Fractal Sets and Applications (EM7)

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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: 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

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

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	Activity Semester Workload Lectures 39 Self study 78 Homework - Projects 70.5 Course total 187.5
Student Performance Evaluation	Weekly assignments Final project Written examination at the end of the semester

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.