Course Name Code Semester T+U Hours Credit ECTS
Topoloji ve Kategori MAT 617 0 3 + 0 3 6
Precondition Courses <p>Topology I, Topology II</p>
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Prof.Dr. METİN BAŞARIR
Course Lecturers
Course Assistants
Course Category Field Proper Education
Course Objective

Knowing of topological spaces, connectedness spaces and topolojical groups, The concepts of category, morfizm, functor and grupoid

Course Content

Connectedness,curvature connectedness, homotopy, fundemental groups, cover spaces, topological groups, seperation axioms in topological groups, topological cover spaces, category, special objects and morfizm, product spaces, Pullback and Pushout diagrams, functors, grupoids, grupoid cover morfizms.

# Course Learning Outcomes Teaching Methods Assessment Methods
Week Course Topics Preliminary Preparation
1 Connectedness spaces
2 Homotopy
3 Topological groups
4 Topological group homomofizm
5 Connectedness topological groups
6 Seperation axioms in topological groups
7 Topological groups
8 Topological cover groups
9 Mid Exam
10 Category
11 Special objects
12 Product spaces
13 Pullback and Pushout diagrams, functors
14 Grupoids, grupoid cover morfizms
Course Notes <p>[1] Mucuk, O., Topoloji ve Kategori, Nobel Yayın, Ankara, 2010.</p>
Course Resources

[2] Brown, R., Topoloji ve Grupoids, Bokksurge LLC, U.K, 2006.

[3] Lipschutz, S., General Topology, Schaum's Outline Series, New York, 1965.

[4] Massey, W. S., Algebraic Topology: An Introduction, Sipringer-Verlag, New York, 1990.

Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 60
1. Ödev 10
2. Ödev 10
1. Kısa Sınav 20
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 18 18
Assignment 2 15 30
Final examination 1 18 18
Total Workload 162
Total Workload / 25 (Hours) 6.48
dersAKTSKredisi 6