DISCRETE MATHEMATICS

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.

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.

1. 1

   Determine an argument using logical notation and whether the argument is or not valid

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

2. 2

   Execute proof writing and evaluation.

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

3. 3

   Comprehend set fundamentals, operations, and validation of elementary set equalities.

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

4. 4

   Comprehend the properties of functions, relationships between them, and introductory knowledge of graph theory and cryptology.

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

WEEKLY PLAN

1. WEEK 1

   Fundamentals

   Preparation: Chapter

2. WEEK 2

   Fundamentals of Logic

   Preparation: Chapter 2.1

3. WEEK 3

   Logic, Conditional Statements

   Preparation: Chapter 2.2, 2.3

4. WEEK 4

   Logic of Quantified Statements

   Preparation: Chapter 3

5. WEEK 5

   Introduction to Number Theory, Direct Proof and Counterexample

   Preparation: Chapter 4

6. WEEK 6

   Sequences, Mathematical Induction

   Preparation: Chapter 5.1, 5.2

7. WEEK 7

   Strong Induction, Recursion and Structural Induction

   Preparation: Chapter 5

8. WEEK 8

   Introduction to Set theory

   Preparation: Chapter 6.1

9. WEEK 8

   Functions

   Preparation: Chapter 7.1-7.3

10. WEEK 9

    Cardinality applications to computability

    Preparation: Chapter 7.4

11. WEEK 10

    Relation

    Preparation: Chapter 8.1, 8.2

12. WEEK 11

    Equivalence Relation and Modular Arithmetic

    Preparation: Chapter 8.3, 8.4

13. WEEK 12

    Basic Cryptography

    Preparation: Chapter 8.4

14. WEEK 13

    Basic Problems on Graphs and Tree representation

    Preparation: Chapter 10.1-10.5

15. WEEK 14

    Applications of Graph theory

    Preparation: Chapter 10.5, 10.7

ASSESSMENT

• Rate of Midterm Exam to Success30%
• Rate of Final Exam to Success70%

WORKLOAD

READING

• Discrete Mathematics and Its Applications, Kenneth H. Rosen, 7th edition, McGraw-Hill, 2012

TEACHING STAFF

• Assist.Prof. Cihan Bilge GÜRBÜZCOORDINATOR
• Assist.Prof. Cihan Bilge GÜRBÜZ