MATH 471 Hyperbolic Geometry Fall 2021
Webpages:
https://users.metu.edu.tr/beyaz/471/(Last updated October 14, 2021)
Check frequently: https://metuclass.metu.edu.tr/
Schedule (Subject to change):
1-Introduction
2-Upper half plane 1.1, Riemann sphere 1.2
3-Points at infinity 1.3, Group of Mobius transformations 2.1
4-Transitivity of Möb+ 2.2, Cross ratio 2.3
5-Classification wrt conjugacy 2.4, A linear representation 2.5
6-Reflections and Möb 2.6, Conformality of Möb 2.7
7-Möb(H) and preserving the upper half plane 2.8, Transitivity of Möb+(H) 2.9
8-Classification in Möb+(H) 2.10
9-Curves and arclength 3.1, Arclength elements in H 3.2, Metric in the upper half plane 3.3-3.4
10-Formulae for hyperbolic distance in H 3.5, Isometries of H 3.6
11-The Poincare disc model 4.1
12-Hyperbolic area 5.3, Gauss-Bonnet theorem 5.4, Trigonometry 5.6
13-Applications of Gauss-Bonnet theorem 5.5, Other versions
Sources:
Hyperbolic Geometry by James W. Anderson, Second Edition, Springer-Verlag 2005
https://personalpages.manchester.ac.uk/staff/charles.walkden/hyperbolic-geometry/
Catalog Description:
Parallel postulate and the need for non-Euclidean geometry, models of
the hyperbolic plane, Möbius group, classification of Möbius
transformations, classical geometric notions such as length, distance,
isometry, parallelism, convexity, area, trigonometry in the hyperbolic
plane, groups acting on the hyperbolic plane, fundamental domains.
Lectures:
Monday 8:40-10:20 M13
Wednesday 11:40-12:20 M13
Grading:
Exam 1 (30 points)
Exam 2 (30 points)
Final Exam (40 points)
Notes:
**The lectures will be conducted face to face. I plan to upload lecture
notes and videos to ODTUClass.
**The exams will be in class. Any student who did not miss both
of Exam 1 and Exam 2 can take the final exam. If the exams are to be conducted online
as a result of unseen circumstances, you will need a camera
(smartphone’s camera or webcam) and a reliable internet connection for the the midterm and the final exam. In this case, the midterm exams will be written over Zoom with camera and the final exam will be a written/oral exam over Zoom with camera.
**Make-up Exam: For students who have been unable to take
any one of the exams for legitimate reasons (such as medical
emergencies), a make-up exam will be offered. The make-up exam is
usually harder than the final exam and takes place after it. The grade
obtained at the make-up exam is then treated as the grade obtained in
the exam that was missed.
**Information for Students with Disabilities: To obtain
disability related academic adjustments and/or auxiliary aids, students
with disabilities must contact the course instructor and the METU
Disability Support Office as soon as possible. To contact the Disability
Support Office, you may visit the office located at METU Library-Solmaz
Izdemir Hall, call (+90) 312 210 71 96, or e-mail to
engelsiz^^metu.edu.tr
**Academic Honesty: The METU Honour Code is as follows: "Every
member of METU community adopts the following honour code as one of the
core principles of academic life and strives to develop an academic
environment where continuous adherence to this code is promoted. The
members of the METU community are reliable, responsible and honourable
people who embrace only the success and recognition they deserve, and
act with integrity in their use, evaluation and presentation of facts,
data and documents."
**Attendance will not be taken in this course.