MAT4510 – Geometric Structures

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.

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.

• MAT1100 – Calculus
• MAT1110 – Calculus and Linear Algebra
• MAT1120 – Linear Algebra / MAT1125 – Advanced linear algebra
• MAT2200 – Groups, Rings and Fields
• MAT2400 – Real Analysis
• MAT2410 – Introduction to Complex Analysis
• MAT3500 – Topology / MAT4500 – Topology (can be taken simultaneously)

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 or final oral exam, which counts 100 % towards the final grade.

The form of examination will be announced by the lecturer by 1 October/1 March for the autumn semester and the spring semester respectively.

This course has 1 mandatory assignment that must be approved before you can participate in the final exam.

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass, the original examination.