Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
FRACTAL GEOMETRY MAT 354 6 2 + 0 2 4
Ön Koşul Dersleri Students are assumed to be familiar with the course Transformations and Geometries.
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. SOLEY ERSOY Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı To introduce and to appreciate the structure of living and not living beings in nature Dersin İçeriği Fractals and its history, Known fractals examples, such as Sierpinski, Koch snowflake, Antisnowflake, Polygon and circle fractals, Spacefilling curves, Jurassicpark fractals, Transformations on plane I, measures, reflections, Transformations on plane II, translations, ratios, Self-similarity of fractals, Dimension of some known fractals, Ratio dimension, Koch curve and its fractal dimension, Minkowski fractal and its dimension, Hausdorff dimension, Length of a fractal curve, Box dimension, Similarity dimension.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She defines the basic concepts related to fractal geometry, 1 - 2 - 3 - A - C - 2 - He/She constructs fractals, 3 - 5 - 6 - A - C - 3 - He/She illustrates fractals, 2 - 4 - 12 - A - C - 4 - He/She indicates examples of fractals are subsets of 2-dimensional Euclidean space, 3 - 6 - 12 - A - C - 5 - He/She recognizes the characteristic properties and unchangeable structure of any object, 3 - 12 - A - C - 6 - He/She adapts structure of the objects in nature to fractal geometry, 3 - 4 - 6 - A - C - 7 - He/She evaluates the objects in nature according to mathematics, 3 - 8 - 12 - A - C - D -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 12:Case Study 6:Motivations to Show 5:Demonstration 8:Group Study Ölçme Yöntemleri: A:Testing C:Homework D:Project / Design

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Fractals and its history [1] Page 1-3
2 Known fractals examples, such as Sierpinski, Koch snowflake, Antisnowflake [1] Page 3-13
3 Polygon and circle fractals, Spacefilling curves, Jurassicpark fractals [1] Page 14-19
4 Transformations on plane I, measures, reflections, Transformations on plane II, translations, ratios [1] Page 20-27
5 Self-similarity of fractals, Dimension of some known fractals, Ratio dimension, Koch curve and its fractal dimension, [1] Page 27-34
6 Minkowski fractal and its dimension, Hausdorff dimension, [1] Page 34-36
7 Length of a fractal curve, Box dimension [1] Page 36-54
8 Similarity dimension Moran equation and other dimensions [1] Page 55-63
9 Some applications and Midterm
10 Applications of fractals in nature I, human being [1] Page 65-66
11 Applications of fractals in nature II, plants [1] Page 67-68
12 Applications of fractals in nature III, galaxies, rings of Saturn [1] Page 68-71
13 Applications of fractals in nature IV, population growth [1] Page 74-94
14 Applications of fractals in nature V, clouds [1] Page 94-95

#### Kaynaklar

Ders Notu [1] Hacısalihoğlu, H. Hilmi N. YAZ, Fraktal Geometri, Ankara Universitesi, 2004.
Ders Kaynakları [2] Edgar, G. Ölçüm, Topoloji ve Fraktal geometri, Çeviri, Ankara, 2006.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language. X
5 He/ she has the knowledge of computer software information as a mathematician needs. X
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them. X
8 He/ she uses the ability of abstract thinking. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
KisaSinav 2 10
Odev 1 10
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 2 32
Hours for off-the-classroom study (Pre-study, practice) 16 2 32
Mid-terms 1 10 10
Quiz 2 7 14
Assignment 1 8 8
Final examination 1 15 15
Toplam İş Yükü 111
Toplam İş Yükü /25(s) 4.44
Dersin AKTS Kredisi 4.44
; ;