Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
INTRODUCTION TO GRAPH THEORY MAT 468 8 2 + 0 2 5
Ön Koşul Dersleri Introduction to Fixed Point Theory, Analysis I-II, Topology I-II
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MAHPEYKER ÖZTÜRK Dersi Verenler Dersin Yardımcıları Assist.Prof.Dr. Mahpeyker ÖZTÜRK Dersin Kategorisi Dersin Amacı To comprehend graph and its properties, to learn the applications of Graph theory to fixed point theory Dersin İçeriği Graph and its types, Eulerian trail (or Eulerian path) and Hamilton cycles, Trees and the applications of Graph theory to fixed point theory
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He\she comprehends the graph and its types. 1 - 2 - 4 - 14 - 15 - A - C - 2 - He\she understands the concept of connectivity on a graph. 1 - 2 - 4 - 14 - 15 - A - C - 3 - He\she analysis the Eulerian trail (or Eulerian path) and Hamilton cycles. 1 - 2 - 4 - 14 - 15 - A - C - 4 - He\she explains the graph isomorphism. 1 - 2 - 4 - 14 - 15 - A - C - 5 - He\she comments trees and their elemantary properties. 1 - 2 - 4 - 14 - 15 - A - C - 6 - He\she undertands and comments the applications of graph theory to fixed point theory. 1 - 2 - 4 - 14 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Grpahs and types of graphs
2 Distance in a graph
3 Connectedness
4 Eulerian trail (or Eulerian path)
5 Hamilton cycles
6 Isomorphism of a graph
7 Trees and their elementary properties
8 Operations in graphs
9 Mid-term exams
10 Banach fixed point theorem in metric spaces
11 Contraction mappings
12 Applications of graph theory to contraction mappings
13 Weakly contracrion mappings
14 Applications of graph theory to weak contraction mappings

#### Kaynaklar

Ders Notu R. Johnsonbaugh, Discrete Mathematics,Prentice-Hall, Inc., New Jersey,
1997.
Ders Kaynakları 1. V. Berinde, Iterative Approximation of Fixed Points, Springer, 2007
2. Topics in Metric Fixed Point Theory, 1990
3. Handbook of Metric Fixed Point Theory,2001
4. An Introduction to Metric Spaces and Fixed Point Theory, 2001

#### 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.
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 50
KisaSinav 1 15
Odev 1 20
KisaSinav 2 15
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 10 20
Assignment 1 5 5
Final examination 1 10 10
Toplam İş Yükü 109
Toplam İş Yükü /25(s) 4.36
Dersin AKTS Kredisi 4.36
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