Course Name Code Semester T+U Hours Credit ECTS
Geometric Topology MAT 571 0 3 + 0 3 6
Precondition Courses <p>Students are assumed to be familiar with the course Differential Geometry I and Differential Geometry II, Topology I and Topology II.</p>
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Prof.Dr. SOLEY ERSOY
Course Lecturers Prof.Dr. SOLEY ERSOY,
Course Assistants
Course Category Field Proper Education
Course Objective

The aim of this course is to give some differential topological fundamental notions for the studies of graduate students who study at geometry and topology branch.

Course Content

Toplogy of subsets of Euclidean space, open and closed subsets of sets in , continuous maps, homeomorphims, connectedness, compactness, arcs, discs, 1-spheres, surfaces in , surfaces via gluing, properties of surfaces, connected sum and the classification of compact connected surfaces, simplices, simplicial complexes and simplicial surfaces (simplicial complexes with underlying spaces that are topological surfaces), the Euler characteristic, simplical curvature and the Gauss Bonnet thoerem

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she recalls the fundamental notions of topology Lecture, Question-Answer, Discussion, Testing, Homework,
2 He/she defines the fundamental notions of surface theory Lecture, Question-Answer, Discussion, Testing, Homework,
3 He/she interprets connectedness, compactness notions on subsets of Euclidean space Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
4 He/she investigates properties of surfaces Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
5 He/she defines simplices, simplicial complexes and simplicial surfaces Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
6 He/she classifies compact connected surfaces Lecture, Question-Answer, Discussion, Testing, Homework,
7 He/she explains and proves the theorem of Gauss Bonnet Lecture, Question-Answer, Discussion, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Toplogy of subsets of Euclidean space
2 Open and closed subsets of sets in
3 Continuous maps, homeomorphims,
4 Connectedness, compactness
5 Arcs, discs, 1-spheres,
6 Surfaces in , surfaces via gluing,
7 Properties of surfaces
8 Connected sum
9 The classification of compact connected surfaces,
10 Simplices, simplicial complexes
11 Simplicial surfaces (simplicial complexes with underlying spaces that are topological surfaces),
12 The Euler characteristic,
13 Simplical curvature
14 Gauss Bonnet thoerem
Resources
Course Notes <p>1. Ethan D. Bloch, &quot;A First Course in Geometric Topology and Differential Geometry&quot; Birkh&auml;user Boston, 1996.</p>
Course Resources

2. Daverman R.J. and Sher R.B., Editors, Handbook of Geometric Topology, North- Holland, Amsterdam 2002.
3. Armstrong, M.A. Basic Topology, Springer Verlag, 1983.

Order Program Outcomes Level of Contribution
1 2 3 4 5
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Ödev 30
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 20 20
Assignment 1 10 10
Final examination 1 30 30
Total Workload 156
Total Workload / 25 (Hours) 6.24
dersAKTSKredisi 6