GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
Elective Course-5 (Topology)/MTÖ407
Course Title: Elective Course-5 (Topology)
Credits 2 ECTS 4
Course Semester 7 Type of The Course Elective
COURSE INFORMATION
 -- (CATALOG CONTENT)
 -- (TEXTBOOK)
 -- (SUPPLEMENTARY TEXTBOOK)
 -- (PREREQUISITES AND CO-REQUISITES)
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- COURSE OBJECTIVES
 -- COURSE LEARNING OUTCOMES
Show whether a give family of subsets is topology and identify closure-, interior-, accumulations Points-, and boundary of subset according to a given topology, and show the related relations.
Recognize the base and the neighbourhood base at a point of a given Topological space.
Explain the continuity, open functions, closed functions and homeomorphism between Topological spaces.
Explain and compare main separations axioms and give examples.
Explain compact and noncompact Topological spaces and give examples.
Recognize the connected and disconnected Topological spaces and give examples.
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face.
 --WEEKLY SCHEDULE
1. Week  Topology and Topological space concepts, open sets, Topological space examples, comparison of Topologies on a set, closed sets
2. Week  Neighbourhood and properties of neighborhood families; generating of Topologies with neighborhoods; closure, interior, derived set, boundary of a subset in a Topological space and the relationship between these concepts
3. Week  Properties of a sets closure and interior in a Topological space; generating a topology with the concepts of closure and interior concepts; subspace and properties of subspace topology
4. Week  The neighbourhood base of a Point in a Topological space; properties of neighborhood base; generating a topology with the neighborhood base; first countable spaces; the base of a topology; properties of the base; generating a topology with the base
5. Week  Subbases, topology generated by the subbase, dense subsets, separable spaces; comparison of first countable and second countable spaces.
6. Week  Properties of continuous functions, open and closed functions, homeomorphisms
7. Week  Midterm Exam
8. Week  Topologies generated with functions, weak Topologies, product spaces; concepts of strong topology , quotient topology and quotient space
9. Week  Convergence of the sequences in the Topological spaces, subsequences, sequentially continuous functions, adequacy of sequences in first countable spaces
10. Week  Separation axioms, properties and comparison of T0-, T1- and T2- spaces, examples and applications
11. Week  Regular, completly regular and normal spaces and some properties; examples and applications
12. Week  Compactness in Topological spaces, countable compactness and sequential compactness concepts
13. Week  Connectedness in Topological spaces, connected and disconnected spaces, concept of path-connected space
14. Week  Preparation for the final exam
15. Week  Final Exam
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
40
 Assignment
0
0
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Percent of In-term Studies  
40
 Percentage of Final Exam to Total Score  
60
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
2
28
 Weekly Tutorial Hours
0
 Reading Tasks
12
3
36
 Searching in Internet and Library
10
3
30
 Material Design and Implementation
0
 Report Preparing
0
 Preparing a Presentation
0
 Presentation
0
 Midterm Exam and Preperation for Midterm Exam
1
3
3
 Final Exam and Preperation for Final Exam
2
3
6
 Other (should be emphasized)
0
 TOTAL WORKLOAD: 
103
 TOTAL WORKLOAD / 25: 
4.12
 Course Credit (ECTS): 
4
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1Acquisition of scientific thinking skillsX
2Making research and investigation independentlyX
3Acquisition of carefully observing and analytically thinking skillsX
4Acquisition of learning and teaching mathematics problemsX
5Comprehending, applying and explaining the importance of mathematical conceptsX
6Developing the thinking, producing, argumenting and probing abilitiesX
7Having the algorithm and sotftware writing abilities for solving computer supported problems
8Developing the ability of reaching information, evaluating and presenting informationX
9Improving yourself parallel to the developing technology
10Understands the disciplinary structure of mathematics, its historical development, related philosophical approaches and problems.
 -- NAME OF LECTURER(S)
   (Related Instructor)
 -- WEB SITE(S) OF LECTURER(S)
   (.)
 -- EMAIL(S) OF LECTURER(S)
   (.)