Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
2MATH132INTRODUCTION TO DISCRETE MATHEMATICS3+246

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course The aim of this course is to teach methods involving abstrack concepts; to teach finiteness and infiniteness notions; to teach countable and uncountable sets; to introduce cardinal numbers; to teach fundamentals of topological spaces and metric spaces.
Course Content Division Algorithm, The Fundamental Theorem of Arithmetic, The Euclidean Algorithm, Counting Problems, The Binomial Theorem, Linear Recurrence Relations, Inclusion and Exlusion, Graph Terminology, The Degree of a Graph Vertex, The Handshaking Lemma, Graphs with Matrices, Eulerian and Hamiltonian paths in a graph.


Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. Engin Büyükaşık enginbuyukasik@iyte.edu.tr
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Aldous & Wilson, Graphs and Applications : An Introductory Approach
Kenneth Rosen, Discrete Mathematics and Its Applications

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 40
Quizzes 0 % 0
Homeworks 5 % 20
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
8
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 3 14 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 7 8 56
Application (Homework, Reading, Self Study etc.) 2 14 28
Exams and Exam Preparations 11 1 11
Total Work Load   Number of ECTS Credits 6 137

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Understand the basic notions of number theory
2 Understand the counting techniques
3 Learn about advanced counting techniques
4 Learn about applications of counting techniques
5 Understand the basic notions of graph theory


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Integers and Division Rosen 3.4
2 Integers and Algorithms, Applications of Number Theory Rosen 3.6, 3.7
3 Counting; The Basics of Counting, The Pigeonhole Principle Rosen 5.1, 5.2
4 Permutations and Combinations, Binomial Coefficients Rosen 5.3, 5.4
5 Generalized Permutations and Combinations Rosen 5.7
6 Recurrence Relations Rosen 7.1
7 Solving Linear Recurrence Relations Rosen 7.2
8 Divide and Conquer Relations Rosen 7.3
9 Inclusion and Exclusion, Applications of Inclusion and Exclusion Rosen 7.5, 7.6
10 Graph Terminology, Types of Graphs Rosen 9.2
11 Degree of a Vertex, Adjacency and Indicence Matrices, Handshaking Lemma Rosen 9.1, 9.2
12 Graph Isomorphism Rosen 9.3
13 Connectivity of Graphs (paths, cycles) Rosen 9.4
14 Eulerian and Hamiltonian Graphs Rosen 9.5


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4 4 4 4
C2 4 4 4 4 4 4
C3 4 4 4 4 4 4
C4 4 4 4 4 4 4
C5 4 4 4 4 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=254408&lang=en