Topology (MATH372) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Topology	MATH372	Area Elective	3	0	0	3	6

Pre-requisite Course(s)
N/A

Course Language	English
Course Type	Elective Courses
Course Level	Bachelor’s Degree (First Cycle)
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Discussion, Question and Answer, Team/Group, Brain Storming.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	The aim of this course is to introduce the student some algebraic and differential topological ideas at an early stage emphasizing unity with geometry and more generally introduce the student to the relation of the modern axiomatic approach in mathematics to geometric intuition.
Course Learning Outcomes	The students who succeeded in this course; prove elementary theorems involving sets and functions, understand topological spaces and continuous functions, determine whether a topological space has any of various topological properties, prove elementary theorems involving the concepts of continuous function, compactness, connectedness, the countability and the separation axioms, understand homotopy, the fundamental group of a space and covering spaces, understand the classification of surfaces.
Course Content	Fundamental concepts, functions, relations, sets and Axiom of Choice, well-ordered sets, topological spaces, basis, the Order Topology, the Subspace Topology, closed sets and limit points, continuous functions, the Product Topology, Metric Topology, the Quotient Topology, connectedness and compactness, Countability and Separation Axioms, the fundam

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	Fundamental Concepts, Functions	pp. 4-20
2	Relations, Sets and Axiom of Choice, Well-ordered Sets	pp. 21-50, 57-66
3	Topological Spaces, Basis, The Order Topology	pp. 75-86
4	The Subspace Topology, Closed Sets and Limit Points	pp. 88-100
5	Continuous Functions, The Product Topology	pp. 102-117
6	Metric Topology, The Quotient Topology	pp. 119-126, 136-144
7	Midterm
8	Connectedness	pp. 147-162
9	Compactness	pp. 163-185
10	Countability and Separation Axioms	pp. 190-222
11	Homotopy, The Fundamental Group	pp.322-334
12	Covering Spaces, The Fundamental Group of The Circle, Retractions and Fixed Points	pp. 335-353
13	The Fundamental Theorem of Algebra, The Borsuk-Ulam Theorem, Homotopy Type	pp. 353-365
14	Fundamental Groups of Surfaces	pp. 368-375
15	The Classification Theorem	pp. 462-476
16	Final Exam

Sources

Course Book	1. J.R. Munkres, Topology, Second Edition, Prentice Hall, NJ, 2000.
Other Sources	2. M. C. Gemignani, Elementary Topology, Addison-Wesley, 1972
	3. M. D. Crossley, Essential Topology, Springer-Verlag, 2005
	4. L. C. Kinsey, Topology of Surfaces, Springer-Verlag, 1997

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	3	15
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	50
Final Exam/Final Jury	1	35
Toplam	6	100

Percentage of Semester Work	65
Percentage of Final Work	35
Total	100

Course Category

Core Courses
Major Area Courses	X
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area					X
2	Can apply gained knowledge and problem solving abilities in inter-disciplinary research					X
3	Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary				X
4	Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study				X
5	Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework	X
6	Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility			X
7	Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation					X
8	To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2)					X
9	Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge				X
10	Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach.				X
11	Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.				X

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	14	3	42
Presentation/Seminar Prepration
Project
Report
Homework Assignments	3	16	48
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	12	24
Prepration of Final Exams/Final Jury	1	18	18
Total Workload			132