Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
MB0033		Metic and Topological Spaces	2/2/0	DE	Turkish	5

Course Goals	Creating the topological and metric space structure required for modern analysis.
Prerequisite(s)	None
Corequisite(s)	None
Special Requisite(s)	None
Instructor(s)	Assist. Prof. Dr. Uğur Gönüllü
Course Assistant(s)
Schedule	Thursday: 09:00-11:00, B1-8 Friday: 11:00-12:30, B1-8
Office Hour(s)	Wednesday: 11:00-12:30, 3-A-15
Teaching Methods and Techniques	Lecture and Recitation
Principle Sources	T. Terzioğlu, An Introduction to Real Analysis, Matematik Vakfı, 2000.
Other Sources	S.A. Kılıç, M. Erdem, Metrik ve Topolojik Uzaylar, VİPAŞ, 1999. Micheal O Searcoid, Metric Spaces, Springer SUMS, 2007.

Course Schedules
Week	Contents	Learning Methods
1. Week	The Real Number System: The Axioms, Consequences of the Least Upper Bound Property	Lecture and recitation
2. Week	The Real Number System: Absolute Value and Intervals, Sequences of Real Numbers	Lecture and recitation
3. Week	The Real Number System: Theorem of Bolzano and Weierstrass, Limit Superior and Limit Inferior	Lecture and recitation
4. Week	Metric Spaces: Definition and Some Examples	Lecture and recitation
5. Week	Metric Spaces: Open and Closed Subsets	Lecture and recitation
6. Week	Metric Spaces: Sequences in Metric Space, Continuity of Functions	Lecture and recitation
7. Week	Metric Spaces: Cartesian Product of Metric Spaces, Completion of a Metric Space	Lecture and recitation
8. Week	Compactness and Connectedness: Compact sets, Compactness and Convergence of Sequences	Lecture and recitation
9. Week	Compactness and Connectedness: Continuity and Compactness, Connectedness	Lecture and recitation
10. Week	Compactness and Connectedness: Connected Components	Lecture and recitation
11. Week	Application: Contraction Mapping Theorem	Lecture and recitation
12. Week	Application: The Arzela-Ascoli Theorem	Lecture and recitation
13. Week	Application: Extension Theorem of Tietze	Lecture and recitation
14. Week	Application: Baire's Theorem	Lecture and recitation
15. Week
16. Week
17. Week

Assessments
Evaluation tools	Quantity	Weight(%)
Homework / Term Projects / Presentations	1	50
Final Exam	1	50

Program Outcomes PO-1 Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science. PO-2 Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science. PO-3 Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence. PO-4 Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline. PO-5 Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science. PO-6 Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish. PO-7 Using time effectively in inventing solutions by implementing analytical thinking. PO-8 Understanding professional ethics and responsibilities. PO-9 Having the ability to behave independently, to take initiative, and to be creative. PO-10 Understanding the importance of lifelong learning and developing professional skills continuously. PO-11 Using professional knowledge for the benefit of the society.

Learning Outcomes LO-1 Understanding the metric and topological space concepts. LO-2 Analysing and synthesizing inner, outer, closure points, neighborhoods and equivalent metrics with open and closed clusters. LO-3 Analysing and evaluating convergence and continuity. LO-4 Understanding completeness, compactness and connectivity. LO-5 Applying these concepts.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10	PO 11
LO 1
LO 2
LO 3
LO 4
LO 5