|
1
|
| Course Title
|
Algebra I
|
| Independent Teaching Activities
|
Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
|
| Course Type
|
Special Background
|
| Prerequisite Courses
|
-
|
| Language of Instruction and Examinations
|
Greek
|
| Is the Course Offered to Erasmus Students
|
Yes (in English)
|
| Course Website (URL)
|
See eCourse, the Learning Management System maintained by the University of Ioannina.
|
Learning Outcomes
| Learning outcomes
|
The objectives of the course are: The postgraduate student to reach a good level of theoretical background on topics related to the theory of group actions, the Sylow theorems and the general theory of modules over associative rings.
|
| General Competences
|
The aim of the course is to enpower the postgraduate student to analyse and compose basic notions of advanced Algebra. This will allow him to work in an international interdisciplinary environment.
|
Syllabus
Group actions on a set, Sylow theorems and applications, Direct and semidirect products, Finitely generated abelian groups, Free groups, Amalgamated free product of groups, Jordan-Hoelder theorem, Modules and homomorphisms between modules, Free modules, Direct sum and product of modules, Exact sequences and functors, Noetherian rings and modules, Semisimple rings and modules, Elements of multilinear and tensor algebra.
Teaching and Learning Methods - Evaluation
| Delivery
|
Face to face
|
| Use of Information and Communications Technology
|
-
|
| Teaching Methods
|
| Activity
|
Semester Workload
|
| Lectures
|
39
|
| Study and analysis of bibliography
|
78
|
| Preparation of assignments and interactive teaching
|
70.5
|
| Course total
|
187.5
|
|
| Student Performance Evaluation
|
Written exam at the end of semester (obligatory), problem solving or/and intermediate exams (optional).
|
Attached Bibliography
Θα καθορίζεται από τον διδάσκοντα / Will be determined by the teacher