MATH 401 | Course Introduction and Application Information - Department of Mathematics

Course Name

Topology I

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 401	Fall	3	0	3	6

Prerequisites	None
Course Language	English
Course Type	Required
Course Level	First Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Öğr. Gör. Dr. Tuğçe KATICAN
Assistant(s)	Araş. Gör. Dr. Ayşe BELER Araş. Gör. Merve KAHRAMAN ARİMAN Araş. Gör. Sıla Selenay KOÇ

Course Objectives

This course aims to teach the fundamentals of point set topology and constitute an awareness of need for the topology in Mathematics.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	will be able to use axioms of set algebra.
2	will be able to define topology, and its construction.
3	will be able to distunguish open and closed subsets.
4	will be able to construct closure, interior, and boundary of a set.
5	will be able to define the product topology, and the quotient topology.

Course Description

This course aims to cover basic theory and applications of Topology.

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Introduction and fundamental concepts of set theory and logic	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.Chapter 1, pp.4
2	Indexed family of elements and family subsets	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.Chapter 1, pp. 36-39
3	Countable and uncountable sets	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.Chapter 1, pp. 44
4	Infinite sets and the axiom of choice	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.Chapter 1, pp. 57
5	Topological spaces	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903. Chapter 2, pp. 75
6	Open and closed subsets of topological spaces	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.Chapter 2, pp. 92
7	Closure, interior and boundary of sets, limit points	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903. Chapter 2, pp. 102
8	Midterm
9	Continuous maps and their properties, subspace and the subspace topology	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.Chapter 2, pp. 102-112
10	Metric spaces and metric topology	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.Chapter 2, pp. 119
11	Hausdorff spaces	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903. Chapter 2, pp. 119-129
12	Homeomorphisms	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.Chapter 2, pp. 129
13	The product topology	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903. Chapter 2, pp. 112
14	The order topology, the quotient topology	James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.Chapter 2, pp. 136
15	Semester review
16	Final exam

Course Notes/Textbooks

James R. Munkres,“Topology”, Prentice Hall, 2000,ISBN-13: 978-0876922903.

Suggested Readings/Materials

''Principles of Topology'', Fred H. Croom,Dover Publications; First edition , 2016,ISBN-13:978-0486801544

''Theory and Problems of General Topology'', Schaum's Outline Series, McGrawHill,1st edition,2011,ISBN-13:978-0071763479

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques	2	30
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	30
Final Exam	1	40
Total

Weighting of Semester Activities on the Final Grade	3	60
Weighting of End-of-Semester Activities on the Final Grade	1	40
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques	2	5	10
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	35	35
Final Exam	1	45	45
		Total	180

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.		-	-	-	X	-
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.		-	-	X	-	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.		-	-	-	-	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.		-	-	-	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.		-	-	-	X	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.		-	-	-	X	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.		-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.		-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.		-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.		-	-	-	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.		-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.		-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.		-	-	-	-	-