Course Name Code Semester T+U Hours Credit ECTS
Combinatorial Geometry II MAT 533 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Dr.Öğr.Üyesi İBRAHİM ÖZGÜR
Course Lecturers
Course Assistants Research assistants of geometry
Course Category
Course Objective To introduce non-Euclidean finite geometries and its combinatorial properties.
Course Content Polar spaces, Quadrics, Linear subspaces, Generalized quadrangles, Subquadrangles, Partial geometries, Strongly regular graphs, Subgeometries, Paschs axiom.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She designs polar spaces, Lecture, Question-Answer, Motivations to Show, Oral Exam, Homework,
2 He/She defines absolute points and quadrics, Lecture, Question-Answer, Oral Exam, Homework,
3 He/She explains linear subspaces, Lecture, Question-Answer, Homework,
4 He/She constructs projective spaces inside polar spaces, Lecture, Question-Answer, Homework,
5 He/She formulates polar spaces and generalized quadrangles Lecture, Question-Answer, Drilland Practice, Homework,
6 He/She suggests generalized subspace, generalized subspaces with s=t=3 and some properties of them, Lecture, Question-Answer, Drilland Practice, Homework,
7 He/She constitutes the construction of partial geometries and some Partial geometries, Lecture, Question-Answer, Homework,
8 He/She generates Strongly regular graphs and subgeometries, Lecture, Question-Answer, Homework,
9 He/She constitutes subgeometries, Paschs axiom. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Polar spaces
2 Absolute points , Quadrics
3 Linear subspaces
4 Irreducibility
5 Projective spaces inside polar spaces
6 Some combinatorial properties
7 Generalized quadrangles , definition and some basic results
8 Generalized quadrangles with s=t=3
9 Subquadrangles
10 Collineations of generalized quadrangles
11 Partial geometries
12 A method of constructing proper partial geometries
13 Strongly regular graphs
14 Subgeometries, Paschs axiom
Resources
Course Notes Combinatorics of Finite Geometries, Lynn. M. Batten, Cambridge, 1986.
Course Resources Finite Geometries, Tosiro Tsuzuko, 1990.
The Theory of Finite Linear Spaces, L.,M., Batten ve A. Beutelspacher, 1993.
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
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
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
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
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
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
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
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
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
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. Kısa Sınav 10
2. Kısa Sınav 10
1. Ödev 10
Total 100
1. Yıl İçinin Başarıya 40
1. Final 60
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 4 64
Mid-terms 1 15 15
Final examination 1 15 15
Total Workload 142
Total Workload / 25 (Hours) 5.68
dersAKTSKredisi 6