Algebra I (ΑΛ1)

Graduate Courses Outlines - Department of Mathematics

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)	-

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

1. Marmaridis Nikos, Introduction to Group Theory (Greek), Leipsoi 2013.
2. Dummit, David, Foote, Richard M., Abstract algebra. Third edition. John Wiley & Sons, Inc., Hoboken, NJ, 2004.