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 |
|
|||||||
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;
|
Course Description | This course aims to cover basic theory and applications of topology. |
|
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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