COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Topology II
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 402
Spring
3
0
3
6
Prerequisites
 MATH 401To attend the classes (To enrol for the course and get a grade other than NA or W)
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 Topology is a natural, geometric, and intuitively appealing branch of mathematics which can be effective vehicle to understand advanced mathematical topics. The secondtier of this course is designed to cover the usual topics of point set topology such as Metric spaces, connectedness, compactness, metrization, e.t.c.
Learning Outcomes The students who succeeded in this course;
  • will be able to define metric topology and its properties.
  • will be able to explain the compactness of a topological space.
  • will be able to distinguish the differences between the limit point compactness, sequential compactness, local compactness, and countable compactness.
  • will be able to compare the topological spaces with the help of seperation axioms.
  • will be able to construct compactifications of topological spaces.
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 Metric Spaces: Open Sets and Closed Sets in Metric Spaces, Interior Closure and Boundary. James R. “Munkres, Topology”, Prentice Hall.
2 Cauchy Sequences and Completeness of Metric Spaces. James R. “Munkres, Topology”, Prentice Hall.
3 Continuity On Metric Space and Uniform Continuity. James R. “Munkres, Topology”, Prentice Hall.
4 Connectedness: Connected and Disconnected Spaces. James R. “Munkres, Topology”, Prentice Hall.
5 Theorems On Connectedness, Connected Subsets of The Real Line. James R. “Munkres, Topology”, Prentice Hall.
6 Path Connected Spaces. James R. “Munkres, Topology”, Prentice Hall.
7 Locally Connected and Locally Path Connected Spaces. James R. “Munkres, Topology”, Prentice Hall.
8 Compactness: Compact Spaces and Subspaces, Compactness and Continuity. James R. “Munkres, Topology”, Prentice Hall.
9 Properties Related To Compactness. James R. “Munkres, Topology”, Prentice Hall.
10 Limit Point Compactness, Sequentially Compactness. James R. “Munkres, Topology”, Prentice Hall.
11 One Point Compactification, Local Compactness. James R. “Munkres, Topology”, Prentice Hall.
12 Seperation Properties and Metrization: T0, T1 and T2 Spaces. James R. “Munkres, Topology”, Prentice Hall.
13 Regular Spaces and Normal Spaces, Seperation by Continuous Functions. James R. “Munkres, Topology”, Prentice Hall.
14 Metrization, The StoneČech Compactification. James R. “Munkres, Topology”, Prentice Hall.
15 Course Review
16 Course Review
Course Notes/Textbooks

James R. Munkres, “Topology”, Prentice Hall.

Suggested Readings/Materials

Stephen Willard, “General Topology”, Dover Publications.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
1
10
Laboratory / Application
Field Work
Quizzes / Studio Critiques
6
15
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
35
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
8
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
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
14
3
Field Work
Quizzes / Studio Critiques
3
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
28
Final Exams
1
36
    Total
182

 

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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