1	Course Title:	ABSTRACT MATHEMATICS II
2	Course Code:	MAT0506
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	2
6	Semester:	4
7	ECTS Credits Allocated:	4
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. BASRİ ÇELİK
16	Course Lecturers:	Prof.Dr. Atilla AKPINAR
17	Contactinformation of the Course Coordinator:	basri@uludag.edu.tr 0224.2941762
18	Website:
19	Objective of the Course:	Provide an understanding about the importance of equivalence relations, equipollent sets and cardinal numbers in mathematics.
20	Contribution of the Course to Professional Development	To be able to practice the professional applications of mathematical and geometric concepts.

21

Learning Outcomes:

1 Recognize types of relation.; 2 Learns the equivalence relation, and prove the theorems on this subject.; 3 Learns the relationship between equivalence relations and functions.; 4 Recognizes the equipotent sets.; 5 Can solve the problems about equivalence relations and equipotent sets.; 6 Can make the operations about the cardinal numbers.; 7 Learns the ways to found Natural Numbers set using finite sets. Also learns countable and countable sets.; 8 Learns induction and the theorems which could be proved by inductive theorem.; 9 Learns combinatorial analysis, order relations, isomorphism of ordered sets, and can solve the problems with related to order relations and combinatorial analysis. ;

22	Course Content:

Week	Theoretical	Practical
1	Description of course. Finding a set of definitions.
2	Relation types, equivalence relations.
3	Equivalence relations and functions.
4	Equipotent sets.
5	Equivalence relations and equipotent sets problems.
6	Cardinal numbers.
7	Operations with cardinal numbers.
8	Finite and infinite sets. Natural numbers.
9	Midterm and feedback
10	Examples of theorems could be proved by induction and induction.
11	Combinatorial analysis.
12	Order relations.
13	Isomorphism of ordered sets.
14	Combinatorial analysis and the problems of order relations.

23	Textbooks, References and/or Other Materials:	1)Soyut Matematik I, Basri Çelik, Dora Yayınevi, 2010, Bursa. 2)Abstract Algebra, Roger Godement, Hermann Publishers, 1968, Paris. 3)Soyut Matematik, Sait Akkaş, H. Hilmi Hacısalihoğlu, Zühtü Özel, Arif Sabuncuoğlu, gazi üniversitesi Yayın No:43, 1984, Ankara.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course	Homeworks and online exams
Information

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ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	2	28
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	14	14
Others	14	1	14
Final Exams	1	22	22
Total WorkLoad			134
Total workload/ 30 hr			4
ECTS Credit of the Course			4

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 PQ11 PQ12 LO1 0 0 5 0 0 0 0 0 5 0 0 0 LO2 0 0 5 0 0 0 0 0 5 0 0 0 LO3 0 0 5 0 0 0 0 0 5 0 0 0 LO4 0 0 5 0 0 0 0 0 5 0 0 0 LO5 0 0 5 0 0 0 0 0 5 0 0 0 LO6 0 0 5 0 0 0 0 0 5 0 0 0 LO7 0 0 5 0 0 0 0 0 5 0 0 0 LO8 0 0 5 0 0 0 0 0 5 0 0 0 LO9 0 0 5 0 0 0 0 0 5 0 0 0

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High