Wiki Τμήματος Μαθηματικών
Topological Matrix Groups (MAE826): Διαφορά μεταξύ των αναθεωρήσεων

Topological Matrix Groups (MAE826): Διαφορά μεταξύ των αναθεωρήσεων

Από Wiki Τμήματος Μαθηματικών
(Νέα σελίδα με '=== General === {| class="wikitable" |- ! School | School of Science |- ! Academic Unit | Department of Mathematics |- ! Level of Studies | Undergraduate |- ! Course Code | MAE729 |- ! Semester | 7 |- ! Course Title | Topological Matrix Groups |- ! Independent Teaching Activities | Interactive, Presentations (Weekly Teaching Hours: 3, Credits: 6) |- ! Course Type | Special Background, skills development |- ! Prerequisite Courses | - |- ! Language of Instruction an...')
 
Χωρίς σύνοψη επεξεργασίας
 
(13 ενδιάμεσες αναθεωρήσεις από τον ίδιο χρήστη δεν εμφανίζεται)
Γραμμή 1: Γραμμή 1:
* [[Τοπολογικές Ομάδες Πινάκων (ΜΑΕ826)|Ελληνική Έκδοση]]
{{Course-UnderGraduate-Top-EN}}
{{Menu-OnAllPages-EN}}
=== General ===
=== General ===
{| class="wikitable"
{| class="wikitable"
Γραμμή 16: Γραμμή 20:
! Course Code
! Course Code
|
|
MAE729
MAE826
|-
|-
! Semester
! Semester
|
|
7
8
|-
|-
! Course Title
! Course Title
Γραμμή 46: Γραμμή 50:
|-
|-
! Course Website (URL)
! Course Website (URL)
| http://users.uoi.gr/nkechag/TopologicalGroupTheory.pdf
| See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina.
|}
|}
=== Learning Outcomes ===
=== Learning Outcomes ===
{| class="wikitable"
{| class="wikitable"
Γραμμή 81: Γραμμή 86:
|-
|-
! Use of Information and Communications Technology
! Use of Information and Communications Technology
| -
|
Communication with students
Communication with students
|-
|-
Γραμμή 113: Γραμμή 118:
Written Examination, Oral Presentation, written assignments.
Written Examination, Oral Presentation, written assignments.
|}
|}
=== Attached Bibliography ===
=== Attached Bibliography ===
* J. F. Adams, Lectures on Lie groups, University of Chicago Press, 1969.
 
* M. L. Curtis, Matrix Groups, Springer-Verlag, 1979.
<!-- In order to edit the bibliography, visit the webpage -->
* R. Howe. Very basic Lie theory, American math. monthly,90, 1983.
<!-- https://wiki.math.uoi.gr/index.php/%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF:MAE826-Biblio -->
 
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:
 
{{MAE826-Biblio}}

Τελευταία αναθεώρηση της 12:38, 15 Ιουνίου 2023

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE826

Semester

8

Course Title

Topological Matrix Groups

Independent Teaching Activities

Interactive, Presentations (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) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The aim of the course is to provide an introduction to Lie theory through matrix groups. The main subject of study is the closed subgroups of the general linear group. Our study is extended from real to complex and quaternion numbers. The corresponding linear groups are in fact topological groups and an introduction of basic properties of topological group is also provided. The Lie algebra of a matrix group is defined. The special orthogonal, unitary and symplectic groups provide important example of Lie algebras. Lie algebras are studied using the exponential map. Finally Lie groups are defined.

General Competences
  • Study particular characteristics of group theory in topology and geometry
  • Independent and team work
  • Working in an interdisciplinary.

Syllabus

  • General linear groups
  • Real and Complex algebras, Quaternions. Matrix algebras
  • Inner product, orthogonal, unitary and symplectic groups
  • Homomorphisms
  • Differential curves, tangent vectors. Dimension of a matrix group
  • Differential homomorphisms
  • Expontential and logarithmic funcions. Lie algebras
  • Special orthogonal and symplectic groups
  • Topological groups, manifolds
  • Maximal tori
  • Differential manifolds, Lie groups.

Teaching and Learning Methods - Evaluation

Delivery

Face-to-face, Distance learning

Use of Information and Communications Technology

Communication with students

Teaching Methods
Activity Semester Workload
Lectures 39
Working hours in class 8
Project 30
Assignments 33
Final exam 41
Course total 150
Student Performance Evaluation

Written Examination, Oral Presentation, written assignments.

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. F. Adams, Lectures on Lie groups, University of Chicago Press, 1969.
  • M. L. Curtis, Matrix Groups, Springer-Verlag, 1979.
  • R. Howe. Very basic Lie theory, American math. monthly,90, 1983.
Ανακτήθηκε από «https://wiki.math.uoi.gr/index.php?title=Topological_Matrix_Groups_(MAE826)&oldid=4622»