Course Name Code Semester T+U Hours Credit ECTS
Hiperbolic Geometry MAT 580 0 3 + 0 3 6
 Precondition Courses Students are assumed to be familiar with the course Differential Geometry I and Differential Geometry II. Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Prof.Dr. SOLEY ERSOY Course Lecturers Course Assistants Course Category Field Proper Education Course Objective The hyperbolic geometry course aims to give the fundamental knowledge for the studies of graduate students who study at geometry branch. Course Content Euclids parallel postulate, independence of the parallel postulate, Euclid n-space, spherical n- space, elliptic n-space, spherical arc length, spherical volume, spherical trigonometry, Lorentzian n- space, hyperbolic n- space, hyperbolic arc length, hyperbolic volume, hyperbolic trigonometry, reflections, stereographic projection, Mobius transformation, conformal disc model of hyperbolic space, Poincaré half-plain model, isometries of hyperbolic space
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She knows the fundamental consepts of hyperbolic geometry Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
2 He/She defines the fundamental calculations on Euclidean n-space, spherical n-space and eliptical n-space. Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
3 He/She calculate hyperbolic arc length and hyperbolic volume Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
4 He/She defines Mobious transformations, Poincare half plain model and isometries of the hyperbolic spaces. Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Euclids parallel postulate, independence of the parallel postulate, Euclid n-space
2 Spherical n- space, elliptic n-space, spherical arc length, spherical volume
3 Spherical trigonometry
4 Lorentzian n- space, hyperbolic n- space
5 Hyperbolic arc length
6 Hyperbolic volume
7 Hyperbolic trigonometry
8 Reflections
9 Mid term exam
10 Stereographic projection
11 Mobius transformation
12 Conformal disc model of hyperbolic space
13 Poincaré half-plain model
14 Isometries of hyperbolic space
Resources
Course Notes 1.Ratcliffe, J. G., (1994), Foundations of Hyperbolic Manifolds, Springer-Verlag.
Course Resources 1. Fenchel, W., Walter de Gruyter, (1989), Elementary Geometry in Hyperbolic Space
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
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
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