The course is aimed at equipping students with logical and mathematical thinking. The course is designed to accomplish five major themes:
(i) Mathematical reasoning,
(ii) combinatorial analysis,
(iii) discrete structures,
(iv) algorithmic thinking,
(v) applications and modeling.
Course Content
This course contains; Fundamentals,Fundamentals of Logic ,Logic, Conditional Statements,Logic of Quantified Statements,Introduction to Number Theory, Direct Proof and Counterexample,Sequences, Mathematical Induction,Strong Induction, Recursion and Structural Induction,Introduction to Set theory,Functions,Cardinality applications to computability,Relation,Equivalence Relation and Modular Arithmetic,Basic Cryptography ,Basic Problems on Graphs and Tree representation,Applications of Graph theory.
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
Determine an argument using logical notation and whether the argument is or not valid
10, 12, 16, 9
A, E
Execute proof writing and evaluation.
10, 12, 16, 9
A, E
Comprehend set fundamentals, operations, and validation of elementary set equalities.
10, 12, 16, 9
A, E
Comprehend the properties of functions, relationships between them, and introductory knowledge of graph theory and cryptology.
Introduction to Number Theory, Direct Proof and Counterexample
Chapter 4
6
Sequences, Mathematical Induction
Chapter 5.1, 5.2
7
Strong Induction, Recursion and Structural Induction
Chapter 5
8
Introduction to Set theory
Chapter 6.1
8
Functions
Chapter 7.1-7.3
9
Cardinality applications to computability
Chapter 7.4
10
Relation
Chapter 8.1, 8.2
11
Equivalence Relation and Modular Arithmetic
Chapter 8.3, 8.4
12
Basic Cryptography
Chapter 8.4
13
Basic Problems on Graphs and Tree representation
Chapter 10.1-10.5
14
Applications of Graph theory
Chapter 10.5, 10.7
Resources
Discrete Mathematics and Its Applications, Kenneth H. Rosen, 7th edition,
McGraw-Hill, 2012
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
An ability to apply knowledge of mathematics, science, and engineering
X
2
An ability to identify, formulate, and solve engineering problems
X
3
An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
4
An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
X
5
An ability to design and conduct experiments, as well as to analyze and interpret data
6
An ability to function on multidisciplinary teams
7
An ability to communicate effectively
8
A recognition of the need for, and an ability to engage in life-long learning
X
9
An understanding of professional and ethical responsibility
10
A knowledge of contemporary issues
11
The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
X
Assessment Methods
Contribution Level
Absolute Evaluation
Rate of Midterm Exam to Success
30
Rate of Final Exam to Success
70
Total
100
ECTS / Workload Table
Activities
Number of
Duration(Hour)
Total Workload(Hour)
Course Hours
14
3
42
Guided Problem Solving
0
0
0
Resolution of Homework Problems and Submission as a Report
0
0
0
Term Project
14
3
42
Presentation of Project / Seminar
0
0
0
Quiz
3
5
15
Midterm Exam
1
20
20
General Exam
1
30
30
Performance Task, Maintenance Plan
0
0
0
Total Workload(Hour)
149
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(149/30)
5
ECTS of the course: 30 hours of work is counted as 1 ECTS credit.
Detail Informations of the Course
Course Description
Course
Code
Semester
T+P (Hour)
Credit
ECTS
DISCRETE MATHEMATICS
-
Spring Semester
3+0
3
5
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of Course
English
Course Level
First Cycle (Bachelor's Degree)
Course Type
Elective
Course Coordinator
Assist.Prof. Cihan Bilge KAYASANDIK
Name of Lecturer(s)
Assist.Prof. Cihan Bilge KAYASANDIK
Assistant(s)
Slides, Lecture Notes and Textbook
Aim
The course is aimed at equipping students with logical and mathematical thinking. The course is designed to accomplish five major themes:
(i) Mathematical reasoning,
(ii) combinatorial analysis,
(iii) discrete structures,
(iv) algorithmic thinking,
(v) applications and modeling.
Course Content
This course contains; Fundamentals,Fundamentals of Logic ,Logic, Conditional Statements,Logic of Quantified Statements,Introduction to Number Theory, Direct Proof and Counterexample,Sequences, Mathematical Induction,Strong Induction, Recursion and Structural Induction,Introduction to Set theory,Functions,Cardinality applications to computability,Relation,Equivalence Relation and Modular Arithmetic,Basic Cryptography ,Basic Problems on Graphs and Tree representation,Applications of Graph theory.
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
Determine an argument using logical notation and whether the argument is or not valid
10, 12, 16, 9
A, E
Execute proof writing and evaluation.
10, 12, 16, 9
A, E
Comprehend set fundamentals, operations, and validation of elementary set equalities.
10, 12, 16, 9
A, E
Comprehend the properties of functions, relationships between them, and introductory knowledge of graph theory and cryptology.
Introduction to Number Theory, Direct Proof and Counterexample
Chapter 4
6
Sequences, Mathematical Induction
Chapter 5.1, 5.2
7
Strong Induction, Recursion and Structural Induction
Chapter 5
8
Introduction to Set theory
Chapter 6.1
8
Functions
Chapter 7.1-7.3
9
Cardinality applications to computability
Chapter 7.4
10
Relation
Chapter 8.1, 8.2
11
Equivalence Relation and Modular Arithmetic
Chapter 8.3, 8.4
12
Basic Cryptography
Chapter 8.4
13
Basic Problems on Graphs and Tree representation
Chapter 10.1-10.5
14
Applications of Graph theory
Chapter 10.5, 10.7
Resources
Discrete Mathematics and Its Applications, Kenneth H. Rosen, 7th edition,
McGraw-Hill, 2012
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
An ability to apply knowledge of mathematics, science, and engineering
X
2
An ability to identify, formulate, and solve engineering problems
X
3
An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
4
An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
X
5
An ability to design and conduct experiments, as well as to analyze and interpret data
6
An ability to function on multidisciplinary teams
7
An ability to communicate effectively
8
A recognition of the need for, and an ability to engage in life-long learning
X
9
An understanding of professional and ethical responsibility
10
A knowledge of contemporary issues
11
The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
