Syllabus ( MATH 115 )

Basic information


Course title: 
Discrete Mathematics 
Course code: 
MATH 115 
Lecturer: 
Assoc. Prof. Dr. Selçuk TOPAL

ECTS credits: 
6 
GTU credits: 
3 (3+0+0) 
Year, Semester: 
1, Fall 
Level of course: 
First Cycle (Undergraduate) 
Type of course: 
Compulsory

Language of instruction: 
English

Mode of delivery: 
Face to face

Pre and corequisites: 
None 
Professional practice: 
No 
Purpose of the course: 
The aim of the course is to introduce students to the fundamentals of discrete structures. Discrete Mathematics is fundamental for mathematical thinking, information technologies and computer sciences. Topics of this course include Logic, Methods of Proof, Sets, Functions, Relations, Counting and Graph theory. 



Learning outcomes


Upon successful completion of this course, students will be able to:

Formulate proofs in basic level and apply elementary logic
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Adapt to a fastchanging technological environment, improving their knowledge and abilities constantly.
Method of assessment

Written exam

Discuss and use set theoretic techniques
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Using technology as an efficient tool to understand mathematics and apply it.

Exhibiting professional and ethical responsibility.
Method of assessment

Written exam

Homework assignment

Solve problems in combinatorics (permutations, combinations, counting)
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Using technology as an efficient tool to understand mathematics and apply it.
Method of assessment

Written exam

Perform various operations with relations and functions
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Using technology as an efficient tool to understand mathematics and apply it.

Exhibiting professional and ethical responsibility.
Method of assessment

Written exam

Explain and use the concepts of graphs and trees
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Using technology as an efficient tool to understand mathematics and apply it.
Method of assessment

Written exam

Homework assignment


Contents


Week 1: 
Logic; Propositional Equivalences 
Week 2: 
Predicates and Quantifiers 
Week 3: 
Methods of Proof 
Week 4: 
Sets; Set Operations; Functions 
Week 5: 
The Integers and Division 
Week 6: 
Mathematical Induction 
Week 7: 
The Basics of Counting; The Pigeonhole Principle 
Week 8: 
Permutations and Combinations; InclusionExclusion, Midterm 
Week 9: 
Relations and Their Properties

Week 10: 
Representing Relations; Recurrence Relations 
Week 11: 
Equivalence Relations 
Week 12: 
Axiomatic Structure of Real Numbers 
Week 13: 
Introduction to Groups, Rings, and Fields

Week 14: 
Introduction to Graphs; Graph Terminology, Graph Isomorphism, Introduction to Trees 
Week 15*: 
 
Week 16*: 
Final Exam 
Textbooks and materials: 

Recommended readings: 
1. Kenneth H. Rosen, Discrete Mathematics and Its Applications, Fifth Edition, McGrawHill. 2. George Polya, How to Solve It, Princeton University Press. 3. R.P. Grimaldi, Discrete and Combinatorial Mathematics, AddisonWesley. 4. E.G. Goodaire and M.M. Parmenter, Discrete Mathematics, Prentice Hall 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
8 
30 
Other interm studies: 

0 
Project: 

0 
Homework: 

0 
Quiz: 
3,5,7,9,11,13 
20 
Final exam: 
16 
50 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
4 
14 

Practice, Recitation: 
0 
0 

Homework: 
1 
6 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
1 
6 

Own study for midterm exam: 
15 
1 

Midterm: 
2 
1 

Personal studies for final exam: 
20 
1 

Final exam: 
2 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



>