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
8
Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
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 Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Introduction and Fundamental Concepts of Set Theory And Logic. James R. Munkres, “Topology”, Prentice Hall.
2 Indexed Family of Elements and Family Subsets. James R. Munkres, “Topology”, Prentice Hall.
3 Countable and Uncountable Sets. James R. Munkres, “Topology”, Prentice Hall.
4 Infinite Sets and The Axiom of Choice. James R. Munkres, “Topology”, Prentice Hall.
5 Topological Spaces. James R. Munkres, “Topology”, Prentice Hall.
6 Open and Closed Subsets of Topological Spaces. James R. Munkres, “Topology”, Prentice Hall.
7 Closure, Interior and Boundary of Sets. Limit Points. James R. Munkres, “Topology”, Prentice Hall.
8 Continuous Maps and Their Properties. James R. Munkres, “Topology”, Prentice Hall.
9 Subspace and The Subspace Topology. James R. Munkres, “Topology”, Prentice Hall.
10 Metric Spaces and Metric Topology. James R. Munkres, “Topology”, Prentice Hall.
11 Hausdorff Spaces. James R. Munkres, “Topology”, Prentice Hall.
12 Homeomorphisms. James R. Munkres, “Topology”, Prentice Hall.
13 The Product Topology. James R. Munkres, “Topology”, Prentice Hall.
14 The Order Topology, The Quotient Topology. James R. Munkres, “Topology”, Prentice Hall.
15 Review of semester.
16 Review of semester.
Course Notes/Textbooks The extracts above and exercises will be given.
Suggested Readings/Materials Fred H. Croom, Principles of Topology, The Saunders Series; Theory and Problems of General Topology, Schaum\'s Outline Series, McGrawHill

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
3
15
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
2
50
Final Exam
1
35
Total

Weighting of Semester Activities on the Final Grade
5
65
Weighting of End-of-Semester Activities on the Final Grade
1
35
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
16
5
Field Work
Quizzes / Studio Critiques
3
7
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
26
Final Exams
1
20
    Total
221

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

X
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

X
14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

X
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

X

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

 

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