FACULTY OF ARTS AND SCIENCES

Department of Mathematics

MATH 402 | Course Introduction and Application Information

Course Name
Topology II
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 402
Fall/Spring
3
0
3
6

Prerequisites
  MATH 401 To attend the classes (To enrol for the course and get a grade other than NA or W)
Course Language
English
Course Type
Elective
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 cover topics such as metric space topology and properties, connectivity, compactness and so on, which are classic topics of point set topology.
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 Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Metric Spaces: Open sets and closed sets in metric spaces, interior, closure and boundary “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
2 Cauchy sequences and completeness of metric spaces “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
3 Continuity on metric space and uniform continuity “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
4 Connectedness: connected and disconnected spaces “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
5 Theorems on connectedness, connected subsets of the real line “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
6 Path connected spaces “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
7 Locally connected and locally path connected spaces “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
8 Compactness: Compact spaces and subspaces, compactness and continuity “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
9 Properties related to compactness “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
10 Limit point compactness, sequentially compactness “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
11 One point compactification, local compactness “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
12 Seperation properties and metrization: T0, T1 and T2 spaces “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
13 Regular spaces and normal spaces, seperation by continuous functions “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
14 Metrization, the StoneČech compactification “Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903
15 Semester Review
16 Final Exam

 

Course Notes/Textbooks

“Topology” by James R. Munkres, Prentice Hall, 2nd, Eastern economy edition, 2000. ISBN-13: 978-0876922903

Suggested Readings/Materials

“General Topology” by Stephen Willard, Dover Publications.2004. ISBN-13: 978-0486434797

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
2
60
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
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
0
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
2
30
60
Final Exam
1
30
30
    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.

X
5

To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.

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.

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.

X
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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