MAT4510 – Geometric Structures
Schedule, syllabus and examination date
Changes in the course due to coronavirus
Autumn 2020 we plan for teaching and examinations to be conducted as described in the course description and on semester pages. However, changes may occur due to the corona situation. You will receive notifications about any changes at the semester page and/or in Canvas.
Spring 2020: Teaching and examinations was digitilized. See changes and common guidelines for exams at the MN faculty spring 2020.
The course gives an introduction to geometry and topology, with emphasis on classical geometries, topological classification of surfaces, and differential geometry for Riemannian surfaces.
After completing the course you
- can describe axioms for planar geometry, and models realizing these in the hyperbolic, Euclidean and elliptic cases
- can work with Möbius-transforms, as well as distances, angles and areas in hyperbolic geometry
- know about topological, combinatorial and differentiable surfaces, and can classify combinatorial surfaces up to homeomorphism
- can describe Riemannian metrics and curvature, by means of the first and second fundamental forms, as well as the Theorema Egregium
- know about geodesic curves on Riemannian surfaces, and the Gauss-Bonnet theorem.
Admission to the course
Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.
Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.
Recommended previous knowledge
- MAT1100 – Calculus
- MAT1110 – Calculus and Linear Algebra
- MAT1120 – Linear Algebra
- MAT2400 – Real Analysis
- MAT2200 – Groups, Rings and Fields
- MAT2410 – Introduction to Complex Analysis
- MAT3500 – Topology / MAT4500 – Topology (can be taken simultaneously)
- 10 credits overlap with MAT3510 – Geometric structures (discontinued).
4 hours of lectures/exercises per week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Final written exam 4 hours which counts 100 % towards the final grade.
This course has 1 mandatory assignment that must be approved before you can sit the final exam.
Examination support material
No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more: