ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE

Syllabus ( MATH 571 )


   Basic information
Course title: General Topology
Course code: MATH 571
Lecturer: Assoc. Prof. Dr. Ayşe SÖNMEZ
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 1/2, Fall and Spring
Level of course: Second Cycle (Master's)
Type of course: Area Elective
Language of instruction: Turkish
Mode of delivery: Face to face
Pre- and co-requisites: none
Professional practice: No
Purpose of the course: The aim of course is to give the infrastructure in the field of topology for researchers who want to specialize in the field of mathematics, develop abstract thinking by means of sets and analysis.
   Learning outcomes Up

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

  1. Development of abstract thinking skills

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results

    Method of assessment

    1. Written exam
    2. Homework assignment
  2. Explain the basic concepts of Topology

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

    Method of assessment

    1. Written exam
  3. Make use of topology in many areas of mathematics

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    3. Work effectively in multi-disciplinary research teams

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Fundamental concepts in topological spaces
Week 2: Methods of generating topologies
Week 3: Continuous functions
Week 4: Closed and open functions, homeomorphisms
Week 5: Axioms of separation
Week 6: Compact spaces, locally compact spaces
Week 7: Sequentially compactness, countably compactness
Week 8: Midterm exam
Week 9: Euclid space of real numbers
Week 10: Metric spaces
Week 11: Continuous functions in metric spaces
Week 12: Totally bounded and complete metric spaces
Week 13: Metrization
Week 14: Paracompact Spaces
Week 15*: Connected Spaces
Week 16*: Final exam
Textbooks and materials: Stephen Willard, “General Topology”
Ryszard Engelking, “General Topology”
Recommended readings: G.J.O. Jameson, “Topology and Normed Spaces”
  * 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: 3,5,7,9,11,13 10
Quiz: - 0
Final exam: 16 50
  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: 7 6
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 20 1
Mid-term: 3 1
Personal studies for final exam: 20 1
Final exam: 3 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
-->