Theory of information and chaos
| Title | ΘΕΩΡΙΑ ΠΛΗΡΟΦΟΡΙΑΣ ΚΑΙ ΧΑΟYΣ / Theory of information and chaos |
| Code | 0570 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Coordinator | Ioannis Antoniou |
| Common | Yes |
| Status | Active |
| Course ID | 40002857 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 16
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses | Spring | - | 5 |
| Academic Year | 2017 – 2018 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600099250
|
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600099250
Prerequisites
Required Courses
- 0101 Linear Algebra I
- 0102 Introduction to Algebra
- 0103 Linear Algebra II
- 0131 Group Theory
- 0134 Galois Theory
- 0106 Algebraic Structures I
- 0107 Algebraic Structures II
- 0136 Number Theory
Learning Outcomes
Τhe students after the successful examinations of this course have a good knowledge of the methods of Non Commutative Algebra and its applications in other sciences. Moreover they come in contact with the research of this topic.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Adapt to new situations
- Make decisions
- Work autonomously
- Work in teams
- Work in an international context
- Generate new research ideas
- Appreciate diversity and multiculturality
- Respect natural environment
- Demonstrate social, professional and ethical commitment and sensitivity to gender issues
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Elements from the theory of modules. Exact sequents.Artinian and Noetherian modules. Modules over principal ideal domain. Tensor products. The funcrors Hom and Tor. Semisimple rings. Central simple algebras. Elements from the representation theory of finite dimensional Algebras.
Keywords
Arinian and Noetherian modules, Jordan forms, categories, tensor products, Hom-Tor, semisimple rings, representations.
Educational Material Types
- Notes
Student Assessment
Description
Written examiations, lectures. solution of exercises.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative)
- Written Assignment (Formative)
- Written Exam with Problem Solving (Formative)
- Report (Formative)
Bibliography
Additional bibliography for study
1. C.Curtis and I. Reiner, Methods of Representation Theory with Applications to finite groups and Orders, John Wiley and Sons, 1981
2. D.S. Dummit, R.M. Foote, Abstract Algebra, Wiley, 2004.
3. S. Lang, Algebra, Springer, 2002.
4. Σ. W. Hungerford, Algebra, Holt,Rinehart and Winston, Inc. 1974.
5. I. Assem, D. Simson and A. Skowronski, Elements of the Representation Theory of Associative Algebras, London Mathematical Society, Students Texts 65, 2006.
6. R. Pierce,Associative Algebras, Springer, 1982.
7. M. Hazewinkel, N. Gubareni, V.V. Kirichenko, Algebras, Rings and Modules, I, Springer, 2004.
Last Update
23-09-2013
