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Course Code: 
MATH 154
Semester: 
Spring
Course Type: 
Core
P: 
2
Lab: 
2
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
7
Course Language: 
English
Course Objectives: 
The aim of this course is to introduce the topics and techniques of discrete methods and combinatorial reasoning with wide variety of applications.
Course Content: 

Fundamental principle of counting. Introduction to discrete probability. Pigeonhole principle. Fundamentals of logic. The principle of inclusion and exclusion. Recurrence relations. Introduction to graph theory.

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Teaching Methods

Assessment Methods

1) Understands and solves problems in counting using the basic principles of counting.

1,2

A

2) Uses the principle of inclusion and exclusion to solve related problems indirectly.

1,2

A

3) Expresses  a given argument in symbolic logic and decides whether it is a valid argument or not using the laws of logic and inference rules.

1,2

A

4) Solves first-order linear recurrence relations, second-order linear homogeneous recurrence relations with constant coefficients and some particular nonhomogeneous recurrence relations.

1,2

A

5) Models a given particular situation or a problem  using  graph theory.

1,2

A

6) Decides whether or not given graphs are isomorphic.

1,2

A

Course Flow

Week

Topics

Study Materials

1

The rules of sum and product. Permutations

1.1, 1.2

2

Combinations: The binomial theorem

1.3

3

Combinations with repetition

1.4

4

An introduction to discrete probability. The pigeonhole principle

((II) 6.1), 5.5

5

Basic connectives and truth tables

2.1

6

Logical equivalence: The laws of logic

2.2

7

Logical implication: The rules of inference

2.3

8

The use of quantifiers

2.4

9

The principle of inclusion and exclusion

8.1

10

The first-order linear recurrence relation

10.1

11

The Second-order linear homogeneous recurrence relation with constant coefficients

10.2

12

The nonhomogeneous recurrence relation

10.3

13

An introduction to graph theory: Definitions and basic examples

11.1

14

Subgraphs, complements and graph isomorphism

11.2

Recommended Sources

Textbook

  1. Discrete and Combinatorial Mathematics, R.P. Grimaldi, Addison-Wesley, 5th edition, 2004.

Additional Resources

  1. Discrete Mathematics and Its Applications, K. H. Rosen, Mc Graw Hill, 6th edition, 2007.

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

1

100

Quizzes

   

Assignments

   

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

60

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

40

Total

 

100

 

COURSE CATEGORY

Core Courses

Course’s Contribution to Program

No

Program Learning Outcomes

Contribution

1

2

3

4

5

1

The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)

       

x

2

Acquiring fundamental knowledge on fundamental research fields in mathematics

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 responsibilty

     

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

Activities

Quantity

Duration
(Hour)

Total
Workload
(Hour)

Course Duration (14x Total course hours)

14

4

56

Hours for off-the-classroom study (Pre-study, practice)

14

6

84

Mid-terms (Including self study)

1

15

15

Quizzes

     

Assignments

     

Final examination (Including self study)

1

20

20

Total Work Load

 

 

175

Total Work Load / 25 (h)

 

 

7

ECTS Credit of the Course

 

 

7