FACULTY OF ARTS AND SCIENCES

Department of Mathematics

MATH 401 | Course Introduction and Application Information

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
Course Coordinator
Course Lecturer(s)
Assistant(s)
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 The students who succeeded in this course;
  • will be able to use axioms of set algebra.
  • will be able to define topology, and its construction.
  • will be able to distunguish open and closed subsets.
  • will be able to construct closure, interior, and boundary of a set.
  • 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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
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

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
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

ECTS / WORKLOAD TABLE

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

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
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.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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