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Course Code: 
MATH 440
Course Type: 
Area Elective
P: 
2
Lab: 
3
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
7
Prerequisite Courses: 
Course Language: 
English
Courses given by: 
Course Objectives: 
Çizgeler, bilimdeki, işletmedeki ve endüstrideki pek çok problemde model olarak kullanılır. Bu dersin amacı, öğrencilere grafikler, yönlendirilmiş grafikler ve ağaçlar gibi çizgelerin temel bilgileriyle birlikte, çizgelerin gerçek hayat uygulamalarını ve çok bilinen bazı algoritmalarını tanıtmaktır.
Course Content: 

Fundamental concepts of graphs and digraphs. Trees and distance. Matching and factorization.  Connectivity, networks.  Graph coloring. Planar.

Course Methodology: 
1: Lectures, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes Teaching Methods Assessment Methods
1) Manipulate the basic concepts associated with graphs such as paths, cycles, vertex degrees, and counting. Directed graphs.

Use these definitions in proofs, and calculate specific values.

1,2 A
2)  The concept of tree, spanning trees, optimization. 1,2 A
3) Cuts and connectivity.  Network Flow problems and algorithms 1,2 A
4) Matching and Covers. Algorithms and Applications 1,2 A
5) Vertex Colorings 1,2 A
6). Characterization of Planar Graphs. Parameters of Planarity. 1,2 A

Course Flow

COURSE CONTENT
Week Topics Study Materials
1 What Is a Graph? Paths, Cycles, and Trails. Vertex Degrees  
2 Counting. Directed Graphs  
3 Basic Properties of Trees. Spanning Trees and Enumeration  
4 Optimization and Trees  
5 Matching and Covers. Algorithms and Applications.  
6 Matching in General Graphs.  
7 Cuts and Connectivity. K-connected Graphs.  
8 Network Flow Problems  
9 Vertex Colorings and Upper Bounds  
10 Structure of k-chromatic Graphs. Enumerative Aspects.  
11 Embeddings and Euler's Formula. Characterization of Planar Graphs.  
12 Parameters of Planarity.  
13 Line Graphs and Edge-Coloring. Hamiltonian Cycles.  
14 Planarity, Coloring, and Cycles.  

 

Recommended Sources

RECOMMENDED SOURCES
Textbook 1. Douglas B. West - Introduction to Graph Theory (Pearson)

2. Wilson RJ - Introduction to Graph Theory (Longmans)

Additional Resources  

Assessment

ASSESSMENT
IN-TERM STUDIES NUMBER PERCENTAGE
Mid-terms 1 100
Quizzes - 0
Assignments - 0
Total   100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE 1 60
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE   40
Total   100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM
No Program Learning Outcomes Contribution
1 2 3 4 5  
1 Relate mathematics to other disciplines and develop mathematical models for multidisciplinary         X  
2 Acquiring fundamental knowledge on fundamental research fields in mathematics and its application to science, industry, and business.         X  
3 Ability form and interpret the relations between research topics in mathematics         X  
4 Ability to define, formulate and solve mathematical problems         X  
5 Consciousness of professional ethics and responsibility     X      
6 Ability to communicate actively     X      
7 Ability of self-development in fields of interest         X  
8 Ability to learn, choose and use necessary information technologies     X      
9 Lifelong education     X      

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities Quantity Duration
(Hour)
Total
Workload
(Hour)
Course Duration (14x Total course hours) 14 3 42
Hours for off-the-classroom study (Pre-study, practice) 14 3 42
Mid-terms (Including self-study) 2 10 20
Quizzes -    
Assignments -    
Final examination (Including self-study) 1 15 15
Total Work Load     119
Total Work Load / 25 (h)     4,76
ECTS Credit of the Course     5