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Syllabus ( MATH 206 )


   Basic information
Course title: Topology
Course code: MATH 206
Lecturer: Assoc. Prof. Dr. Ayşe SÖNMEZ
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 2, Spring
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: To teach the fundamental concepts of Topology
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Define fundamental concepts of topology

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
  2. Use countibility and separation axioms

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Homework assignment
  3. Explain the basic information about the concept of compactness

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Ability to work in interdisciplinary research teams effectively.
    3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
   Contents Up
Week 1: Preliminaries (The Basics of Set Theory, Functions)
Week 2: Preliminaries (Infinite Sets)
Week 3: Topological Spaces
Week 4: The Euclidean Topology
Week 5: Limit Points
Week 6: Homeomorphisms
Week 7: Continuous Mappings
Week 8: General Review
Week 9: Metric Spaces
Week 10: Completeness
Week 11: Compactness
Week 12: The Heine-Borel Theorem
Week 13: Finite Products
Week 14: Tychonoff's Theorem for finite products, Products and connectedness
Week 15*: -
Week 16*: Final exam
Textbooks and materials: Topology Without Tears, Sidney A. Morris
Recommended readings: An Introduction to Set Theory and Topology, Ronald C. Freiwald
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 4 14
Practice, Recitation: 0 0
Homework: 2 10
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 2
Mid-term: 2 1
Personal studies for final exam: 10 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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