Fractal Sets and Applications (EM7): Διαφορά μεταξύ των αναθεωρήσεων
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[[ | * [[Μορφοκλασματικά Σύνολα και Εφαρμογές (Fractals) (ΕΜ7)|Ελληνική Έκδοση]] | ||
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=== General === | === General === | ||
| Γραμμή 15: | Γραμμή 17: | ||
|- | |- | ||
! Course Code | ! Course Code | ||
| | | EM7 | ||
|- | |- | ||
! Semester | ! Semester | ||
| | | 2 | ||
|- | |- | ||
! Course Title | ! Course Title | ||
| | | Fractal Sets and Applications | ||
|- | |- | ||
! Independent Teaching Activities | ! Independent Teaching Activities | ||
| Γραμμή 27: | Γραμμή 29: | ||
|- | |- | ||
! Course Type | ! Course Type | ||
| | | Special Background | ||
|- | |- | ||
! Prerequisite Courses | ! Prerequisite Courses | ||
| Γραμμή 34: | Γραμμή 36: | ||
! Language of Instruction and Examinations | ! Language of Instruction and Examinations | ||
| | | | ||
Greek | |||
|- | |- | ||
! Is the Course Offered to Erasmus Students | ! Is the Course Offered to Erasmus Students | ||
| Yes | | Yes (in English) | ||
|- | |- | ||
! Course Website (URL) | ! Course Website (URL) | ||
| Γραμμή 49: | Γραμμή 51: | ||
! Learning outcomes | ! Learning outcomes | ||
| | | | ||
The course is an introduction to Fractals and structures that have self-similarity under scale change. The objectives of the course are: | |||
* Acquiring the theoretical background from the postgraduate student on topics related to Fractals. | |||
* Obtaining the background from the student in analytical and computational methods to solve problems related to the Fractals. | |||
* Understanding basic concepts of Fractals and extending to applications and nature. | |||
Upon completion of the course the postgraduate student will be able to use analytical and computational techniques to study problems related to Fractals and to further deepen their understanding. | |||
|- | |- | ||
! General Competences | ! General Competences | ||
| | | | ||
The course aims to enable the postgraduate student to: | |||
* Develop the ability to analyse and synthesise basic knowledge of Fractals. | |||
* Adapt to new situations | |||
* Decision-making | |||
* Working independently | |||
* Team work | |||
All the above will give the students the opportunity to work in an international multidisciplinary environment. | |||
|} | |} | ||
=== Syllabus === | === Syllabus === | ||
Self-similarity under scale change, Fractal sets, Hausdorff dimension, Mandelbrot and Julia sets, Affine transformations in Euclidean space, Transformations in metric spaces, Theorem of contraction of images, Fractal construction, Collage theorem, Applications of Fractal sets. The course includes training in computational methods in the computer laboratory (Applied and Computational Mathematics Lab). | |||
=== Teaching and Learning Methods - Evaluation === | === Teaching and Learning Methods - Evaluation === | ||
| Γραμμή 66: | Γραμμή 78: | ||
! Delivery | ! Delivery | ||
| | | | ||
In class | |||
|- | |- | ||
! Use of Information and Communications Technology | ! Use of Information and Communications Technology | ||
| | | | ||
Use of computer (Mechanics) lab | |||
|- | |- | ||
! Teaching Methods | ! Teaching Methods | ||
| Γραμμή 81: | Γραμμή 93: | ||
| 39 | | 39 | ||
|- | |- | ||
| | | Self study | ||
| | | 78 | ||
|- | |- | ||
| | | Homework - Projects | ||
| | | 70.5 | ||
|- | |- | ||
| Course total | | Course total | ||
| Γραμμή 93: | Γραμμή 105: | ||
! Student Performance Evaluation | ! Student Performance Evaluation | ||
| | | | ||
* Weekly assignments | |||
* Final project | |||
* Written examination at the end of the semester | |||
|} | |} | ||
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Τελευταία αναθεώρηση της 05:15, 16 Ιουνίου 2023
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General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | EM7 |
| Semester | 2 |
| Course Title | Fractal Sets and Applications |
| 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) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The course is an introduction to Fractals and structures that have self-similarity under scale change. The objectives of the course are:
Upon completion of the course the postgraduate student will be able to use analytical and computational techniques to study problems related to Fractals and to further deepen their understanding. |
|---|---|
| General Competences |
The course aims to enable the postgraduate student to:
All the above will give the students the opportunity to work in an international multidisciplinary environment. |
Syllabus
Self-similarity under scale change, Fractal sets, Hausdorff dimension, Mandelbrot and Julia sets, Affine transformations in Euclidean space, Transformations in metric spaces, Theorem of contraction of images, Fractal construction, Collage theorem, Applications of Fractal sets. The course includes training in computational methods in the computer laboratory (Applied and Computational Mathematics Lab).
Teaching and Learning Methods - Evaluation
| Delivery |
In class | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology |
Use of computer (Mechanics) lab | ||||||||||
| Teaching Methods |
| ||||||||||
| Student Performance Evaluation |
|
Attached Bibliography
- Ο Θαυμαστός Κόσμος των Fractal, 2004, Α. Μπούντης, Εκδότης: Liberal Books Μονοπρόσωπη ΕΠΕ.
- Fractals Everywhere, 2nd edition, 2000, M. F. Barnsley, Publisher: Morgan Kaufmann.