Advanced Topics in Algebra
| Title | ΠΡΟΧΩΡΗΜΕΝΑ ΘΕΜΑΤΑ ΑΛΓΕΒΡΑΣ / Advanced Topics in Algebra |
| Code | 0137 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Common | Yes |
| Status | Active |
| Course ID | 600012737 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Winter | - | 5.5 |
| Academic Year | 2017 – 2018 |
| Class Period | Winter |
| Faculty Instructors |
|
| Class ID | 600099098
|
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600099098
- At the Website of the School:
Language of Instruction
- Greek (Instruction, Examination)
Learning Outcomes
Understanding the basic notions of the course.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Work autonomously
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Infinite dimensional vector spaces, Dual spaces, Quotient spaces, The Isomorphism Theorems, Invariant spaces, The minimum polynomial (diagonalization), Generalized eigenvectors, Jordan canonical form, (left)R-modules, submodules, spanning sets, quotient modules, isomorphism theorems.
Keywords
Dual space, Minimum polynomial, Jordan canonical form, Modules
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Tutorial | 13 | 0.4 | |||
| Exams | 3 | 0.1 | |||
| Total | 55 | 1.8 |
Student Assessment
Description
Examinations.
Student Assessment methods
- Written Exam with Extended Answer Questions (Summative)
- Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
Άλγεβρα, Δ. Μ. Πουλάκης, ISBN 978-960-456-388-3, Εκδόσεις ΖΗΤΗ, Θεσσαλονίκη, 2015
S. Roman, Advanced Linear Algebra, 3rd Edition, Springer, 2008.
Additional bibliography for study
S.H. Friedberg, A.J. Insel and L.E. Spence, Linear Algebra, Prentice-Hall International (UK) Ltd, 1989.
T.S. Blyth and E.F. Robertson, Further Linear Algebra, Springer-Verlag London, 2002.
D.J.S. Robinson, A course in Linear Algebra with applications, World Scientific Publishing Co. Ltd, 1991.
Last Update
14-05-2017
