Προβολή πηγαίου κώδικα για τη σελίδα Group Theory (MAE525)

[[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
|
MAE525
|-
! Semester
|
5
|-
! Course Title
|
Group Theory
|-
! Independent Teaching Activities
| Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6)
|-
! Course Type
|
Special background, skills development.
|-
! Prerequisite Courses
| -
|-
! Language of Instruction and Examinations
|
Greek, English
|-
! Is the Course Offered to Erasmus Students
|
Yes
|-
! Course Website (URL)
|
http://users.uoi.gr/nkechag/GroupsNotesLONG3.pdf
|}

=== Learning Outcomes ===
{| class="wikitable"
|-
! Learning outcomes
|
Familiarity with: group, abelian group, subgroup, normal subgroup, quotient group, direct product of groups, homomorphism, isomorphism, kernel of a homomorphism.  Apply group theory to describe symmetry, describe the elements of symmetry group of the regular n-gon (the dihedral group D2n). Compute with the symmetric group. Know how to show that a subset of a group is a subgroup or a normal subgroup. State and apply Lagrange's theorem. State and prove the isomorphism theorems. Sylow theorems. The classification of finite abelian groups. Normal series, central series, nilpotent groups. Applications in Geometry.
|-
! General Competences
|
* Study particular characteristics of group theory in topology and geometry.
* Independent and team work.
* Working in an interdisciplinary.
|}

=== Syllabus ===
* Basic properties in groups.
* Symmetries.
* Subgroups, Direct products, Cosets.
* Symmetric groups.
* Normal Subgroups, Quotient groups.
* Homomorphisms.
* Semidirect product.
* Classification of finite abelian groups.
* Sylow theorems.
* Normal series, Solvable groups. Central series, Nilpotent groups. 
=== Teaching and Learning Methods - Evaluation ===
{| class="wikitable"
|-
! Delivery
|
Classroom (face-to-face)
|-
! Use of Information and Communications Technology
|
Communication with students
|-
! Teaching Methods
|
{| class="wikitable"
! Activity
! Semester Workload
|-
| Lectures (13X3)
| 39
|-
| Working independently
| 78
|-
| Exercises-Homeworks
| 33
|-
| Course total 
| 150
|}
|-
! Student Performance Evaluation
|
Written Examination, Oral Presentation, written assignments  in Greek (in case of Erasmus students in English) which includes resolving application problems. 
|}
=== Attached Bibliography ===

See [https://service.eudoxus.gr/public/departments#20 Eudoxus]. Additionally:
* An Introduction to the Theory of Groups (Graduate Texts in Mathematics) 4th Edition by Joseph Rotman.