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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4051 GRAPH THEORY ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR SELÇUK DEMIR

Offered to

Mathematics (Evening) Mathematics

Course Objective

This course introduces students to the study of graph theory as a tool representing connections between data in a variety of other fields to show how graph theory and its algorithms can be used to solve problems in mathematics and elsewhere.

Learning Outcomes of the Course Unit

1   To be able to comprehendbasic notions of graph 2   To be able to use Euler, Hamilton and planar graphs 3   To be able to identify tree structures 4   To be able to implement graph theoretical algorithms 5   To be able to construct graphs in a variety of problems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 What is graph Examples of problems, models and definitions Disc. and Comb. Math. , R. GrimaldiSec. 11.1, Int. ToGraphTh. D.B. West, Ch1. 2 Graph theory terminology Disc. and Comb. Math. , R. GrimaldiSec. 11.2, Int. ToGraphTh. D. West, Ch1. 3 Representing graphs and graph isomorphism Disc. and Comb. Math. , R. GrimaldiSec. 11.3, Int. ToGraphTh. D.West, Ch1. 4 Connectivity Int. ToGraphTh. D.West, Ch1. 5 Euler and Hamilton graphs Disc. and Comb. Math. , R. GrimaldiSec. 11.5, Int. ToGraphTh. D.West, Sec1.4. Sec7.1 6 Planar Graphs Disc. and Comb. Math. , R. GrimaldiSec. 11.4, Int. ToGraphTh. D.West, Sec1.4. Sec6.1 7 Graph coloring Disc. and Comb. Math. , R. GrimaldiSec. 11.6, Int. ToGraphTh. D.West, Sec5.1, 5.2 8 Trees and counting problems Disc. and Comb. Math. , R. GrimaldiSec. 12.1-12.2, Int. ToGraphTh. D.West, Sec2.1 9 Mid-term Exam 10 Application of trees Disc. and Comb. Math. , R. GrimaldiSec. 12.1-12.2 11 Spanning trees Disc. and Comb. Math. , R. GrimaldiSec. 13.1, Int. ToGraphTh. D.West, Sec2.2 12 Minimal spanning trees Disc. and Comb. Math. , R. GrimaldiSec. 13.2, Int. ToGraphTh. D.West, Sec2.3 13 Shortest path algorithms Disc. and Comb. Math. , R. GrimaldiSec. 13.2, Int. ToGraphTh. D.West, Sec2.3 14 Matching Int. ToGraphTh. D.West, Sec3.1

Recomended or Required Reading

Textbook(s):1.Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. ISBN 9780201726343. 2. Supplementary Book(s):Discrete mathematics and its applications, K. Rosen 6th ed. ISBN 9780073229720. References:3.Douglas B. West, Introduction to Graph Theory, 2nd ed. 2001, Pentice Hall. Pub. ISBN 0-13-014400-2.

Planned Learning Activities and Teaching Methods

Face to face and presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE 1 MIDTERM EXAM 1 2 MTE 2 MIDTERM EXAM 2 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE1 * 0.30 + MTE2 * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE1 * 0.30 + MTE2 * 0.30 + RST * 0.40

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-mail: halil.oruc@deu.edu.tr Tel: (232) 3018577

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Tutorials 0 Lectures 13 4 52 Preparations before/after weekly lectures 12 3 36 Preparation for midterm exam 1 20 20 Preparation for final exam 1 25 25 Preparation for quiz etc. 5 5 25 Final 1 2,5 3 Midterm 1 2,5 3 Quiz etc. 5 0,6 3 TOTAL WORKLOAD (hours) 167

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 5 4 4 LO.2 5 4 3 4 3 4 4 LO.3 5 4 3 4 3 4 4 LO.4 5 4 4 3 4 3 4 4 LO.5 5 4 3 3 4 4 4