Course Name Code Semester T+U Hours Credit ECTS
Algebraic Topology MAT 592 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Doç.Dr. İSMET ALTINTAŞ
Course Lecturers
Course Assistants
Course Category
Course Objective

The Algebraic Topology course aims to make students comprehend the topics that provide a basis for the work of Master and PhD students working in the field of topology.

Course Content

Basic topological concepts, topological manifolds and surfaces, compact surface forms, classification of compactly connected surfaces, simplexel complexes, triangulation of surfaces, Euler characteristic, Inversion matrix, homotopy, homotopy groups, homology, cellular subdivisions, betti numbers, homology groups. Cover spaces

# Course Learning Outcomes Teaching Methods Assessment Methods
Week Course Topics Preliminary Preparation
1 Basic topological concepts
2 Topological manifolds and surfaces
3 Compact connected surfaces and surface forms
4 Connected sums of compact surfaces
5 Classification of compact surfaces and classification theorem
6 Simplex complexes
7 Triangulation of compact surfaces, Euler characterization
8 Notation matrix and its properties
9 Simple closed curves and their properties, homotopy curves, homotopy type
10 Homotopy groups
11 Homology, homologous curves, type of homology
12 Cell subdivisions of cells and surfaces, Betti numbers
13 Homology groups
14 Cover spaces
Course Notes <p>1. R.A. Piccinini, Lectures on homotopy theory, Elsevier science publ., Nort-Holland, 19922.<br /> 2. I.M. Singer and J.A. Thorpe, Lecture notes on elementary topology and geometry, Springer-Verlag, New York, 1967.<br /> 3. J. Mayer, Algebraic topology, Prentice-Hall, New Jersey, 1972.</p>
Course Resources

1. W.S. Massey, Singular homology theory, Springer-Verlag, New York, 1980.
2. M.E. Bozhüyük, Genel topolojiye giriş, Atatürk Üniversitesi, Erzurum, 1984.
3. .G. W. Whitehead, Homotopy Theory, The M.I.T. Pres, London, 1966

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.
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.
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 14 14
Assignment 1 14 14
Final examination 1 14 14
Total Workload 138
Total Workload / 25 (Hours) 5.52
dersAKTSKredisi 6