Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
8MATH412HYPERBOLIC GEOMETRY3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course Introduction of Lobacevskiy hyperbolic geometry and applications
Course Content Hyperbolic plane. The Mobius group. Conformality. Length and distance. Isometries. Planar models hyperbolic plane. Lobachevsly model. Poincare disk model. Klein model. Applications.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. Oktay Pashaev
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Hyperbolic Geometry by J. W. Anderson, Springer, 2005.
Introduction of Lobacevskiy hyperbolic geometry and applications

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 72 72
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 42 42
Exams and Exam Preparations 1 72 72
Total Work Load   Number of ECTS Credits 6 186

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To understand basic principles of hyperbolic geometry
2 To be able to solve typical problems associated with this theory.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 A model for hyperbolic plane. The Riemann sphere.
2 The general Mobius group. Cross ratio.
3 Classification of Mobius transformations. Conformality. Transitivity.
4 The geometry of the action
5 1st Midterm
6 Length and distance
7 From arc-lenth to metric
8 Isometries.
9 Planar models of hyperbolic plane
10 2nd Midterm
11 Lobachevskiy model
12 Poincare disk model.
13 Klein model.
14 Hyperbolic polygons. Applications to fractals


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
All 4 3 3 3 1 2 2 2 4 3 3 3
C1 4 3 3 3 1 2 2 2 4 3 3 3
C2 4 3 3 3 1 2 2 2 4 3 3 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163244&lang=en